The sum of squares of deviation from mean of 10 observations is 250. Mean of the data is 10. Find the coefficient of variation

Option c: 50%. Solution: Given: sum(xi - x-bar)^2 = 250, n = 10, x-bar = 10 Step 1: Calculate Variance. sigma^2 = 250/10 = 25 Step 2: Calculate SD. sigma = sqrt(25) = 5 Step 3: Calculate CV. CV = sigma/x-bar x 100 = 5/10 x 100 = 50% Hence, Option C is the correct answer.

Central Tendency & DispersionMTP March 21Question 3168 of 473

All Questions

The sum of squares of deviation from mean of $\displaystyle 10$ observations is $\displaystyle 250$ . Mean of the data is $\displaystyle 10$ . Find the coefficient of variation

Options

\displaystyle 10\%

\displaystyle 25\%

\displaystyle 50\%

\displaystyle 0\%

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Correct Answer

✅ Option c — $\displaystyle 50\%$

All Options:

A $\displaystyle 10\%$
B $\displaystyle 25\%$
C $\displaystyle 50\%$
D $\displaystyle 0\%$

Detailed Solution & Explanation

**Given:**

\displaystyle \sum(x_i - \bar{x})^2 = 250

\displaystyle n = 10

\displaystyle \bar{x} = 10

**Step 1: Calculate Variance.**

\sigma^2 = \frac{250}{10} = 25

**Step 2: Calculate SD.**

\sigma = \sqrt{25} = 5

**Step 3: Calculate CV.**

CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{5}{10} \times 100 = 50\%

Hence, **Option C** is the correct answer.

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The sum of squares of deviation from mean of 10\displaystyle 1010 observations is 250\displaystyle 250250. Mean of the data is 10\displaystyle 1010. Find the coefficient of variation