Question

What is the standard deviation of the given data set: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).

• A. 13.33
• B. 13.31
• C. 13.14
• D. 13.08

Hint:

Standard deviation measures how spread out numbers are from the mean. Use variance = average of squared differences, then take square root.

Answer 1

The Correct Option is D

First, compute the mean: Mean = $\dfrac{25 + 50 + 45 + 30 + 70 + 42 + 36 + 48 + 34 + 60}{10} = \dfrac{440}{10} = 44$ Now compute the squared deviations: $\sum (x_i - \bar{x})^2 = (25-44)^2 + (50-44)^2 + \ldots + (60-44)^2 = 1710$ Variance = $\dfrac{1710}{10} = 171$ Standard Deviation = $\sqrt{171} \approx 13.08$