To find the standard deviation of Susie's test scores, we can follow these steps:
- Calculate the mean (average) of the scores.
- Calculate the variance by finding the squared differences from the mean, averaging those, and then taking the square root to obtain the standard deviation.
Step 1: Calculate the mean
The scores are: 91, 75, 79, 85, and 87.
Mean = (91 + 75 + 79 + 85 + 87) / 5
Mean = (417) / 5 = 83.4
Step 2: Calculate the squared differences from the mean
- (91 - 83.4)² = (7.6)² = 57.76
- (75 - 83.4)² = (-8.4)² = 70.56
- (79 - 83.4)² = (-4.4)² = 19.36
- (85 - 83.4)² = (1.6)² = 2.56
- (87 - 83.4)² = (3.6)² = 12.96
Step 3: Calculate the variance
Variance = (Sum of squared differences) / (Number of scores) Variance = (57.76 + 70.56 + 19.36 + 2.56 + 12.96) / 5 Variance = (163.2) / 5 = 32.64
Step 4: Calculate the standard deviation
Standard deviation = √Variance Standard deviation = √32.64 ≈ 5.71
So the standard deviation of Susie's grades is approximately 5.71.
The best answer is C. 5.71.
3 answers