Central Tendency & DispersionMTP Nov 20Question 3165 of 473
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What is the coefficient of variation of the following numbers 53,52,61,60,64\displaystyle 53, 52, 61, 60, 64

Options

A18.09\displaystyle 18.09
B8.09\displaystyle 8.09
C12.23\displaystyle 12.23
D15.45\displaystyle 15.45
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Correct Answer

✅ Option b — 8.09\displaystyle 8.09

All Options:

  • A18.09\displaystyle 18.09
  • B8.09\displaystyle 8.09
  • C12.23\displaystyle 12.23
  • D15.45\displaystyle 15.45

Detailed Solution & Explanation

**Given data:** 53, 52, 61, 60, 64; n=5\displaystyle n = 5 **Step 1: Calculate Mean.** xˉ=53+52+61+60+645=2905=58\bar{x} = \frac{53+52+61+60+64}{5} = \frac{290}{5} = 58 **Step 2: Calculate squared deviations.** xi(xi−58)(xi−58)253−52552−6366139602464636∑=110\begin{array}{|c|c|c|} \hline x_i & (x_i - 58) & (x_i - 58)^2 \\ \hline 53 & -5 & 25 \\ 52 & -6 & 36 \\ 61 & 3 & 9 \\ 60 & 2 & 4 \\ 64 & 6 & 36 \\ \hline & & \sum = 110 \\ \hline \end{array} **Step 3: Calculate Variance.** σ2=1105=22\sigma^2 = \frac{110}{5} = 22 **Step 4: Calculate SD.** σ=22≈4.690\sigma = \sqrt{22} \approx 4.690 **Step 5: Calculate CV.** CV=4.69058×100≈8.09%CV = \frac{4.690}{58} \times 100 \approx 8.09\% Hence, **Option B** is the correct answer.

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