A bibliography of financial, statistical, and engineering methods

The following books provide detailed information on financial, statistical, and engineering methods.

Abramowitz, Milton, and Irene A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 10th ed. New York, NY: Dover Publications, 1974.

Antkies, Candace Mary. Standard Securities Calculation Methods: Fixed Income Securities Formulas for Price, Yield and Accrued Interest: Volume 1. New York, NY: Securities Industry Association.

Antkies, Candace Mary. Standard Securities Calculation Methods, Fixed Income Securities Formulas for Analytic Measures: Volume 2. New York, NY: Securities Industry Association.

Devore, Jay L. Probability and Statistics for Engineering and the Sciences. 5th ed. Pacific Grove, CA: Duxbury Press, 1998.

Fabozzi, Frank J. The Handbook of Fixed-Income Securities. 6th ed. New York, NY: Mcgraw-Hill Trade, 2000.

Hewlett-Packard, HP-12C Solutions Handbook. Palo Alto, CA: Hewlett-Packard, 2001.

McCall, Robert B. Fundamental Statistics for the Behavioral Sciences. 7th ed. Pacific Grove, CA: Brooks Cole, 1998.

Monks, Joseph G. Operations Management: Theory and Problems. 3rd ed. New York, NY: Macmillan/McGraw-Hill, 1988.

Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. New York, NY: Cambridge University Press, 1993.

Sokal, Robert R., and F. James Rohlf. Biometry: The Principles and Practice of Statistics in Biological Research. 3rd ed. New York, NY: W. H. Freeman, 1994.

Stigum, Marcia, and John Mann. Money Market Calculations: Yields, Break-Evens, & Arbitrage. 2nd ed. Homewood, IL: Irwin Professional, 1991.

See Also

• List of worksheet functions (by category)

Excel > Function reference > Statistical

Statistical functions

Click one of the links in the following list to see detailed help about the function.

See Also

• List of worksheet functions (alphabetical)
• List of worksheet functions (by category)

Excel > Function reference > Statistical

AVEDEV function

Excel 2007

Returns the average of the absolute deviations of data points from their mean. AVEDEV is a measure of the variability in a data set.

Syntax

AVEDEV(number1,number2,...)

Number1, number2, ...   are 1 to 255 arguments for which you want the average of the absolute deviations. You can also use a single array or a reference to an array instead of arguments separated by commas.

Remarks

• AVEDEV is influenced by the unit of measurement in the input data.
• Arguments must either be numbers or be names, arrays, or references that contain numbers.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• The equation for average deviation is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVERAGE function
• AVERAGEA function
• DEVSQ function
• Statistical functions
• STDEV function
• STDEVP function
• VAR function
• VARP function

Excel > Function reference > Statistical

AVERAGE function

Excel 2007

This article describes the formula syntax and usage of the AVERAGE function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

Returns the average (arithmetic mean) of the arguments. For example, if the range (range: Two or more cells on a sheet. The cells in a range can be adjacent or nonadjacent.) A1:A20 contains numbers, the formula =AVERAGE(A1:A20) returns the average of those numbers.

Syntax

AVERAGE(number1, [number2],...)

The AVERAGE function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• number1  Required. The first number, cell reference (cell reference: The set of coordinates that a cell occupies on a worksheet. For example, the reference of the cell that appears at the intersection of column B and row 3 is B3.), or range for which you want the average.
• number2, ...  Optional. Additional numbers, cell references or ranges for which you want the average, up to a maximum of 255.

Remarks

• Arguments can either be numbers or names, ranges, or cell references that contain numbers.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• If a range or cell reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• Arguments that are error values or text that cannot be translated into numbers cause errors.
• If you want to include logical values and text representations of numbers in a reference as part of the calculation, use the AVERAGEA function.
• If you want to calculate the average of only the values that meet certain criteria, use the AVERAGEIF function or the AVERAGEIFS function.

