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: SD{new} = |k| x SD{old} Here k = -1/2, so |k| = 1/2: SD{new} = 1/2 x 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.

Central Tendency & DispersionMTP 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.

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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