What do the Standard Deviation and Range tell me?

Both the standard deviation and the range are measures of spread. They describe how the responses to a survey item vary across all participants. For any item in your evaluation instrument that includes scale responses (e.g., Strongly Disagree to Strongly Agree, Never to Always), the Microsoft Excel download will provide you with a table of Basic Descriptive Statistics, including the Standard Deviation and Range. When you are using a scale, each possible response in the scale will be coded with a value that reflects its position on the scale relative to other responses. These values are used to calculate the measures of Central Tendency (see the What do the measures of Central Tendency - Mean, Median, and Mode - tell me? FAQ for more on Central Tendency) as well as the Standard Deviation and Range. For example, if the scale you used was a 5-point scale from Strongly Disagree to Strongly Agree, Strongly Disagree would be assigned a 1, Disagree a 2, all the way up to Strongly Agree with a 5.

The Standard Deviation is of interest to us because it tells how much variation or dispersion there is around the average (the Mean, What do the measures of Central Tendency - Mean, Median, and Mode - tell me? FAQ). A low Standard Deviation, closer to 0.00, tells us that the responses were close to the Mean, and probably close to each other, whereas a high Standard Deviation tells us that the responses were spread out over a broad range. For example, if we had 5 total responses, and they were 2 (Disagree), 3 (Neither Agree or Disagree), 3 (Neither Agree or Disagree), 3 (Neither Agree or Disagree), and 3 (Neither Agree or Disagree), the high number of similar responses (3) and the small range of responses (all between 2 and 3) will lead to a low Standard Deviation, 0.45. This indicates that participants generally responded to the question similarly to one another. However, if our 5 responses were 1 (Strongly Disagree), 1, 1, 5 (Strongly Agree), and 5, the dissimilarity of responses overall and the large range will result in a relatively high Standard Deviation, 2.19. This indicates that responses in the set were about two values from each other (e.g., the difference between 2, “Disagree,” and 4, “Agree”).

The Range is a valuable compliment to the Standard Deviation because it tells you the actual range of responses that participants selected. The Minimum value in the Range tells you the value of the lowest response in the scale selected by any participant; the Maximum value tells you the value of the highest response selected. With our example response sets above, in the set of 2, 3, 3, 3, and 3, the Minimum value would be 2 and the Maximum would 3, a much smaller overall range than the Minimum of 1 and Maximum of 5 in our other response set. This corresponds to the Standard Deviations we found: the set with the smaller range (Minimum 2, Maximum 3) had a lower Standard Deviation (0.45), or less variation, than our set of with the greater range (Minimum 1, Maximum 5) and a Standard Deviation of 2.19.

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