Assertion(A): For a distribution, if x_ i ^ 2 =232, x_ i =16 and … - Vidyadip

MCQ

Assertion(A): For a distribution, if $\Sigma x_{i}^{2}=232, \Sigma x_{i}=16$ and $n=8$, then standard deviation (S.D.) is 5 .
Reason(R): Standard deviation (S.D.) $=\sqrt{\frac{\Sigma x_{i}^{2}}{n}-\left(\frac{\Sigma x_{i}}{n}\right)^{2}}$.

✓
Both A and R are true and R is the correct explanation of A .
B
Both A and R are true but R is not the correct explanation of A .
C
A is true but R is false.
D
A is false but $R$ is true.

✓

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A .

(a) Both A and R are true and R is the correct explanation of A .
Explanation: Assertion (A): $\sum x_{i}^{2}=232$
$\sum x_{i}=16, \mathrm{x}=8$
Standard deviation $(\sigma)=\sqrt{\frac{\sum x_{i}^{2}}{n}-\left(\frac{\sum x_{i}}{n}\right)^{2}}$
$\sigma=\sqrt{\frac{232}{8}-\left(\frac{16}{8}\right)^{2}}$
$=\sqrt{29-4}$
$=\sqrt{25}$
$\sigma=5$
Hence, A is correct.
Reason (R): Standard deviation (S.D)
$=\sqrt{\frac{\sum x_{i}^{2}}{x}-\left(\frac{\sum x_{i}}{x}\right)^{2}}$
R is also true.
Hence, Both A and R are true and R is the correct explanation of A .

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