Question

1. The sum of deviations of 'n' observation
from 40 is (-20) and the sum of deviations
of the same 'n' observations from 35 is 30.
Then the arithmetic mean of these
observations is.
2013
1) 30 2) 35 3) 48 4) 38​

Answer 1

Answer:

38

Step-by-step explanation:

Given  

1. The sum of deviations of 'n' observation from 40 is (-20) and the sum of deviations of the same 'n' observations  

Let n be the number of observations.

Now ∑ (Xi – 40) = - 20

So ∑ Xi – 40 n = - 20----------1

Also

∑ (Xi – 35) = 30

So  ∑ Xi – 35 n = 30 -----------2

Now subtracting 1 and 2 we get

∑ Xi – 40 n = - 20

 ∑ Xi – 35 n = 30

Now – 5 n = - 50

Or n = 10

Substituting n = 10 in equation 1 we get

∑ Xi – 40 (10) = - 20

∑ Xi = - 20 + 400

∑ Xi = 380

Now mean = ∑ Xi / n

                  = 380 / 10

Mean = 38