Question

the mean and SD for a group of 100 obsevations are 65 and 70.3 respectively. if 60 of these observations have mean and SD 70 and 3 respectively, what is the SD for the group of 40 observations ​

Answer 1

Step-by-step explanation:

Method to Solve :

Total of 100 observations is (65)(100) = 6500

Total of 60 observations = (70)(60) = 4200

Total of 40 observations = 6500-4200 = 2300

mean of 40 observations = 2300/40 = 57.5

Let SSQ represent the sum of squared deviation from the mean

SSQ100 = (n-1) s^2 = (99)(7.03)^2 = 4892.6691

SSQ60 = (n1-1) s1^2 = (59)(3)^2 = 531

SSQ40 = (n2-1) s2^2 = (39) s2^2

((n1-1)s1^2 +(n2-1)s2^2)/(n1+n2-1) = s^2

((59)(9) + (39) s2^2)/ (59+39) = (7.03)^2

(531 + 39 s2^2 ) / 98 = 49.4209

(531 + 39 s2^2 ) = 49.4209 (98)

(531 + 39 s2^2 ) = 4843.2482

39 s2^2 = 4312.2482

s2^2 = 110.5705

s2 = sqrt(110.5705) = 10.5153