 Note    The AVERAGE function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

• Average, which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
• Median, which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.
• Mode, which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

Tip  When you average cells, keep in mind the difference between empty cells and those containing the value zero, especially if you have cleared the Show a zero in cells that have a zero value check box in the Excel Options dialog box. When this option is selected, empty cells are not counted, but zero values are.

To locate the Show a zero in cells that have a zero value check box:

• Click the Microsoft Office Button , click Excel Options, and then, in the Advanced category, look under Display options for this worksheet.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

Related Office Online discussions

Read related questions and answers from other Microsoft Office customers.

• The sum and average function view all numbers as zero??
• Weighted Average for Different Aggragates of Duplicate Entries?
• Weighted avg of numbers not in contiguous row-ie array w lookup?
• Can you AVERAGE IF and not null?
• XL how to change a cell reference in a formula to variable value?
• Is there an AVERAGE IF function in Excel?
• Where is the "average" button on Mictosoft Excel?

See Also

• AVEDEV function
• AVERAGEA function
• AVERAGEIF function
• AVERAGEIFS function
• Calculate the average of a group of numbers
• GEOMEAN function
• HARMEAN function
• MEDIAN function
• MODE function
• TRIMMEAN function

Excel > Function reference > Statistical

AVERAGEA function

Excel 2007

Calculates the average (arithmetic mean) of the values in the list of arguments.

Syntax

AVERAGEA(value1,value2,...)

Value1, value2, ...   are 1 to 255 cells, ranges of cells, or values for which you want the average.

Remarks

• Arguments can be the following: numbers; names, arrays, or references that contain numbers; text representations of numbers; or logical values, such as TRUE and FALSE, in a reference.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• Arguments that contain TRUE evaluate as 1; arguments that contain FALSE evaluate as 0 (zero).
• Array or reference arguments that contain text evaluate as 0 (zero). Empty text ("") evaluates as 0 (zero).
• If an argument is an array or reference, only values in that array or reference are used. Empty cells and text values in the array or reference are ignored.
• Arguments that are error values or text that cannot be translated into numbers cause errors.
• If you do not want to include logical values and text representations of numbers in a reference as part of the calculation, use the AVERAGE function.

 Note    The AVERAGEA function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

• Average   which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
• Median   which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.
• Mode   which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

Tip  When averaging cells, keep in mind the difference between empty cells and those containing the value zero, especially if you have cleared the Show a zero in cells that have a zero value check box in the Working with Office Applications section of the Advanced category on the Excel Options dialog box under the File menu. Empty cells are not counted but zero values are.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVEDEV function
• AVERAGE function
• Statistical functions

Excel > Function reference > Statistical

AVERAGEIF function

Excel 2007

Returns the average (arithmetic mean) of all the cells in a range that meet a given criteria.

Syntax

AVERAGEIF(range,criteria,average_range)

Range  is one or more cells to average, including numbers or names, arrays, or references that contain numbers.

Criteria  is the criteria in the form of a number, expression, cell reference, or text that defines which cells are averaged. For example, criteria can be expressed as 32, "32", ">32", "apples", or B4.

Average_range  is the actual set of cells to average. If omitted, range is used.

Remarks

• Cells in range that contain TRUE or FALSE are ignored.
• If a cell in average_range is an empty cell, AVERAGEIF ignores it.
• If range is a blank or text value, AVERAGEIF returns the #DIV0! error value.
• If a cell in criteria is empty, AVERAGEIF treats it as a 0 value.
• If no cells in the range meet the criteria, AVERAGEIF returns the #DIV/0! error value.
• You can use the wildcard characters, question mark (?) and asterisk (*), in criteria. A question mark matches any single character; an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.
• Average_range does not have to be the same size and shape as range. The actual cells that are averaged are determined by using the top, left cell in average_range as the beginning cell, and then including cells that correspond in size and shape to range. For example:

 Note    The AVERAGEIF function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

• Average   which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
• Median   which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.
• Mode   which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

Example: Averaging property values and commissions

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

Example: Averaging profits from regional offices

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVERAGE function
• AVERAGEIFS function
• IF function
• Statistical functions

Excel > Function reference > Statistical

AVERAGEIFS function

Excel 2007

Returns the average (arithmetic mean) of all cells that meet multiple criteria.

