Question

A survey asked a group of medical doctors how many children they had fathered. The results are summarized by this ungrouped frequency distribution.

Number of Children	0	1	2	3	4	6
Number of Doctors	16	22	15	16	4	6

(a) Calculate the sample mean for the number of children the doctors had fathered. (Give your answer correct to two decimal places.)


(b) Calculate the variance for the number of children the doctors had fathered using the short-cut formula and verify it with your graphing calculator. (Give your answer correct to two decimal places.)


(c) Calculate the standard deviation for the number of children the doctors had fathered. (Give your answer correct to two decimal places.)

Answer 1

Ta Sample Man can be Calculated stort by the following formula i re är { titi Here x denotes the number of children fi denotes the frequency of doctors is a as shown below Number of children Number of f. Xi doctors - 16 22 of we o 36 Ef = 79 EfX; = 152)

we know fix = 152 i si Sample Mean = {fixi Efi 79 = 12 = 192 ③ Variance = 82 = ² (x; _ x)² + n -1 79 in-1=178) where n = {f 0 16 1-12 -1.92 3.6864 58.9824 22 1-92 -0.92 0.846418.6208 2 15 1.92 0.08 0.0064 0.096 16 1-92 109 17.28 1.1664 4 1.92 2.08 T 4.3 264 17.3056 6 1.92 4.08 16.6464/99,8784 {{x; -x) + = 212.162 $x; -*]24 = 21201632 s² = {(x; -x)²f = 212-1632 = 2.72 n Variance (2.72 78

standard deviation 2 W Variance S2N232 S = 1.65