JAMIA 2024 — Mathematics PYQ

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Question

JAMIA 2024 — Mathematics PYQ

JAMIA | Mathematics | 2024

If the coefficient of variation is 100, the mean of the data is 25, then find the standard deviation

Choose the correct answer:

Explanation

Given Data

Coefficient of Variation ( $CV$ ) = $100$
Mean ( $\bar{x}$ ) = $25$

Step 1: Formula for Coefficient of Variation

The formula relating $CV$ , standard deviation ( $\sigma$ ), and mean ( $\bar{x}$ ) is:

CV = \left( \frac{\sigma}{\bar{x}} \right) \times 100

Step 2: Substitute the Values

Substitute the given values into the formula:

100 = \left( \frac{\sigma}{25} \right) \times 100

Step 3: Solve for Standard Deviation ( $\sigma$ )

Divide both sides by $100$ :

1 = \frac{\sigma}{25}

Now, multiply both sides by $25$ :

\sigma = 1 \times 25

\sigma = 25

Final Answer

The standard deviation of the data is:

25