Syntax

AVERAGEIFS(average_range,criteria_range1,criteria1,criteria_range2,criteria2…)

Average_range   is one or more cells to average, including numbers or names, arrays, or references that contain numbers.

Criteria_range1, criteria_range2, …   are 1 to 127 ranges in which to evaluate the associated criteria.

Criteria1, criteria2, …   are 1 to 127 criteria in the form of a number, expression, cell reference, or text that define which cells will be averaged. For example, criteria can be expressed as 32, "32", ">32", "apples", or B4.

Remarks

• If average_range is a blank or text value, AVERAGEIFS returns the #DIV0! error value.
• If a cell in a criteria range is empty, AVERAGEIFS treats it as a 0 value.
• Cells in range that contain TRUE evaluate as 1; cells in range that contain FALSE evaluate as 0 (zero).
• Each cell in average_range is used in the average calculation only if all of the corresponding criteria specified are true for that cell.
• Unlike the range and criteria arguments in the AVERAGEIF function, in AVERAGEIFS each criteria_range must be the same size and shape as sum_range.
• If cells in average_range cannot be translated into numbers, AVERAGEIFS returns the #DIV0! error value.
• If there are no cells that meet all the criteria, AVERAGEIFS returns the #DIV/0! error value.
• You can use the wildcard characters, question mark (?) and asterisk (*), in criteria. A question mark matches any single character; an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.

 Note    The AVERAGEIFS function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

• Average   which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
• Median   which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.
• Mode   which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

Example: Averaging student grades

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

Example: Averaging real estate prices

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVERAGE function
• AVERAGEIF function
• IF function
• Statistical functions

Excel > Function reference > Statistical

BETADIST function

Excel 2007

Returns the cumulative beta probability density function. The beta distribution is commonly used to study variation in the percentage of something across samples, such as the fraction of the day people spend watching television.

Syntax

BETADIST(x,alpha,beta,A,B)

X   is the value between A and B at which to evaluate the function.

Alpha   is a parameter of the distribution.

Beta   is a parameter of the distribution.

A   is an optional lower bound to the interval of x.

B   is an optional upper bound to the interval of x.

Remarks

• If any argument is nonnumeric, BETADIST returns the #VALUE! error value.
• If alpha ≤ 0 or beta ≤ 0, BETADIST returns the #NUM! error value.
• If x < A, x > B, or A = B, BETADIST returns the #NUM! error value.
• If you omit values for A and B, BETADIST uses the standard cumulative beta distribution, so that A = 0 and B = 1.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• BETAINV function
• Statistical functions

Excel > Function reference > Statistical

BETAINV function

Excel 2007

Returns the inverse of the cumulative beta probability density function for a specified beta distribution. That is, if probability = BETADIST(x,...), then BETAINV(probability,...) = x. The beta distribution can be used in project planning to model probable completion times given an expected completion time and variability.

Syntax

BETAINV(probability,alpha,beta,A,B)

Probability   is a probability associated with the beta distribution.

Alpha   is a parameter of the distribution.

Beta   is a parameter the distribution.

A   is an optional lower bound to the interval of x.

B   is an optional upper bound to the interval of x.

Remarks

• If any argument is nonnumeric, BETAINV returns the #VALUE! error value.
• If alpha ≤ 0 or beta ≤ 0, BETAINV returns the #NUM! error value.
• If probability ≤ 0 or probability > 1, BETAINV returns the #NUM! error value.
• If you omit values for A and B, BETAINV uses the standard cumulative beta distribution, so that A = 0 and B = 1.

