Central Tendency & DispersionMTP May 18Question 3157 of 473
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The standard deviation of 25,32,43,53,62,59,48,31,24,33\displaystyle 25, 32, 43, 53, 62, 59, 48, 31, 24, 33 is

Options

A13.23\displaystyle 13.23
B12.33\displaystyle 12.33
C11.33\displaystyle 11.33
DNone of these
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Correct Answer

✅ Option a — 13.23\displaystyle 13.23

All Options:

  • A13.23\displaystyle 13.23
  • B12.33\displaystyle 12.33
  • C11.33\displaystyle 11.33
  • DNone of these

Detailed Solution & Explanation

**Given data:** 25, 32, 43, 53, 62, 59, 48, 31, 24, 33; n=10\displaystyle n = 10 **Step 1: Calculate Mean.** xˉ=25+32+43+53+62+59+48+31+24+3310=41010=41\bar{x} = \frac{25+32+43+53+62+59+48+31+24+33}{10} = \frac{410}{10} = 41 **Step 2: Calculate squared deviations.** xi(xi−41)(xi−41)225−1625632−98143245312144622144159183244874931−1010024−1728933−864∑=1752\begin{array}{|c|c|c|} \hline x_i & (x_i - 41) & (x_i - 41)^2 \\ \hline 25 & -16 & 256 \\ 32 & -9 & 81 \\ 43 & 2 & 4 \\ 53 & 12 & 144 \\ 62 & 21 & 441 \\ 59 & 18 & 324 \\ 48 & 7 & 49 \\ 31 & -10 & 100 \\ 24 & -17 & 289 \\ 33 & -8 & 64 \\ \hline & & \sum = 1752 \\ \hline \end{array} **Step 3: Calculate Variance.** σ2=175210=175.2\sigma^2 = \frac{1752}{10} = 175.2 **Step 4: Calculate SD.** σ=175.2≈13.23\sigma = \sqrt{175.2} \approx 13.23 So Option A (13.23) is the correct answer, not Option C (11.33). Hence, **Option A** is the correct answer.

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