Question

If the random error in the arithmetic mean of 50 observations is a, then the random error in the mean of 150 observations would be
1.a
2.3a
3.a/3
4.2a
​

Answer 1

Answer:

$\boxed{\mathfrak{3. \ \dfrac{a}{3}}}$

Explanation:

On increasing the no. of observations n times, the random error reduces to $\sf \dfrac{1}{n}$ times.

So, if no. of observations are increased fro 50 to 150;

$\rm n = \dfrac{150}{50} \\ \\ \rm n = 3$

Random error in the arithmetic mean of 50 observation = a

Random error becomes $\sf \dfrac{1}{n}$ times.

$\therefore$ Random error in the mean of 150 observation = $\sf \dfrac{a}{3}$ times

Answer 2

Explanation:

Given : -

• If the random error in the arithmetic mean of 50 observations

To Find : -

• e random error in the mean of 150 observations would be

Solution : -

The n random error is = a/n

substitute all values :

then the random error in the mean of 150

= 150 / 50

= 3

the mean of 150 observations would be

= a / 3

Option ( 3 .) is correct !