Given a value for probability, BETAINV seeks that value x such that BETADIST(x, alpha, beta, A, B) = probability. Thus, precision of BETAINV depends on precision of BETADIST. BETAINV uses an iterative search technique. If the search has not converged after 100 iterations, the function returns the #N/A error value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• BETADIST function
• Statistical functions

Excel > Function reference > Statistical

BINOMDIST function

Excel 2007

Returns the individual term binomial distribution probability. Use BINOMDIST in problems with a fixed number of tests or trials, when the outcomes of any trial are only success or failure, when trials are independent, and when the probability of success is constant throughout the experiment. For example, BINOMDIST can calculate the probability that two of the next three babies born are male.

Syntax

BINOMDIST(number_s,trials,probability_s,cumulative)

Number_s   is the number of successes in trials.

Trials   is the number of independent trials.

Probability_s   is the probability of success on each trial.

Cumulative   is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

Remarks

• Number_s and trials are truncated to integers.
• If number_s, trials, or probability_s is nonnumeric, BINOMDIST returns the #VALUE! error value.
• If number_s < 0 or number_s > trials, BINOMDIST returns the #NUM! error value.
• If probability_s < 0 or probability_s > 1, BINOMDIST returns the #NUM! error value.
• The binomial probability mass function is:

where:

is COMBIN(n,x).

The cumulative binomial distribution is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• COMBIN function
• CRITBINOM function
• FACT function
• HYPGEOMDIST function
• NEGBINOMDIST function
• PERMUT function
• PROB function
• Statistical functions

Excel > Function reference > Statistical

CHIDIST function

Excel 2007

Returns the one-tailed probability of the chi-squared distribution. The ק2 distribution is associated with a ק2 test. Use the ק2 test to compare observed and expected values. For example, a genetic experiment might hypothesize that the next generation of plants will exhibit a certain set of colors. By comparing the observed results with the expected ones, you can decide whether your original hypothesis is valid.

Syntax

CHIDIST(x,degrees_freedom)

X   is the value at which you want to evaluate the distribution.

Degrees_freedom   is the number of degrees of freedom.

Remarks

• If either argument is nonnumeric, CHIDIST returns the #VALUE! error value.
• If x is negative, CHIDIST returns the #NUM! error value.
• If degrees_freedom is not an integer, it is truncated.
• If degrees_freedom < 1 or degrees_freedom > 10^10, CHIDIST returns the #NUM! error value.
• CHIDIST is calculated as CHIDIST = P(X>x), where X is a ק2 random variable.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CHIINV function
• CHITEST function
• Statistical functions

Excel > Function reference > Statistical

CHIINV function

Excel 2007

Returns the inverse of the one-tailed probability of the chi-squared distribution. If probability = CHIDIST(x,...), then CHIINV(probability,...) = x. Use this function to compare observed results with expected ones in order to decide whether your original hypothesis is valid.

Syntax

CHIINV(probability,degrees_freedom)

Probability   is a probability associated with the chi-squared distribution.

Degrees_freedom   is the number of degrees of freedom.

Remarks

• If either argument is nonnumeric, CHIINV returns the #VALUE! error value.
• If probability < 0 or probability > 1, CHIINV returns the #NUM! error value.
• If degrees_freedom is not an integer, it is truncated.
• If degrees_freedom < 1 or degrees_freedom > 10^10, CHIINV returns the #NUM! error value.

Given a value for probability, CHIINV seeks that value x such that CHIDIST(x, degrees_freedom) = probability. Thus, precision of CHIINV depends on precision of CHIDIST. CHIINV uses an iterative search technique. If the search has not converged after 100 iterations, the function returns the #N/A error value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CHIDIST function
• CHITEST function
• Statistical functions

Excel > Function reference > Statistical

CHITEST function

Excel 2007

Returns the test for independence. CHITEST returns the value from the chi-squared (ק2) distribution for the statistic and the appropriate degrees of freedom. You can use ק2 tests to determine whether hypothesized results are verified by an experiment.

Syntax

CHITEST(actual_range,expected_range)

Actual_range   is the range of data that contains observations to test against expected values.

