# Built-in Statistical Functions

Excel provides a variety of statistical functions, which we list below. Since these have been covered in the rest of the website, we won’t go into any detail here.

### Basic statistical functions

Figure 1 – Table of basic Excel statistics functions

### Correlation and covariance functions

Figure 2 – Table of Excel correlation and covariance functions

### Regression functions

Figure 3 – Table of Excel regression functions

### Other statistical functions

Figure 4 – Table of other Excel statistical functions

### Statistical distribution functions

The following table provides a list of the distributions supported by Excel. For each, the name of cumulative distribution functions (CDF) is given, and where available the name of the inverse function is also provided. For a few of the distributions, the CDF function also has an option to provide the probability density function (PDF). Finally, additional test functions are listed where available.

Figure 5 – Table of Excel 2007 distribution functions

### Excel 2010 functions

All the functions defined in previous versions of Excel are available in Excel 2010, but the mathematical accuracy of many of these functions has been improved in Excel 2010. In addition a few new functions have been added and more consistent naming conventions have been introduced, including the following:

Figure 6 – Table of new Excel 2010 statistical functions

For example, if R = {4,6,4,7,6,6}, then RANK(4,R) = 5, RANK(6,R) = 2 and RANK(7,R) = 1, while RANK.AVG(4,R) = 5.5, RANK.AVG(6,R) = 3 and RANK.AVG(7,R) = 1. Also RANK.EQ is the same as RANK. Similarly, RANK(4,R,1) = 1, RANK(6,R,1) = 3 and RANK(7,R,1) = 6, while RANK.AVG(4,R,1) = 1.5, RANK.AVG(6,R,1) = 4 and RANK.AVG(7,R,1) = 6.

MODE.MULT is an array function which is useful with multimodal data. Before using the function you need to highlight a vertical range (i.e. column vector) with at least as many cells as modes and then enter =MODE.MULT(R) and Ctrl-Shft-Enter. If you highlight more cells than modes the extra cells will contain the error values #N/A.

The function GAMMALN.PRECISE, which is equivalent to GAMMALN, has also been added in Excel 2010,

In Excel 2010 there are the following alternative names for the distribution functions:

Figure 7 – Table of Excel 2010 distribution functions

The functions that end in .DIST all provide both the probability distribution function (when the cum parameter is FALSE) as well as the left-tailed cumulative distribution function (when the cum parameter is TRUE). These are all left-tailed functions. For the chi-square and F distributions there is also a right tailed version (indicated by .RT in the above table) of the distribution and inverse cumulative functions. There is also a right tailed version of the  distribution function and a two-tailed version of the t distribution and its inverse.

The syntax for the various new  distribution functions is T.DIST(x,df,cum), T.DIST.RT(x,df) and T.DIST.2T(x,df). The syntax for the new inverse function is T.INV(p,df) and T.INV.2T(p,df). We have the following equivalences between the Excel 2007 and Excel 2010 versions of the t distribution functions:

Figure 8 – Table of equivalences for the t distribution

Note that while the old t distribution functions worked differently from the normal and binomial distribution functions, the new functions are all consistent. Also we can now explicitly calculate the pdf of the t distribution as T.DIST(x, df, FALSE) instead of having to use a complicated formula based on Definition 1 of t Distribution.

We also have the following equivalences between the Excel 2007 and Excel 2010 versions of the chi-square distribution functions:

Figure 9 – Table of equivalences for the chi-square distribution

Also we can now explicitly calculate the pdf of the chi-square distribution as CHISQ.DIST(x, df, FALSE). The equivalences for the F distribution between Excel 2007 and 2010 are similar.

Figure 10 – Table of equivalences for the F distribution

### Excel 2013 functions

All the functions defined in previous versions of Excel are available in Excel 2013, but the following additional functions are available:

Figure 11 – Table of new Excel 2013 statistical functions

### 10 Responses to Built-in Statistical Functions

1. Ernest Bledsoe says:

Thank You.

2. Subin says:

Thank u somuch…

3. Joe Horwath says:

Great summary , thanks ; now of coures an example for the use of each would be invaluable for understanding and the mechanics of their use and utility . Again thanks , Charles

4. Joe Horwath says:

Great summary , thanks ; found your Eamples Workbook , thank you

5. Joe Horwath says:

6. khushboo says:

Bakwaas

• Charles says:

Khushboo,
It seems that you don’t like this webpage or perhaps the website. What don’t you like?
Charles

7. Few in today ‘s world are given without taking a thing. And you are of little greatest people. Charles, preach, your reward in the hereafter is greater than today.
Mahmoud Arafa

• Charles says:

Mahmoud,
Thank you for your comment, but you are too kind. I am just trying to do my part.
Charles

8. Rosanne Howarth says:

Thanks so much for the great summary