For a normal distribution, which of the following is true?

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SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. mean ≠ median = mode
  2. mean = median = mode
  3. mean = median ≠ mode
  4. mean = mode ≠ mode

Answer (Detailed Solution Below)

Option 2 : mean = median = mode
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Detailed Solution

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Calculation

Normal distributiln = A normal distribution comes with a perfectly symmetrical shape that means distribution curve can divided in the middle to produce two equal halves.

F2 Vishal.S 21-05-21 Savita D1

The normal distribution function is denotted by

\(f\left( x \right) = \frac{1}{{\sigma \sqrt {2\pi } }}{e^{ - \frac{1}{2}}}{\left( {\frac{{x - \mu }}{\sigma }} \right)^2}\)

f(x) = Probability density function

σ = Standard deviation

μ = Mean

In normal distribution the symmetry about the center and in it the mean = medan = mode = μ

∴ The mean = medan = mode = μ in normal distribution

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