Expected_range   is the range of data that contains the ratio of the product of row totals and column totals to the grand total.

Remarks

• If actual_range and expected_range have a different number of data points, CHITEST returns the #N/A error value.
• The ק2 test first calculates a ק2 statistic using the formula:

where:

Aij = actual frequency in the i-th row, j-th column

Eij = expected frequency in the i-th row, j-th column

r = number or rows

c = number of columns

• A low value of ק2 is an indicator of independence. As can be seen from the formula, ק2 is always positive or 0, and is 0 only if Aij = Eij for every i,j.
• CHITEST returns the probability that a value of the ק2 statistic at least as high as the value calculated by the above formula could have happened by chance under the assumption of independence. In computing this probability, CHITEST uses the ק2 distribution with an appropriate number of degrees of freedom, df. If r > 1 and c > 1, then df = (r - 1)(c - 1). If r = 1 and c > 1, then df = c - 1 or if r > 1 and c = 1, then df = r - 1. r = c= 1 is not allowed and #N/A is returned.
• Use of CHITEST is most appropriate when Eij’s are not too small. Some statisticians suggest that each Eij should be greater than or equal to 5.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CHIDIST function
• CHIINV function
• Statistical functions

Excel > Function reference > Statistical

CONFIDENCE function

Excel 2007

Returns a value that you can use to construct a confidence interval for a population mean. The confidence interval is a range of values. Your sample mean, x, is at the center of this range and the range is x ± CONFIDENCE. For example, if x is the sample mean of delivery times for products ordered through the mail, x ± CONFIDENCE is a range of population means. For any population mean, ל0, in this range, the probability of obtaining a sample mean further from ל0 than x is greater than alpha; for any population mean, ל0, not in this range, the probability of obtaining a sample mean further from ל0 than x is less than alpha. In other words, assume that we use x, standard_dev, and size to construct a two-tailed test at significance level alpha of the hypothesis that the population mean is ל0. Then we will not reject that hypothesis if ל0 is in the confidence interval and will reject that hypothesis if ל0 is not in the confidence interval. The confidence interval does not allow us to infer that there is probability 1 – alpha that our next package will take a delivery time that is in the confidence interval.

Syntax

CONFIDENCE(alpha,standard_dev,size)

Alpha   is the significance level used to compute the confidence level. The confidence level equals 100*(1 - alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level.

Standard_dev   is the population standard deviation for the data range and is assumed to be known.

Size   is the sample size.

Remarks

• If any argument is nonnumeric, CONFIDENCE returns the #VALUE! error value.
• If alpha ≤ 0 or alpha ≥ 1, CONFIDENCE returns the #NUM! error value.
• If standard_dev ≤ 0, CONFIDENCE returns the #NUM! error value.
• If size is not an integer, it is truncated.
• If size < 1, CONFIDENCE returns the #NUM! error value.
• If we assume alpha equals 0.05, we need to calculate the area under the standard normal curve that equals (1 - alpha), or 95 percent. This value is ± 1.96. The confidence interval is therefore:

Example

Suppose we observe that, in our sample of 50 commuters, the average length of travel to work is 30 minutes with a population standard deviation of 2.5. With alpha = .05, CONFIDENCE(.05, 2.5, 50) returns 0.692952. The corresponding confidence interval is then 30 ± 0.692952 = approximately [29.3, 30.7]. For any population mean, ל0, in this interval, the probability of obtaining a sample mean further from ל0 than 30 is more than 0.05. Likewise, for any population mean, ל0, outside this interval, the probability of obtaining a sample mean further from ל0 than 30 is less than 0.05.

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Statistical functions
• ZTEST function

Excel > Function reference > Statistical

CORREL function

Excel 2007

Returns the correlation coefficient of the array1 and array2 cell ranges. Use the correlation coefficient to determine the relationship between two properties. For example, you can examine the relationship between a location's average temperature and the use of air conditioners.

