1. Calculate the mean of the data set:
Mean = (24 + 99 + 99 + 97 + 72 + 72 + 100 + 84 + 42) / 9
Mean = 699 / 9 = 77.67
2. Calculate the squared deviations from the mean for each data point:
(24 - 77.67)² = (-53.67)² = 2880.49
(99 - 77.67)² = (21.33)² = 455.07
(99 - 77.67)² = (21.33)² = 455.07
(97 - 77.67)² = (19.33)² = 373.65
(72 - 77.67)² = (-5.67)² = 32.15
(72 - 77.67)² = (-5.67)² = 32.15
(100 - 77.67)² = (22.33)² = 498.63
(84 - 77.67)² = (6.33)² = 40.07
(42 - 77.67)² = (-35.67)² = 1272.35
3. Sum the squared deviations:
Sum = 2880.49 + 455.07 + 455.07 + 373.65 + 32.15 + 32.15 + 498.63 + 40.07 + 1272.35 = 5610.63
4. Divide the sum by the number of data points (n = 9) to find the variance:
Variance = 5610.63 / 9 = 623.40
5. Take the square root of the variance to find the standard deviation:
Standard Deviation = √623.40 ≈ 24.97
Final Answer: The standard deviation is approximately 24.97.
Parent Tip: Review the logic above to help your child master the concept of calculating standard deviation worksheet answers.
