The sample standard deviation of the data {2,4,4,4,5,5,7,9} is approximately which value?

• A. 2.14
• B. 2.00
• C. 2.20
• D. 1.98

Answer: (A)

When you measure spread with the sample standard deviation, you take the square root of the average squared deviations from the mean, using n−1 in the denominator to get an unbiased estimate of the population variance.

Compute the mean first: the sum is 40, and there are 8 numbers, so the mean is 40/8 = 5.

Find each deviation from the mean and square it:

• (2−5)² = 9

• (4−5)² = 1 (three times gives 3)

• (5−5)² = 0 (two times gives 0)

• (7−5)² = 4

• (9−5)² = 16

Sum of squared deviations = 9 + 3 + 0 + 4 + 16 = 32.

Divide by n−1 = 7: 32/7 ≈ 4.571.

Take the square root: √4.571 ≈ 2.14.

So the sample standard deviation is approximately 2.14.