Syntax

CORREL(array1,array2)

Array1   is a cell range of values.

Array2   is a second cell range of values.

Remarks

• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• If array1 and array2 have a different number of data points, CORREL returns the #N/A error value.
• If either array1 or array2 is empty, or if s (the standard deviation) of their values equals zero, CORREL returns the #DIV/0! error value.
• The equation for the correlation coefficient is:

where x and y are the sample means AVERAGE(array1) and AVERAGE(array2).

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• COVAR function
• FISHER function
• FISHERINV function
• Statistical functions

Excel > Function reference > Statistical

COUNT function

Excel 2007

This article describes the formula syntax and usage of the COUNT function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

The COUNT function counts the number of cells that contain numbers, and counts numbers within the list of arguments. Use the COUNT function to get the number of entries in a number field that is in a range or array of numbers. For example, you can enter the following formula to count the numbers in the range A1:A20:

=COUNT(A1:A20)

In this example, if five of the cells in the range contain numbers, the result is 5.

Syntax

COUNT(value1, [value2],...)

The COUNT function syntax has these arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• value1  Required. The first item, cell reference, or range within which you want to count numbers.
• value2, ...  Optional. Up to 255 additional items, cell references, or ranges within which you want to count numbers.

 Note    The arguments can contain or refer to a variety of different types of data, but only numbers are counted.

Remarks

• Arguments that are numbers, dates, or a text representation of numbers (for example, a number enclosed in quotation marks, such as "1") are counted.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• Arguments that are error values or text that cannot be translated into numbers are not counted.
• If an argument is an array or reference, only numbers in that array or reference are counted. Empty cells, logical values, text, or error values in the array or reference are not counted.
• If you want to count logical values, text, or error values, use the COUNTA function.
• If you want to count only numbers that meet certain criteria, use the COUNTIF function or the COUNTIFS function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVERAGE function
• Count cells that contain numbers
• Count how often a value occurs
• COUNTA function
• DCOUNT function
• DCOUNTA function
• Statistical functions
• SUM function

Excel > Function reference > Statistical

COUNTA function

Excel 2007

This article describes the formula syntax and usage of the COUNTA function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

The COUNTA function counts the number of cells that are not empty in a range (range: Two or more cells on a sheet. The cells in a range can be adjacent or nonadjacent.).

Syntax

COUNTA(value1, [value2], ...)

The COUNTA function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• value1  Required. The first argument representing the values that you want to count.
• value2, ...  Optional. Additional arguments representing the values that you want to count, up to a maximum of 255 arguments.

Remarks

• The COUNTA function counts cells containing any type of information, including error values and empty text (""). For example, if the range contains a formula that returns an empty string, the COUNTA function counts that value. The COUNTA function does not count empty cells.
• If you do not need to count logical values, text, or error values (in other words, if you want to count only cells that contain numbers), use the COUNT function.
• If you want to count only cells that meet certain criteria, use the COUNTIF function or the COUNTIFS function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVERAGE function
• COUNT function
• Count nonblank cells
• DCOUNT function
• DCOUNTA function
• PRODUCT function
• Statistical functions
• SUM function

Excel > Function reference > Statistical

COUNTBLANK function

Excel 2007

Counts empty cells in a specified range of cells.

Syntax

COUNTBLANK(range)

Range   is the range from which you want to count the blank cells.

Remark

Cells with formulas that return "" (empty text) are also counted. Cells with zero values are not counted.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• COUNTIF function
• Information functions
• Statistical functions

Excel > Function reference > Statistical

COUNTIF function

Excel 2007

This article describes the formula syntax and usage of the COUNTIF function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

The COUNTIF function counts the number of cells within a range that meet a single criterion that you specify. For example, you can count all the cells that start with a certain letter, or you can count all the cells that contain a number that is larger or smaller than a number you specify. For example, suppose you have a worksheet that contains a list of tasks in column A, and the first name of the person assigned to each task in column B. You can use the COUNTIF function to count how many times a person's name appears in column B and, in that way, determine how many tasks are assigned to that person. For example:

=COUNTIF(B2:B25,"Nancy")

 Note    To count cells based on multiple criteria, see COUNTIFS function.

