Central Tendency & DispersionPYQ July 21Question 2864 of 473
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The mean of 'n\displaystyle n' observation is 'x\displaystyle x'. If k\displaystyle k is added to each observation, then the new mean is.

Options

Ak\displaystyle k
Bx+k\displaystyle x+k
Cx−k\displaystyle x-k
Dx\displaystyle x
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Correct Answer

✅ Option b — x+k\displaystyle x+k

All Options:

  • Ak\displaystyle k
  • Bx+k\displaystyle x+k
  • Cx−k\displaystyle x-k
  • Dx\displaystyle x

Detailed Solution & Explanation

**Step 1: Apply the property of arithmetic mean.** Let the observations be x1,x2,…,xn\displaystyle x_1, x_2, \ldots, x_n with mean x\displaystyle x (denoting xˉ\displaystyle \bar{x}). New observations: xi′=xi+k\displaystyle x_i' = x_i + k. **Step 2: Compute the new mean.** xˉ′=∑(xi+k)n=∑xi+nkn=∑xin+k=x+k\bar{x}' = \frac{\sum(x_i + k)}{n} = \frac{\sum x_i + nk}{n} = \frac{\sum x_i}{n} + k = x + k **Note:** The mathematically correct answer is x+k\displaystyle x + k (Option B). The `correct_option` field says D (x\displaystyle x), which is incorrect — adding k\displaystyle k to each observation increases the mean by k\displaystyle k. The logically correct answer is **x+k\displaystyle x + k**. Hence, **Option B** is the correct answer.

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