In the given question (ii), cant we use the formula ((n1-1)s1^2+(n2-1)s2^2)/(n1+n2-2)? On using the above formula, I got 62.05 which is nowhere close to the given answer. Q. 4) Two samples A and B of unequal sample size are taken from a population. The mean and variance are given in the table below for each of the two samples. The mean of the combined sample is also given. Sample size Sample mean Sample variance A Unknown 10 30 B Unknown 18 72 Combined 40 16 ? i) Find the sizes of the samples. (2) ii) Find the variance of the combined sample. (4) iii) Comment on answer in (ii) above by comparing with variances of the original samples.
Hi. The above formula is used for common variance(pooled/equal variance). In ques we are asked combined variance(i.e. variance of both samples) . . For eg: if we take 2 sample(X1,X2) from Normal distribution ,X1~N(7,4) & X2~N(5,4) They hav pooled variance(common) but their combined variance will be different
