The sum of the squares of deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

Question

The sum of the squares of deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is (A) 10% (B) 40% (C) 50% (D) 60%

Tardigrade Admin · Accepted Answer

Let, x i, i=1,2 ldots 10 be 10 observations We have displaystyle∑i=110(x i-50)2=250 Now σ2=(1/10) displaystyle∑i=110(x i-50)2 =(250/10)=25 σ=5 ∴ C . V=(σ/x) × 100 =(5/50) × 100=10 %

Q. The sum of the squares of deviations for $10$ observations taken from their mean $50$ is $250$ . The coefficient of variation is

10%

40%

50%

60%

Let, $x i, i = 1, 2 \dots 10$ be 10 observations
We have $i = 1 \sum 10 (x i - 50)^{2} = 250$
Now $σ^{2} = \frac{1}{10} i = 1 \sum 10 (x i - 50)^{2}$
$= \frac{250}{10} = 25 σ = 5$
$∴ C . V = \frac{σ}{x} \times 100$
$= \frac{5}{50} \times 100 = 10%$

Q. The sum of the squares of deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

10%

40%

50%

60%

Let, xi,i=1,2…10 be 10 observations We have i=1∑10​(xi−50)2=250 Now σ2=101​i=1∑10​(xi−50)2 =10250​=25σ=5 ∴C.V=xσ​×100 =505​×100=10%

Q. The sum of the squares of deviations for $10$ observations taken from their mean $50$ is $250$ . The coefficient of variation is

Let, $x i, i = 1, 2 \dots 10$ be 10 observations
We have $i = 1 \sum 10 (x i - 50)^{2} = 250$
Now $σ^{2} = \frac{1}{10} i = 1 \sum 10 (x i - 50)^{2}$
$= \frac{250}{10} = 25 σ = 5$
$∴ C . V = \frac{σ}{x} \times 100$
$= \frac{5}{50} \times 100 = 10%$