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

Option b: 2.45. Solution: Given data: 6, 9, 10, 3, 7; n = 5 Step 1: Calculate Mean. x = 6+9+10+3+7/5 = 35/5 = 7 Step 2: Calculate squared deviations. |c|c|c| xi & (xi - x) & (xi - x)2 6 & -1 & 1 9 & 2 & 4 10 & 3 & 9 3 & -4 & 16 7 & 0 & 0 & & sum = 30 Step 3: Calculate Variance. sigma2 = 30/5 = 6 Step 4: Calculate SD. sigma = sqrt(6) ≈ 2.449 ≈ 2.45 So the correct answer should be Option B (2.45), not Option D (2.65). sqrt(6) = 2.4495... Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 18Question 3152 of 473

All Questions

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

Options

\displaystyle 2.35

\displaystyle 2.45

\displaystyle 2.55

\displaystyle 2.65

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Correct Answer

✅ Option b — $\displaystyle 2.45$

All Options:

A $\displaystyle 2.35$
B $\displaystyle 2.45$
C $\displaystyle 2.55$
D $\displaystyle 2.65$

Detailed Solution & Explanation

**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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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The SD for the data 6,9,10,3,7\displaystyle 6, 9, 10, 3, 76,9,10,3,7 is