If the Standard Deviation of data 2, 4, 5, 6, 8, 17 is 4.47 , then Standard Deviation of the data 4, 8, 10, 12, 16, 34 is

Option a: 8.94. Solution: Given: SD of 2, 4, 5, 6, 8, 17 = 4.47 Observation: The second dataset 4, 8, 10, 12, 16, 34 is obtained by multiplying each element of the first dataset by 2: 4 = 2 × 2, 8 = 2 × 4, 10 = 2 × 5, 12 = 2 × 6, 16 = 2 × 8, 34 = 2 × 17 Key Property: When every observation is multiplied by a constant k , the SD also gets multiplied by |k| : SDnew = |k| × SDold Step 1: Here k = 2 . SDnew = 2 × 4.47 = 8.94 Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Jun 23Question 3142 of 473

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If the Standard Deviation of data $\displaystyle 2, 4, 5, 6, 8, 17$ is $\displaystyle 4.47$ , then Standard Deviation of the data $\displaystyle 4, 8, 10, 12, 16, 34$ is

Options

\displaystyle 8.94

\displaystyle 2.24

\displaystyle 13.41

\displaystyle 1.24

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Correct Answer

✅ Option a — $\displaystyle 8.94$

All Options:

A $\displaystyle 8.94$
B $\displaystyle 2.24$
C $\displaystyle 13.41$
D $\displaystyle 1.24$

Detailed Solution & Explanation

**Given:** SD of

\displaystyle \{2, 4, 5, 6, 8, 17\} = 4.47

**Observation:** The second dataset

\displaystyle \{4, 8, 10, 12, 16, 34\}

is obtained by multiplying each element of the first dataset by 2:

4 = 2 \times 2, \quad 8 = 2 \times 4, \quad 10 = 2 \times 5, \quad 12 = 2 \times 6, \quad 16 = 2 \times 8, \quad 34 = 2 \times 17

**Key Property:** When every observation is multiplied by a constant

\displaystyle k

, the SD also gets multiplied by

\displaystyle |k|

SD_{new} = |k| \times SD_{old}

**Step 1:** Here

\displaystyle k = 2

SD_{new} = 2 \times 4.47 = 8.94

Hence, **Option A** 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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If the Standard Deviation of data 2,4,5,6,8,17\displaystyle 2, 4, 5, 6, 8, 172,4,5,6,8,17 is 4.47\displaystyle 4.474.47, then Standard Deviation of the data 4,8,10,12,16,34\displaystyle 4, 8, 10, 12, 16, 344,8,10,12,16,34 is