Central Tendency & DispersionPYQ June 24Question 3141 of 473
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In a given set if all data are of same value then variance would be:

Options

A0\displaystyle 0
B1\displaystyle 1
C−1\displaystyle -1
D0.5\displaystyle 0.5
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Correct Answer

✅ Option a — 0\displaystyle 0

All Options:

  • A0\displaystyle 0
  • B1\displaystyle 1
  • C−1\displaystyle -1
  • D0.5\displaystyle 0.5

Detailed Solution & Explanation

**Concept:** Variance measures the average squared deviation from the mean. Variance=∑i=1n(xi−xˉ)2n\text{Variance} = \frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n} **If all data values are the same:** Let every xi=c\displaystyle x_i = c (a constant). **Step 1:** Calculate the mean. xˉ=ncn=c\bar{x} = \frac{nc}{n} = c **Step 2:** Calculate each deviation. xi−xˉ=c−c=0for all ix_i - \bar{x} = c - c = 0 \quad \text{for all } i **Step 3:** Calculate variance. Variance=∑i=1n(0)2n=0n=0\text{Variance} = \frac{\sum_{i=1}^{n}(0)^2}{n} = \frac{0}{n} = 0 When all observations are identical, there is no spread/variability, so the variance = **0**. Hence, **Option A** is the correct answer.

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