The standard deviation of 10, 16, 10, 16, 10, 10, 16, 16 is

Option c: 3. Solution: Given data: 10, 16, 10, 16, 10, 10, 16, 16; n = 8 Count: Four 10s and four 16s. Step 1: Calculate Mean. x = 4 × 10 + 4 × 16/8 = 40 + 64/8 = 104/8 = 13 Step 2: Calculate squared deviations. - For the four 10s: (10 - 13)2 = 9 ; total = 4 × 9 = 36 - For the four 16s: (16 - 13)2 = 9 ; total = 4 × 9 = 36 sum(xi - x)2 = 36 + 36 = 72 Step 3: Calculate Variance. sigma2 = 72/8 = 9 Step 4: Calculate SD. sigma = sqrt(9) = 3 So SD = 3 (Option C). The given correctoption 'b' (6) is incorrect. Hence, Option C is the correct answer.

The standard deviation of $10, 16, 10, 16, 10, 10, 16, 16$ is

The correct answer is Option c: $3$. **Given data:** 10, 16, 10, 16, 10, 10, 16, 16; $n = 8$ Count: Four 10s and four 16s. **Step 1: Calculate Mean.** $$\bar{x} = \frac{4 \times 10 + 4 \times 16}{8} = \frac{40 + 64}{8} = \frac{104}{8} = 13$$ **Step 2: Calculate squared deviations.** - For the four 10s: $(10 - 13)^2 = 9$; total = $4 \times 9 = 36$ - For the four 16s: $(16 - 13)^2 = 9$; total = $4 \times 9 = 36$ $$\sum(x_i - \bar{x})^2 = 36 + 36 = 72$$ **Step 3: Calculate Variance.** $$\sigma^2 = \frac{72}{8} = 9$$ **Step 4: Calculate SD.** $$\sigma = \sqrt{9} = 3$$ So SD = **3** (Option C). The given `correct_option` 'b' (6) is incorrect. Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Apr 21Question 3171 of 473

All Questions

The standard deviation of $\displaystyle 10, 16, 10, 16, 10, 10, 16, 16$ is

Options

\displaystyle 4

\displaystyle 6

\displaystyle 3

\displaystyle 0

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle 3$

All Options:

A $\displaystyle 4$
B $\displaystyle 6$
C $\displaystyle 3$
D $\displaystyle 0$

Detailed Solution & Explanation

**Given data:** 10, 16, 10, 16, 10, 10, 16, 16;

\displaystyle n = 8

Count: Four 10s and four 16s. **Step 1: Calculate Mean.**

\bar{x} = \frac{4 \times 10 + 4 \times 16}{8} = \frac{40 + 64}{8} = \frac{104}{8} = 13

**Step 2: Calculate squared deviations.** - For the four 10s:

\displaystyle (10 - 13)^2 = 9

; total =

\displaystyle 4 \times 9 = 36

- For the four 16s:

\displaystyle (16 - 13)^2 = 9

; total =

\displaystyle 4 \times 9 = 36

\sum(x_i - \bar{x})^2 = 36 + 36 = 72

**Step 3: Calculate Variance.**

\sigma^2 = \frac{72}{8} = 9

**Step 4: Calculate SD.**

\sigma = \sqrt{9} = 3

So SD = **3** (Option C). The given `correct_option` 'b' (6) is incorrect. Hence, **Option C** 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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The standard deviation of 10,16,10,16,10,10,16,16\displaystyle 10, 16, 10, 16, 10, 10, 16, 1610,16,10,16,10,10,16,16 is