Multiple choice

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

  1. 32 and 2

  2. 32 and 4

  3. 28 and 2

  4. 28 and 4
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A Correct answer
Explanation

Adding a constant to every value in a dataset increases the mean by that constant but does not change the standard deviation. Thus, the new mean is 30 + 2 = 32, and the standard deviation remains 2.

AI explanation

When a constant value is added to every observation in a dataset, the mean increases by that exact constant, but the standard deviation remains completely unaffected. Correcting the 2 g under-reporting means adding 2 g to the mean weight of 30 g, which makes the correct mean 32 g. The original spread of the data does not change, leaving the standard deviation at 2 g. The correct mean and standard deviation are 32 and 2, respectively.

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