The mean of two samples of sizes 200 and 300 were found to be 25, 10 respectively. Their standard deviations were 3 and 4 respectively. The variance of combinedsample of size 500 is

Combined mean x¯=n1x¯1+n2x¯2n1+n2                            =200×25+300×10500=16  Let                        d1=x¯1−x¯=25−16=9   and                               d2=x¯2−x¯=10−16=−6Now we know that                             σ2=n1σ12+d12+n2σ22+d22n1+n2=200(9+81)+300(16+36)500=33600500=67.2