Compute the standard deviation for stress. Determine where participants fall in relation to the mean. (Create a diagram that depicts where students fall in relation to standard deviations around the mean.
Participant Group Fights Stress
1 PSY 7 86
2 PSY 3 84
3 PSY 5 92
4 PSY 4 76
5 PSY 5 68
6 PSY 5 79
7 PSY 6 85
8 PSY 5 81
9 PSY 4 90
10 PSY 6 83
11 CBT 1 56
12 CBT 2 59
13 CBT 1 42
14 CBT 3 60
15 CBT 0 40
16 CBT 2 45
17 CBT 1 41
18 CBT 0 35
19 CBT 3 59
20 CBT 1 40
To compute the standard deviation for the stress data and determine where participants fall in relation to the mean, follow these steps:
1. Calculate the mean (average) of the stress values.
- Add up all the stress values and divide by the number of participants: (86 + 84 + 92 + 76 + 68 + 79 + 85 + 81 + 90 + 83 + 56 + 59 + 42 + 60 + 40 + 45 + 41 + 35 + 59 + 40) / 20 = 64.5.
- The mean stress value is 64.5.
2. Calculate the variance of the stress values.
- For each participant, subtract the mean stress value from their individual stress value and square the result.
- Sum up all these squared differences and divide by the number of participants: [(86-64.5)^2 + (84-64.5)^2 + (92-64.5)^2 + ... + (40-64.5)^2] / 20 = 314.675.
- The variance of the stress values is 314.675.
3. Calculate the standard deviation by taking the square root of the variance.
- √314.675 ≈ 17.737.
- The standard deviation for the stress values is approximately 17.737.
To determine where participants fall in relation to the mean, you can use the standard deviation as a measure of dispersion. The standard deviation tells us how much the stress values deviate from the mean.
4. Calculate the number of standard deviations each participant's stress value is from the mean.
- Subtract the mean stress value from each participant's stress value and divide by the standard deviation: (participant's stress value - mean stress value) / standard deviation.
- For example, let's take participant 1: (86 - 64.5) / 17.737 ≈ 1.208.
- Participant 1's stress value is approximately 1.208 standard deviations above the mean.
5. Create a diagram depicting where participants fall in relation to standard deviations around the mean.
- You can create a number line representing the standard deviations. Place the mean stress value in the center and mark points to represent each standard deviation.
- For example, if the mean stress value is 64.5 and the standard deviation is 17.737, you can mark points at 46.763, 64.5, 82.237, etc.
- Place each participant's stress value on the number line according to the number of standard deviations they are from the mean.
- For example, if participant 1 is 1.208 standard deviations above the mean, place their stress value on the line 1.208 standard deviations to the right of the mean.
By following these steps, you can compute the standard deviation for stress and determine where participants fall in relation to the mean.