# How to Use Microsoft Excel’s Data Analysis ToolPak for Descriptive Statistics

## Introduction

Excel makes calculating statistics much easier today than ever before. It literally takes a few keys strokes and clicks to get just about any type of statistical measurement or graph from a data set. Excel is preloaded with statistical functions that can help you find the mean, median, mode, variance and many more statistical measurements. Aside from Excel's functions, the program also allows users the option to install a Data Analysis ToolPak Add-in that is used to perform many types of calculations at once. This tutorial shows an excel user how to use the Data Analysis tool to find descriptive statistics and explains the results.

## Activate the Data Analysis Data ToolPak

If you have never used the Data Analysis ToolPak, it is probably inactive on your Excel program. You can check to see if you have it by first clicking on the data tab. Next, look for the analysis group on the far-right side of your screen. If data analysis option does not exist use the following steps to activate this add-in.

- Click on the File. tab click options, and then click on “Add-Ins.”
- Next, click on the “Go” button to the manage add-ins section.
- Lastly, check the “Analysis Pak” box and click “OK.”

You should now be ready to use the Data Analysis ToolPak from the data tab in the analysis group.

## Data Analysis Example

If following along with this example with an excel worksheet type this data set into Excel vertically in individual cells.

2, 5, 7, 9, 4, 3, 3, 4, 6, 8, 14, 4, 20, 6, 10, 4, 5, 9, 11, 1, 6, 9, 4, 5, 13, 18, 7, 6, 9, 10

Click on “Data Analysis” in the data tab and then click on Descriptive Statistics in the dialog box. Click the OK button.

Next, the range of the data needs to be typed in the input range section of the dialog box. Choose the output range option and choose a cell for the output to display by typing that cell location in the blank field. Lastly, click in the Summary statistics checkbox and click OK to display the results.

## The Results

The results print in two columns. The first column represents a the descriptive statistic and second column shows the results for those statistics. In the following sections I will describe what these descriptive statistics represent.

## Mean

The mean, which is a measure of central tendency, was calculated by taking the average of the whole data set. The sum of the data set is 222 and when divided by 30 gives a mean of 222/30 = 7.4. The mean can be written as the expression: ∑x_{i }/n, where n is the number of values and ∑x_{i} is the sum of data values.

## Standard Error

The standard error is defined as the standard deviation divided by the square root of the sample size. In the above example, the standard error is 4.45/sqrt(30) = 0.813.

## Median

The median is the middle value and another measure of central tendency. To find the median or middle value the data set, you need to arrange the whole data set in ascending or descending order. The value directly in the middle in the median value when there is an odd number of values in the data set. When there is an even number of values, there will be two middle values that need to be averaged to find the median.

## Mode

Another measure of central tendency is the mode. This is the value that appears more frequently than any other value. In the example above, 4 appears more than any other number. There may be a case where there is more than one mode. This occurs when there are two numbers that appear most frequently in a data set but appear the same amount of times.

## Standard Deviation

Standard deviation is the square root of the variance result. There are two scenarios depending on whether the standard deviation is calculated from a population or a sample. For a population standard deviation, the mathematical calculation is sqrt(∑(x_{i}-Xbar)^{2}/n) . When calculating the standard deviation for a sample the calculation is sqrt(∑(x_{i}-Xbar)^{2}/(n-1)). In the above example, the population standard deviation is or 4.378. The sample standard deviation is the square root of or 4.453.

## Variance

The variance is found by calculating the deviation of each value from the mean value. Then, squaring the deviation and finding the average of these squared deviations. To simplify the variance is the mean square deviation. The equation to calculate the population variance is ∑(x_{i}-Xbar)^{2}/n for a population and for a sample variance ∑(x_{i}-Xbar)^{2}/(n-1). In the example above the population variance is 575.2/30=19.173 and the sample variance is 575.2/29 = 19.834.

## Kurtosis

Kurtosis is a measure the distribution. It tells us the peakedness or narrowness of distribution is. A high kurtosis value means the peak of the distribution is tall. A negative kurtosis tells us that a distribution has a more rounded peak. In the above example, the kurtosis is 1.52.

## Skewness

Skewness measures asymmetry of a distribution. Symmetric data has data that is distributed symmetrically about the mean. If perfectly symmetric we would say that the skewness of a distribution is zero. A distribution is positively skewed, or to the right, if the right tail is longer. If the left tail is longer, we say the distribution is negatively skewed or skewed to the left. In the example, the skewness is 1.218. As a result, it can be said that the data is skewed to the right or is positively skewed or has a long right tail.

## Range

The range is the highest value in the data set minus the lowest value. In the example above, the range is 20 (Highest) minus 1 (Lowest) which equals 19.

## Min and Max

The min and the max are the lowest and highest values in the data set respectfully. In the example above, the highest value is 20 and the lowest is 1.

## Sum

The sum or ∑ is simply the addition of all the numbers in the data set. In the example above the sum is 222.

## Count

The count is simply the size of the population or size of the sample. In the example, the count is 30.

## Questions & Answers

**© 2018 Joshua Crowder**

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