Question

if the random error in the arithmetic mean of 50 observations is x then random error in the arithmetic mean of 150 observations would be???

Answer 1

Random error in the arithmetic mean of 150 observations would be $\bold{\frac{x}{1.5}}$.

Solution:

Random error in arithmetic means can be described as it is difficult to predict. It occurs in large number of data and takes long time to figure out.

Let us assume that random error in 100 observations = x  

Random error in 150 observations = if observations increased by 'n' times.

Then random error decreases by $\frac{1}{n}$ times.

Therefore, the random error $\bold{=\frac{x}{1.5}}$.