If the Standard Deviation of 10 observations is 4 and if each item is divided by -2 then Standard Deviation of new series is

Option a: 2. Solution: Given: SD of original series = 4. Each item is divided by -2 (i.e., multiplied by -1/2 ). Property: When each observation is multiplied by a constant k : SDnew = |k| × SDold Here k = -1/2 , so |k| = 1/2 : SDnew = 1/2 × 4 = 2 Note: SD is always non-negative, so even though we divide by -2 , the new SD is +2 , not -2 . Hence, Option A is the correct answer.

If the Standard Deviation of $10$ observations is $4$ and if each item is divided by $-2$ then Standard Deviation of new series is

The correct answer is Option a: $2$. **Given:** SD of original series = 4. Each item is divided by $-2$ (i.e., multiplied by $-\frac{1}{2}$). **Property:** When each observation is multiplied by a constant $k$: $$SD_{new} = |k| \times SD_{old}$$ Here $k = -\frac{1}{2}$, so $|k| = \frac{1}{2}$: $$SD_{new} = \frac{1}{2} \times 4 = 2$$ **Note:** SD is always non-negative, so even though we divide by $-2$, the new SD is $+2$, not $-2$. Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 3209 of 473

All Questions

If the Standard Deviation of $\displaystyle 10$ observations is $\displaystyle 4$ and if each item is divided by $\displaystyle -2$ then Standard Deviation of new series is

Options

\displaystyle 2

\displaystyle -2

\displaystyle 4

DNone of these

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Correct Answer

✅ Option a — $\displaystyle 2$

All Options:

A $\displaystyle 2$
B $\displaystyle -2$
C $\displaystyle 4$
DNone of these

Detailed Solution & Explanation

**Given:** SD of original series = 4. Each item is divided by

\displaystyle -2

(i.e., multiplied by

\displaystyle -\frac{1}{2}

). **Property:** When each observation is multiplied by a constant

\displaystyle k

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

Here

\displaystyle k = -\frac{1}{2}

, so

\displaystyle |k| = \frac{1}{2}

SD_{new} = \frac{1}{2} \times 4 = 2

**Note:** SD is always non-negative, so even though we divide by

\displaystyle -2

, the new SD is

\displaystyle +2

, not

\displaystyle -2

. 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 10\displaystyle 1010 observations is 4\displaystyle 44 and if each item is divided by −2\displaystyle -2−2 then Standard Deviation of new series is