Paragraph : The mean and standard deviation of 100 items are 50, 5 and that of 150 items are 40, 6 respectively. Question : What is the combined standard deviation of all 250 items?

Step-by-step solution

Here, aligned & n₁=100, x ₁=50, ₁=5 & n₂=150, x ₂=40, ₂=6 aligned Combined SD = ₁₂= n₁ ( ₁^2+ D ₁^2 )+n₂ ( ₂^2+ D ₂^2 ) n₁+n₂ aligned ₁₂ & = 100 [5^2+(50-44)^2 ]+ 150 [6^2+(40-44)^2 ] 100+150 & = 100[25+36]+150(36+16) 250 aligned [ array l D ₁= ( x ₁- x ₁₂ ) D ₂= ( x ₂- x ₁₂ ) array ] aligned & = 100 61+150 52 250 & = 6100+7800 250 = 13900 250 & = 1390 25 = 55.6 =7.45 7.5 aligned Hence, combined standard deviation of 250 items =7.5 .