Question Bank • QB_EM_157
NAT • 2 Marks
Section 1: Engineering Mathematics
Probability and Statistics
Subtopic: Mean, median, mode and standard deviation
Question Statement:
Calculate the sample standard deviation $s$ of the dataset: $\{4, 8, 6, 5, 7\}$ (use denominator $n - 1 = 4$; round off to 2 decimal places).
Step-by-Step Solution & Explanation
Mean:
$\bar{x} = \frac{4 + 8 + 6 + 5 + 7}{5} = \frac{30}{5} = 6.0$
Deviations and squares:
$(4-6)^2 = 4$
$(8-6)^2 = 4$
$(6-6)^2 = 0$
$(5-6)^2 = 1$
$(7-6)^2 = 1$
Sum of squared deviations $= 4 + 4 + 0 + 1 + 1 = 10$.
Sample variance:
$s^2 = \frac{10}{5 - 1} = \frac{10}{4} = 2.5$
Sample standard deviation:
$s = \sqrt{2.5} \approx 1.581 \approx 1.58$
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