Central Tendency & DispersionMTP Nov 19Question 3161 of 473
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If the values of all observations are equal then the Standard Deviation of the given observations is

Options

A0\displaystyle 0
B2\displaystyle 2
C1\displaystyle 1
DNone of these
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Correct Answer

✅ Option a — 0\displaystyle 0

All Options:

  • A0\displaystyle 0
  • B2\displaystyle 2
  • C1\displaystyle 1
  • DNone of these

Detailed Solution & Explanation

**Concept:** If all observations are equal (say, each = c\displaystyle c), then: - Mean xˉ=c\displaystyle \bar{x} = c - Each deviation (xi−xˉ)=c−c=0\displaystyle (x_i - \bar{x}) = c - c = 0 - Variance =∑(xi−xˉ)2n=0\displaystyle = \frac{\sum(x_i - \bar{x})^2}{n} = 0 - SD =0=0\displaystyle = \sqrt{0} = 0 So the SD = **0**, which is **Option A**. The given `correct_option` is 'd' (None of these), but Option A clearly states 0, which IS the correct answer. Hence, **Option A** is the correct answer.

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