Question

Let, the coefficient of variation of two datasets be \(50 \) and \(75\) ,respectively and the corresponding variances be \(25\) and \(36\),respectively.Also let \(x_1\) and \(x_2\) denote the corresponding sample means. Then \(x_1+x_2\) is ?

• A. \(2\)
• B. \(10\)
• C. \(18\)
• D. \(16\)
• E. \(20\)

Answer 1

The Correct Option is C

Given:

• Dataset 1: Coefficient of variation (CV) = 50, Variance = 25
• Dataset 2: Coefficient of variation (CV) = 75, Variance = 36
• Let \( \bar{x}_1 \) and \( \bar{x}_2 \) be the sample means

Step 1: Recall the formula for coefficient of variation: \[ CV = \left( \frac{\sigma}{\bar{x}} \right) \times 100 \] where \( \sigma \) is the standard deviation.

Step 2: For Dataset 1: \[ 50 = \left( \frac{\sqrt{25}}{\bar{x}_1} \right) \times 100 \implies 50 = \left( \frac{5}{\bar{x}_1} \right) \times 100 \] \[ \frac{5}{\bar{x}_1} = 0.5 \implies \bar{x}_1 = 10 \]

Step 3: For Dataset 2: \[ 75 = \left( \frac{\sqrt{36}}{\bar{x}_2} \right) \times 100 \implies 75 = \left( \frac{6}{\bar{x}_2} \right) \times 100 \] \[ \frac{6}{\bar{x}_2} = 0.75 \implies \bar{x}_2 = 8 \]

Step 4: Calculate the sum of means: \[ \bar{x}_1 + \bar{x}_2 = 10 + 8 = 18 \]

The value of \( \bar{x}_1 + \bar{x}_2 \) is 18.

Answer 2

Given

Let, the Co-efficient of variation of  1st data = \(CV_1=50\)

Let, the Co-efficient of variation of  2nd data = \(CV_2=75\)

and Variance \((σ_1^{2})=25\) . So, \(σ_1=5\)

        Variance \((σ_2^{2})=36\) . So, \(σ_1=6\)

We know that,

\(CV_1=\dfrac{σ_1}{x_1} × 100\)

\(⇒ x_1=\dfrac{5}{CV_1} × 100\)

\(⇒ x_1=\dfrac{5}{50} × 100\)

\(⇒ x_1=10\)

Similarly solving for 2nd data we get

\(⇒x_2=8\)

Hence , \(x_1+x_2=10+8=18\) (_Ans.)