Wading Through the Data Swamp:
Program Evaluation 201
Standard Deviation for Alcohol Use

You can do these same steps with the kids' responses to the alcohol use question, to see if their alcohol use varies as much as their marijuana use.
- Take each score and subtract the mean (for example, for student #1, subtract 1.64 from 2 = 0.36).
- Square that number (for example, for student #1, square 0.36 = .1296).
- Add the results for each student (all 50 students' results added together = 41.52).
- Divide the total by the number of scores minus one (for Jack's group, 41.52/49 = 0.8304).
- Take the square root of the result of step 4 (square root of 0.8304 = 0.91).
Here are the results:
Standard Deviation for Alcohol Use
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 | 2 | 0.36 | 0.1296 |
| 2 | 1 | -0.64 | 0.4096 |
| 3 | 2 | 0.36 | 0.1296 |
| 4 | 2 | 0.36 | 0.1296 |
| 5 | 2 | 0.36 | 0.1296 |
| 6 | 1 | -0.64 | 0.4096 |
| 7 | 2 | 0.36 | 0.1296 |
| 8 | 0 | -1.64 | 2.6896 |
| 9 | 4 | 2.36 | 5.5696 |
| 10 | 1 | -0.64 | 0.4096 |
| 11 | 2 | 0.36 | 0.1296 |
| 12 | 2 | 0.36 | 0.1296 |
| 13 | 2 | 0.36 | 0.1296 |
| 14 | 1 | -0.64 | 0.4096 |
| 15 | 2 | 0.36 | 0.1296 |
| 16 | 1 | -0.64 | 0.4096 |
| 17 | 2 | 0.36 | 0.1296 |
| 18 | 5 | 3.36 | 11.2896 |
| 19 | 1 | -0.64 | 0.4096 |
| 20 | 2 | 0.36 | 0.1296 |
| 21 | 2 | 0.36 | 0.1296 |
| 22 | 2 | 0.36 | 0.1296 |
| 23 | 0 | -1.64 | 2.6896 |
| 24 | 2 | 0.36 | 0.1296 |
| 25 | 1 | -0.64 | 0.4096 |
| 26 | 2 | 0.36 | 0.1296 |
| 27 | 2 | 0.36 | 0.1296 |
| 28 | 1 | -0.64 | 0.4096 |
| 29 | 2 | 0.36 | 0.1296 |
| 30 | 2 | 0.36 | 0.1296 |
| 31 | 0 | -1.64 | 2.6896 |
| 32 | 2 | 0.36 | 0.1296 |
| 33 | 1 | -0.64 | 0.4096 |
| 34 | 0 | -1.64 | 2.6896 |
| 35 | 2 | 0.36 | 0.1296 |
| 36 | 2 | 0.36 | 0.1296 |
| 37 | 1 | -0.64 | 0.4096 |
| 38 | 2 | 0.36 | 0.1296 |
| 39 | 1 | -0.64 | 0.4096 |
| 40 | 2 | 0.36 | 0.1296 |
| 41 | 0 | -1.64 | 2.6896 |
| 42 | 2 | 0.36 | 0.1296 |
| 43 | 2 | 0.36 | 0.1296 |
| 44 | 1 | -0.64 | 0.4096 |
| 45 | 2 | 0.36 | 0.1296 |
| 46 | 2 | 0.36 | 0.1296 |
| 47 | 2 | 0.36 | 0.1296 |
| 48 | 1 | -0.64 | 0.4096 |
| 49 | 2 | 0.36 | 0.1296 |
| 50 | 2 | 0.36 | 0.1296 |
Mean = 82/50 = 1.64
Standard deviation = The square root of : The sum of (each score - mean)2/(number of scores - 1)
41.52/(50-1) =
0.8304 = 0.91
We can see that the standard deviation of marijuana use (2.67) is much higher than the standard deviation for alcohol use (.91). This tells us that the group score varied greatly for marijuana but only slightly for alcohol. In other words, most participants used alcohol about the same number of times per month. The same is not so for marijuana use. Some kids never used, some used moderately, and others used very frequently.








