Wading Through the Data Swamp:
Program Evaluation 201

Module 1: Descriptive Statistics in Evaluation - Page 15 of 21

Standard Deviation for Marijuana Use
marijuana icon

The first additional statistic Jack should look at is the standard deviation. This is a measure of how much scores vary. It gives you an idea of the distribution of scores without having to list each score.

If you insist, I'll be happy to show you the formula for calculating the standard deviation. Don't worry. The formula is written this way to intimidate you.

formula for standard deviation

If evaluators wanted you to understand it, it would be written in English as follows:

The square root of: The sum of (each score - the mean)2 divided by (number of scores - 1)

Oh, you wanted plain English? O.k., how about walking through this step by step?

  1. Take each score and subtract the mean (for example, for student #1, subtract 1.7 from 0 = -1.7).
  2. Square that number (for example, for student #1, square -1.7 = 2.89). We square this number to get rid of negative numbers.
  3. Add the results for each student (all 50 students' results added together = 348.5).
  4. Divide the total by the number of scores minus one (for Jack's group, 348.5/49 = 7.11).
  5. Take the square root of the result of step 4 (square root of 7.11 = 2.67). We take the square root to decrease the size of our number, therefore making it easier to work with.

Here are the results:

Standard Deviation for Marijuana Use

Picture of a scroll Scrolling Table! You can use the table below to scroll through the data.

Kid # Days
Used(x)		 (Days Used-Mean)
(x-M)		 (Days
Used-Mean)2
(x-M)2
1 0 -1.69 2.86
2 0 -1.69 2.86
3 6 4.09 16.71
4 0 -1.69 2.86
5 4 2.31 5.34
6 0 -1.69 2.86
7 0 -1.69 2.86
8 0 -1.69 2.86
9 6 4.74 22.45
10 0 -1.69 2.86
11 3 1.74 3.02
12 5 3.38 11.41
13 0 -1.69 2.86
14 0 -1.69 2.86
15 3 1.31 1.72
16 0 -1.69 2.86
17 0 -1.69 2.86
18 5 3.34 11.15
19 0 -1.69 2.86
20 0 -1.69 2.86
21 0 -1.69 2.86
22 0 -1.69 2.86
23 0 -1.69 2.86
24 4 2.31 5.34
25 0 -1.69 2.86
26 0 -1.88 3.55
27 0 -1.87 3.51
28 0 -1.69 2.86
29 0 -1.69 2.86
30 7 5.31 28.20
31 0 -1.69 2.86
32 0 -1.69 2.86
33 7 5.48 30.00
34 0 -1.69 2.86
35 5 3.31 10.96
36 3 1.31 1.72
37 0 -1.69 2.86
38 0 -1.69 2.86
39 8 6.31 39.82
40 0 -1.69 2.86
41 0 -1.69 2.86
42 0 -2.18 4.77
43 0 -1.69 2.86
44 0 -1.69 2.86
45 7 5.31 28.20
46 0 -1.69 2.86
47 0 -1.69 2.86
48 5 2.91 8.47
49 7 5.04 25.44
50 0 -1.69 2.86
 
 

Mean = 85/50 = 1.7

Standard deviation = The square root of : The sum of (each score - mean)2/(number of scores - 1)

square root of350.3/(50-1) = square root of7.15 = 2.67

That wasn't so bad, was it? Much more pleasant than the root canal you were going to have instead. This is more like a square root canal. Sorry, I couldn't resist.

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