1
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Question

# The random error in the arithmetic mean of 100 observations of a physical quantity is x, then random error in the arithmetic mean of 400 observations of the same physical quantity will be

A
x4
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B
x2
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C
4x
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D
2x
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Solution

## The correct option is A x4Random error is due to any random causes in the measurement process. It can be reduced by repetitions and averaging of the observations. If more observations are taken then less random error can be found in arithmetic mean. ⇒ Random error ∝ 1/ Number of observations Hence, increasing the number of observations to 4 times will decrease the random error to 1/4 times the initial value. So, x4 will be the random error in 400 observations.

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