Central Tendency & DispersionPYQ May 18Question 2854 of 473

If each item is reduced by 15 A. M is

AReduced by 15

BIncreased by 15

CReduced by 10

DNone of these

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Correct Answer

✅ Option a — Reduced by 15

**Step 1: Recall the effect of subtracting a constant from each observation.** Let the original observations be

\displaystyle x_1, x_2, \ldots, x_n

with mean

\displaystyle \bar{x}

. New observations:

\displaystyle x_i' = x_i - 15

for each

\displaystyle i

. **Step 2: Compute the new mean.**

\bar{x}' = \frac{\sum (x_i - 15)}{n} = \frac{\sum x_i}{n} - 15 = \bar{x} - 15

**Step 3: Conclusion.** The new A.M. is

\displaystyle \bar{x} - 15

, i.e., reduced by 15. Hence, **Option A** is the correct answer.

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