Syntax

COUNTIF(range, criteria)

The COUNTIF function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• range  Required. One or more cells to count, including numbers or names, arrays, or references that contain numbers. Blank and text values are ignored.
• criteria  Required. A number, expression, cell reference, or text string that defines which cells will be counted. For example, criteria can be expressed as 32, ">32", B4, "apples", or "32".

 Notes 

• You can use the wildcard characters — the question mark (?) and the asterisk (*) — in criteria. A question mark matches any single character, and an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.
• Criteria are case insensitive; for example, the string "apples" and the string "APPLES" will match the same cells.

Example 1: Common COUNTIF formulas

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

Example 2: COUNTIF formulas using wildcard characters and handling blank values

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

 Note     To view a number as a percentage, select the cell and then, on the Sheet tab, in the Number group, click Percentage Style .

Related Office Online discussions

Read related questions and answers from other Microsoft Office customers.

• How do I get the filter mode to show the good row count?
• How can I count items in a filtered list?
• Can I use a Reference inside a SUMIF or COUNTIF Function?
• Can I Use a Count Function for Text?
• How do I count cells beginning with specific letter?
• How to not count cells which contain a formula that returns " "?

See Also

• COUNTA function
• COUNTBLANK function
• COUNTIFS function
• Math and trigonometry functions
• Statistical functions

Excel > Function reference > Statistical

COUNTIFS function

Excel 2007

This article describes the formula syntax and usage of the COUNTIFSfunction (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

Applies criteria to cells across multiple ranges and counts the number of times all criteria are met.

Syntax

COUNTIFS(criteria_range1, criteria1, [criteria_range2, criteria2]…)

The COUNTIFS function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• criteria_range1  Required. The first range in which to evaluate the associated criteria.
• criteria1  Required. The criteria in the form of a number, expression, cell reference, or text that define which cells will be counted. For example, criteria can be expressed as 32, ">32", B4, "apples", or "32".
• criteria_range2, criteria2, ...  Optional. Additional ranges and their associated criteria. Up to 127 range/criteria pairs are allowed.

Important  Each additional range must have the same number of rows and columns as the criteria_range1 argument. The ranges do not have to be adjacent to each other.

Remarks

• Each range's criteria is applied one cell at a time. If all of the first cells meet their associated criteria, the count increases by 1. If all of the second cells meet their associated criteria, the count increases by 1 again, and so on until all of the cells are evaluated.
• If the criteria argument is a reference to an empty cell, the COUNTIFS function treats the empty cell as a 0 value.
• You can use the wildcard characters— the question mark (?) and asterisk (*) — in criteria. A question mark matches any single character, and an asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) before the character.

Example 1

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

Example 2

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• COUNTIF function
• Math and trigonometry functions
• Statistical functions

Excel > Function reference > Statistical

COVAR function

Excel 2007

Returns covariance, the average of the products of deviations for each data point pair. Use covariance to determine the relationship between two data sets. For example, you can examine whether greater income accompanies greater levels of education.

Syntax

COVAR(array1,array2)

Array1   is the first cell range of integers.

Array2   is the second cell range of integers.

Remarks

• The arguments must either be numbers or be names, arrays, or references that contain numbers.
• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• If array1 and array2 have different numbers of data points, COVAR returns the #N/A error value.
• If either array1 or array2 is empty, COVAR returns the #DIV/0! error value.
• The covariance is:

where x and y are the sample means AVERAGE(array1) and AVERAGE(array2), and n is the sample size.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CORREL function
• FISHER function
• FISHERINV function
• Statistical functions

Excel > Function reference > Statistical

CRITBINOM function

Excel 2007

Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value. Use this function for quality assurance applications. For example, use CRITBINOM to determine the greatest number of defective parts that are allowed to come off an assembly line run without rejecting the entire lot.

