Question

For the set of values 10, 16, 18, 20, 22, 28, what is the standard deviation?

A) 35
B) 5.51
C) 2.24
D) 7

Answer 1

To calculate the standard deviation of the values 10, 16, 18, 20, 22, 28, find the mean, calculate each value's deviation from the mean, square these deviations, average the squared deviations, and take the square root. The standard deviation is approximately 5.51.

Step-by-step explanation:

To calculate the standard deviation for the set of values: 10, 16, 18, 20, 22, 28, you follow these steps:

1. Find the mean (average) of the values.
2. Subtract the mean from each value to find the deviation for each value.
3. Square each deviation.
4. Find the mean of these squared deviations.
5. Take the square root of the mean of the squared deviations to find the standard deviation.

Calculation:

• Mean = (10 + 16 + 18 + 20 + 22 + 28) / 6 = 114 / 6 = 19
• Deviations: -9, -3, -1, 1, 3, 9
• Squared Deviations: 81, 9, 1, 1, 9, 81
• Mean of Squared Deviations: (81 + 9 + 1 + 1 + 9 + 81) / 6 = 182 / 6 = 30.33
• Standard Deviation = √30.33 ≈ 5.51

Therefore, the standard deviation is 5.51, which corresponds to option B).