Measures of Central Tendency and DispersionMCQPYQ June 22Question 3136 of 473

Find the standard deviation and coefficient of variation for $\displaystyle 1, 9, 8, 7, 5$ .

Options

\displaystyle 2.828, 49.32

\displaystyle 2.828, 48.13

\displaystyle 2.828, 47.13

\displaystyle 2.828, 50.13

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Correct Answer

✅ Option c — $\displaystyle 2.828, 47.13$

All Options:

A $\displaystyle 2.828, 49.32$
B $\displaystyle 2.828, 48.13$
C $\displaystyle 2.828, 47.13$
D $\displaystyle 2.828, 50.13$

Detailed Solution & Explanation

**Given data:** 1, 9, 8, 7, 5;

\displaystyle n = 5

**Step 1: Calculate Mean.**

\bar{x} = \frac{1+9+8+7+5}{5} = \frac{30}{5} = 6

**Step 2: Calculate deviations squared.**

\begin{array}{|c|c|c|} \hline x_i & (x_i - \bar{x}) & (x_i - \bar{x})^2 \\ \hline 1 & -5 & 25 \\ 9 & 3 & 9 \\ 8 & 2 & 4 \\ 7 & 1 & 1 \\ 5 & -1 & 1 \\ \hline & & \sum = 40 \\ \hline \end{array}

**Step 3: Calculate Variance.**

\sigma^2 = \frac{\sum(x_i - \bar{x})^2}{n} = \frac{40}{5} = 8

**Step 4: Calculate SD.**

\sigma = \sqrt{8} = 2\sqrt{2} \approx 2.828

**Step 5: Calculate CV.**

CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{2.828}{6} \times 100 \approx 47.13\%

Wait — let me recheck:

\displaystyle 2.828 / 6 = 0.4713

, so

\displaystyle CV \approx 47.13\%

. However, if we use the exact value

\displaystyle \sigma = \sqrt{8} = 2.8284...

CV = \frac{2.8284}{6} \times 100 = 47.14\%

The closest option to this computation is **

\displaystyle 2.828, 47.13

** which is Option C. But the given `correct_option` is 'a' (

\displaystyle 2.828, 49.32

). Let me verify

\displaystyle 49.32

\displaystyle 49.32\% \Rightarrow \sigma = 49.32\times 6/100 = 2.959

, which doesn't match

\displaystyle \sigma = 2.828

. By direct computation, CV =

\displaystyle \frac{2.828}{6} \times 100 \approx 47.13\%

. So Option C (

\displaystyle 2.828, 47.13

) is mathematically correct. 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.

Related Comparison Tables

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Find the standard deviation and coefficient of variation for 1,9,8,7,5\displaystyle 1, 9, 8, 7, 51,9,8,7,5.