Syntax

CRITBINOM(trials,probability_s,alpha)

Trials   is the number of Bernoulli trials.

Probability_s   is the probability of a success on each trial.

Alpha   is the criterion value.

Remarks

• If any argument is nonnumeric, CRITBINOM returns the #VALUE! error value.
• If trials is not an integer, it is truncated.
• If trials < 0, CRITBINOM returns the #NUM! error value.
• If probability_s is < 0 or probability_s > 1, CRITBINOM returns the #NUM! error value.
• If alpha < 0 or alpha > 1, CRITBINOM returns the #NUM! error value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• BINOMDIST function
• COMBIN function
• FACT function
• HYPGEOMDIST function
• NEGBINOMDIST function
• PERMUT function
• PROB function
• Statistical functions

Excel > Function reference > Statistical

DEVSQ function

Excel 2007

Returns the sum of squares of deviations of data points from their sample mean.

Syntax

DEVSQ(number1,number2,...)

Number1, number2, ...   are 1 to 255 arguments for which you want to calculate the sum of squared deviations. You can also use a single array or a reference to an array instead of arguments separated by commas.

Remarks

• Arguments can either be numbers or names, arrays, or references that contain numbers.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• Arguments that are error values or text that cannot be translated into numbers cause errors.
• The equation for the sum of squared deviations is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• AVEDEV function
• Statistical functions
• STDEV function
• STDEVP function
• VAR function
• VARP function

Excel > Function reference > Statistical

EXPONDIST function

Excel 2007

Returns the exponential distribution. Use EXPONDIST to model the time between events, such as how long an automated bank teller takes to deliver cash. For example, you can use EXPONDIST to determine the probability that the process takes at most 1 minute.

Syntax

EXPONDIST(x,lambda,cumulative)

X   is the value of the function.

Lambda   is the parameter value.

Cumulative   is a logical value that indicates which form of the exponential function to provide. If cumulative is TRUE, EXPONDIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Remarks

• If x or lambda is nonnumeric, EXPONDIST returns the #VALUE! error value.
• If x < 0, EXPONDIST returns the #NUM! error value.
• If lambda ≤ 0, EXPONDIST returns the #NUM! error value.
• The equation for the probability density function is:

• The equation for the cumulative distribution function is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• GAMMADIST function
• POISSON function
• Statistical functions

Excel > Function reference > Statistical

FDIST function

Excel 2007

Returns the F probability distribution. You can use this function to determine whether two data sets have different degrees of diversity. For example, you can examine the test scores of men and women entering high school and determine if the variability in the females is different from that found in the males.

Syntax

FDIST(x,degrees_freedom1,degrees_freedom2)

X   is the value at which to evaluate the function.

Degrees_freedom1   is the numerator degrees of freedom.

Degrees_freedom2   is the denominator degrees of freedom.

Remarks

• If any argument is nonnumeric, FDIST returns the #VALUE! error value.
• If x is negative, FDIST returns the #NUM! error value.
• If degrees_freedom1 or degrees_freedom2 is not an integer, it is truncated.
• If degrees_freedom1 < 1 or degrees_freedom1 ≥ 10^10, FDIST returns the #NUM! error value.
• If degrees_freedom2 < 1 or degrees_freedom2 ≥ 10^10, FDIST returns the #NUM! error value.
• FDIST is calculated as FDIST=P( F>x ), where F is a random variable that has an F distribution with degrees_freedom1 and degrees_freedom2 degrees of freedom.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• FINV function
• FTEST function
• Statistical functions

Excel > Function reference > Statistical

FINV function

Excel 2007

Returns the inverse of the F probability distribution. If p = FDIST(x,...), then FINV(p,...) = x.

The F distribution can be used in an F-test that compares the degree of variability in two data sets. For example, you can analyze income distributions in the United States and Canada to determine whether the two countries have a similar degree of income diversity.

Syntax

FINV(