Question

A distribution consist of three components with frequencies
w200, 250 and 300 having means of
25, 10 and 15 and standard deviations
3,4 and 5 respectively
Calculate
1 )the mean
2) the standard deriation​

Answer 1

Step-by-step explanation:

Given : First sample size(n1)=200, Second sample size(n2)=300

First mean (xˉ1)=25, Second mean (xˉ2)=10

S.D.(σ1)=3 and S.D.(σ2)=4

Combined mean, xˉ=500200×25+300×10=580=16

Let d1=x1ˉ−xˉ=25−16=9

and d2=x2ˉ−xˉ=10−16=−6

∴σ2=n1+n2n1(σ12+d