Question

arithmatic mean of 10 observation is 60 and sum of square of deviation from 50 is 5000.what is standard deviation of observation .​

Answer 1

Given:

(i) The arithmetic mean of 10 obsrvation is 60

(ii) The sum of square of deviation from 50 is 5000.

To find:

(i) The standard deviation of observation .​

Solution:

Given, the mean of 10 observations is 60.

So, the expected value, that is E(X) is equal to 60.

E(X) = 60

Now,we try to find out the expected square value of the observations.

It is given that the sum of the square of deviation from 50 is 5000.

So, it is equal to 10 times of that of the expected squared deviations from 50.

Thus, we get the required value of expected square value of the observations as 4000.

Now, standard deviation =

√[(expected square value of the observations - E(X)²]

= √(4000-60²)

= √400

= 20

So, the standard deviation is 20.