Central Tendency & DispersionPYQ Nov 18Question 3117 of 473
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Standard Deviation for the marks obtained by a student in monthly test in mathematic (out of 50\displaystyle 50) as 30,35,25,20,15\displaystyle 30, 35, 25, 20, 15 is

Options

A25\displaystyle \sqrt{25}
B50\displaystyle \sqrt{50}
C30\displaystyle \sqrt{30}
D10\displaystyle \sqrt{10}
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Correct Answer

✅ Option b — 50\displaystyle \sqrt{50}

All Options:

  • A25\displaystyle \sqrt{25}
  • B50\displaystyle \sqrt{50}
  • C30\displaystyle \sqrt{30}
  • D10\displaystyle \sqrt{10}

Detailed Solution & Explanation

We are given the marks: 30,35,25,20,15\displaystyle 30, 35, 25, 20, 15. The number of observations is n=5\displaystyle n = 5. 1. Calculate the arithmetic mean (xˉ\displaystyle \bar{x}): xˉ=30+35+25+20+155=1255=25\bar{x} = \frac{30 + 35 + 25 + 20 + 15}{5} = \frac{125}{5} = 25 2. Calculate the deviations from the mean (xi−xˉ)\displaystyle (x_i - \bar{x}) and their squares (xi−xˉ)2\displaystyle (x_i - \bar{x})^2: - 30−25=5  ⟹  25\displaystyle 30 - 25 = 5 \implies 25 - 35−25=10  ⟹  100\displaystyle 35 - 25 = 10 \implies 100 - 25−25=0  ⟹  0\displaystyle 25 - 25 = 0 \implies 0 - 20−25=−5  ⟹  25\displaystyle 20 - 25 = -5 \implies 25 - 15−25=−10  ⟹  100\displaystyle 15 - 25 = -10 \implies 100 3. Calculate the sum of squared deviations: ∑(xi−xˉ)2=25+100+0+25+100=250\sum (x_i - \bar{x})^2 = 25 + 100 + 0 + 25 + 100 = 250 4. Calculate variance (σ2\displaystyle \sigma^2) and Standard Deviation (σ\displaystyle \sigma): σ2=2505=50  ⟹  σ=50\sigma^2 = \frac{250}{5} = 50 \implies \sigma = \sqrt{50} Hence, **Option B** is the correct answer.

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