Let in a series $2 n$ observations, half of them are equal to $a$ and remaining half are equal to $- a$ . Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become $5$ ad $20$ , respectively. Then the value of $a^{2} + b^{2}$ is equal to

650

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425

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925

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250

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Solution

The correct option is B $425$
Given series is $a (n times), - a (n times)$
$¯ ¯ ¯ x = 0$
If $b$ is added to each of them, then the new mean is
$^{'} = ¯ ¯ ¯ x + b \Rightarrow b = 5$

Standard deviation deosn't change when same number is added to all, so
$\sqrt{\frac{n a^{2} + n a^{2}}{2 n} - 0} = 20 \Rightarrow a^{2} = 400 ∴ a^{2} + b^{2} = 425$

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Let in a series 2n observations, half of them are equal to a and remaining half are equal to −a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 ad 20, respectively. Then the value of a2+b2 is equal to

The correct option is B 425Given series is a(n times),−a(n times) ¯¯¯x=0 If b is added to each of them, then the new mean is ¯¯¯¯x′=¯¯¯x+b⇒b=5 Standard deviation deosn't change when same number is added to all, so √na2+na22n−0=20⇒a2=400∴a2+b2=425

Let in a series $2 n$ observations, half of them are equal to $a$ and remaining half are equal to $- a$ . Also by adding a constant $b$ in each of these observations, the mean and standard deviation of new set become $5$ ad $20$ , respectively. Then the value of $a^{2} + b^{2}$ is equal to