The measures of variability are methods that are used to find how the data spreads. Variability is also known as the data dispersion. It measures how the data is different from itself.

If the data set contains numbers that are not very different from each other, the set is said to have little variability. If instead the data set contains numbers that are more spread out, or are very different from each other, the set is said to have high variability

• Measures of variability include the range, variance,and standard deviation

The range of a set of data is the difference between the maximum and the minimum.To find the range, first find the largest number in the data set, and the smallest number in the data set. Then subtract the minimum from the maximum. It shows the distance from start to finish.

The variance is a measurement used to calculate how close or how far the data within the set are from the mean. The variance show how far the data spreads from what was expected. There are several steps to calculating the variance of a set of data.

Step 1: Determine the mean of the data set.

Step 2: Take each piece of data and subtract the mean.

Step 3: Square each of the values in Step 2.

***Please note all of your answers in this step should be positive. If you are getting negatives, try again and be sure to utilize parenthesis.

Step 4: Find the sum of the values in Step 3.

Step 5: Divide the sum of the squares that you obtained in Step 4 by the samples size, or the total number of values. The answer will be the variance.

The standard deviation is similar to the variance. It also measures how close or how far the data spreads. It shows the spread of the data from left and right of the mean and can be utilized in estimating the percentage of data covered within each standard deviation. Standard deviation is further used with The Empirical Rule (68%-95%-99.5% Rule) and The Standard Normal Curve. The standard deviation calculation is found by taking the square root of the variance, so there is essentially one more step after you find the variance. Step 6: Take the square root of the variance: the value you obtained in Step 5.

• At the top, select Stat, Choose Summary Stat, then Select Columns
• Choose the column that contains your data by highlighting your choice
• Under Statistics, select mean, median, and mode by clicking these on the left side, then click Compute!

In any Excel entry box:

• =Var.P(select all numbers in your column by highlighting them) for Variance
• =StDev.P(select all numbers in your column by highlighting them) for Standard Deviation

Or, find these all at once with Data Analytics Add On

1. Select Data Tab at the top, Click Data Analysis Add On, then Select Descriptive Statistics

• Under Input Range, select all data/numbers with your mouse
• Check the Summary Statistics Box
• Click “OK”

This will automatically populate a new sheet in Excel with various descriptive statistics data including all the measures of dispersion.

Example One

You decide to measure the average amount of likes you receive on Instagram posts. With the data you collected below, find the range, variance, and standard deviation

5, 17, 21, 95, 42

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