1. Calculate the mean: (22 + 30 + 102 + 36 + 75 + 100 + 81 + 62 + 29) / 9 = 547 / 9 ≈ 60.78
2. For each test score, calculate the difference from the mean (x - x̄):
- 22 - 60.78 = -38.78
- 30 - 60.78 = -30.78
- 102 - 60.78 = 41.22
- 36 - 60.78 = -24.78
- 75 - 60.78 = 14.22
- 100 - 60.78 = 39.22
- 81 - 60.78 = 20.22
- 62 - 60.78 = 1.22
- 29 - 60.78 = -31.78
3. Square each difference:
- (-38.78)² ≈ 1503.89
- (-30.78)² ≈ 947.41
- (41.22)² ≈ 1699.09
- (-24.78)² ≈ 614.05
- (14.22)² ≈ 202.21
- (39.22)² ≈ 1538.21
- (20.22)² ≈ 408.85
- (1.22)² ≈ 1.49
- (-31.78)² ≈ 1009.97
4. Sum of squared differences: 1503.89 + 947.41 + 1699.09 + 614.05 + 202.21 + 1538.21 + 408.85 + 1.49 + 1009.97 ≈ 7925.17
5. Divide by degrees of freedom (n - 1 = 8): 7925.17 / 8 ≈ 990.65 → This is the variance.
6. Take the square root of the variance: √990.65 ≈ 31.47 → This is the standard deviation.
Parent Tip: Review the logic above to help your child master the concept of calculating standard deviation worksheet answers.
