The sum of mean and SD of a series is a + b, if we add 2 to each observation of the series then the sum of mean and SD is:

Option a: a + b + 2. Solution: Given: Mean + SD = a + b. Let Mean = x-bar, SD = sigma so x-bar + sigma = a + b. After adding 2 to each observation: - New Mean = x-bar + 2 (increases by 2) - New SD = sigma (unchanged — SD is independent of origin shift) New sum: text{New Mean} + text{New SD} = (x-bar + 2) + sigma = (x-bar + sigma) + 2 = a + b + 2 Hence, Option A is the correct answer.

The sum of mean and SD of a series is $a + b$, if we add $2$ to each observation of the series then the sum of mean and SD is:

The correct answer is Option a: $a + b + 2$. **Given:** Mean + SD = $a + b$. Let Mean = $\bar{x}$, SD = $\sigma$ so $\bar{x} + \sigma = a + b$. **After adding 2 to each observation:** - New Mean = $\bar{x} + 2$ (increases by 2) - New SD = $\sigma$ (unchanged — SD is independent of origin shift) **New sum:** $$\text{New Mean} + \text{New SD} = (\bar{x} + 2) + \sigma = (\bar{x} + \sigma) + 2 = a + b + 2$$ Hence, **Option A** is the correct answer.

Central Tendency & DispersionMTP June 2023 Series IQuestion 3194 of 473

All Questions

The sum of mean and SD of a series is $\displaystyle a + b$ , if we add $\displaystyle 2$ to each observation of the series then the sum of mean and SD is:

Options

\displaystyle a + b + 2

\displaystyle 6 - a + b

\displaystyle 4 + a - b

\displaystyle a + b + 4

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

Correct Answer

✅ Option a — $\displaystyle a + b + 2$

All Options:

A $\displaystyle a + b + 2$
B $\displaystyle 6 - a + b$
C $\displaystyle 4 + a - b$
D $\displaystyle a + b + 4$

Detailed Solution & Explanation

**Given:** Mean + SD =

\displaystyle a + b

. Let Mean =

\displaystyle \bar{x}

, SD =

\displaystyle \sigma

\displaystyle \bar{x} + \sigma = a + b

. **After adding 2 to each observation:** - New Mean =

\displaystyle \bar{x} + 2

(increases by 2) - New SD =

\displaystyle \sigma

(unchanged — SD is independent of origin shift) **New sum:**

\text{New Mean} + \text{New SD} = (\bar{x} + 2) + \sigma = (\bar{x} + \sigma) + 2 = a + b + 2

Hence, **Option A** is the correct answer.

Ready to Master Central Tendency & Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

The sum of mean and SD of a series is a+b\displaystyle a + ba+b, if we add 2\displaystyle 22 to each observation of the series then the sum of mean and SD is: