A scientist is weighing each of $30$ fishes. Their mean weight worked out is $30 g$ and a standard deviation is $2 g$ . Later, it was found that the measuring scale was misaligned and always under-reported every fish weight by $2 g$ . Find the correct mean and standard deviation (in gram) of fishes.

$28, 4$

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$32, 2$

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$32, 4$

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$28, 2$

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Solution

The correct option is B
$32, 2$

Explanation for the correct option:
Given Data:
Mean weight of fishes $= 30 g m$
Standard deviation $= 2 g m$
According to question,
Every fish weight is increased by $2 g m$
Therefore, over all mean weight is increased by $30 + 2 = 32 g m$
Standard deviation is not effected by the addition of a constant.
Thus, standard deviation will remain same.
Hence, Option ‘B’ is Correct.

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A scientist is weighing each of 30 fishes. Their mean weight worked out is 30g and a standard deviation is 2g. Later, it was found that the measuring scale was misaligned and always under-reported every fish weight by 2g. Find the correct mean and standard deviation (in gram) of fishes.