Measure Of Dispersion

Question

If two samples of sizes 30 and 20 have means as 55 and 60 and variances as 16 and 25 respectively, then what would be the SD of the combined sample of size 50?

Answer 1

Two samples of sizes n₁= 30 and n₂ = 20 have means as 55 and 60 and variances as \(S_{1}^2\)= 16 and \(S_{2}^2\) = 25 respectively

To Find: S.D. of the combined sample of size 50

Solution:

\(x = {\sqrt{n_{1}S_{1}^2 +n_{2}S_{2}^2 \over n_{1}+n_{2}}}\)

   =\( {\sqrt{30*16 +20*25 \over 30+20}}\)

= \( { \sqrt{480+500} \over 50}\)

\(={ \sqrt{980 \over 50}}\)

\(={ \sqrt19.6}\)

= 4.43