Answer to Question #301255 in Statistics and Probability for Tarurendra Kushwah

Question

There are three Groups A,B and C with no. of persons 50, X, 90. The mean and Standard deviations for these groups are 113, Y, 115 and 6, 7, Z respectively. The Combind n , mean and Standard deviation for three groups are 200,116 and 7.746.

(i) What is n ( The value of X ) for Group II .

(ii) Mean (Value of Y ) of Group II?

(iii) S.D. (Value of Z) of Group III ?

Answer 1

(i)

$$50+X+90=200$$

$$X=60$$

(ii)

$$\dfrac{50(113)+60Y+90(115)}{200}=116$$

$$6Y=2320-565-1035$$

$$Y=120$$

(iii)

$$(7.746)^2=\dfrac{50(6)^2+60(7)^2+90(Z)^2}{200}$$

$$+\dfrac{50(113-116)^2+60(120-116)^2+90(115-116)^2}{200}$$

$$90(Z)^2=5760.1032$$

$$Z=8$$