Central Tendency & DispersionPYQ Nov 18Question 2856 of 473

The mean of 20 items of a data is 5 & if each item is multiplied by 3, then the new mean will be

\displaystyle 5

\displaystyle 10

\displaystyle 15

\displaystyle 20

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Correct Answer

✅ Option c — $\displaystyle 15$

**Step 1: State the given information.** Number of items

\displaystyle n = 20

, Original mean

\displaystyle \bar{x} = 5

. **Step 2: Apply the property of mean under multiplication.** If each item

\displaystyle x_i

is multiplied by a constant

\displaystyle k

, the new mean becomes

\displaystyle k \cdot \bar{x}

. Here

\displaystyle k = 3

, so:

\text{New mean} = 3 \times \bar{x} = 3 \times 5 = 15

**Step 3: Verification.** Original sum

\displaystyle = n \times \bar{x} = 20 \times 5 = 100

. New sum

\displaystyle = 3 \times 100 = 300

. New mean

\displaystyle = \frac{300}{20} = 15

. ✓ Hence, **Option C** is the correct answer.

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