Central Tendency & DispersionMTP Nov 18Question 3152 of 473

The SD for the data $\displaystyle 6, 9, 10, 3, 7$ is

\displaystyle 2.35

\displaystyle 2.45

\displaystyle 2.55

\displaystyle 2.65

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Correct Answer

✅ Option b — $\displaystyle 2.45$

**Given data:** 6, 9, 10, 3, 7;

\displaystyle n = 5

**Step 1: Calculate Mean.**

\bar{x} = \frac{6+9+10+3+7}{5} = \frac{35}{5} = 7

**Step 2: Calculate squared deviations.**

\begin{array}{|c|c|c|} \hline x_i & (x_i - \bar{x}) & (x_i - \bar{x})^2 \\ \hline 6 & -1 & 1 \\ 9 & 2 & 4 \\ 10 & 3 & 9 \\ 3 & -4 & 16 \\ 7 & 0 & 0 \\ \hline & & \sum = 30 \\ \hline \end{array}

**Step 3: Calculate Variance.**

\sigma^2 = \frac{30}{5} = 6

**Step 4: Calculate SD.**

\sigma = \sqrt{6} \approx 2.449 \approx 2.45

So the correct answer should be Option B (2.45), not Option D (2.65).

\displaystyle \sqrt{6} = 2.4495...

Hence, **Option B** is the correct answer.

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