Question

If the random error in the arithmetic mean of 100 observations is x, then the random error in the arithmetic mean of 500 observations would be

5x
x/5
25x
x/25​

Answer 1

Given info : if the random error in the arithmetic mean of 100 observations is x

To find : then the random error in the arithmetic mean of 500 observations is..

Solution : concept : random error is inversely proportional to number of observations.

i.e., random error ∝ 1/ no of observations

So, x₁/x₂ = (no of observations)₂/(no of observations)₁

⇒x/x₂ = (500/100)

⇒x₂ = x/5

Therefore the random error in the arithmetic mean of 500 observations is x/5