Solution:
(a)Given observations are 6, y, 7, x, 14.
Mean = 8
Number of observations = 5
Mean = Sum of observations/number of observations
8 = (6+y+7+x+14)/5
40 = 27+x+y
40-27 = x+y
13 = x+y
y = 13-x
Hence the answer is y = 13-x.
(b)Given mean = 11
Number of variates = 9
Variates are 7, 12, 9, 14, 21, 3, 8 ,15
Let the 9th variate be x.
Sum of variates = 7+12+9+14+21+3+8+15+x
= 89+x
Mean = Sum of variates/number of variates
11 = (89+x)/9
11×9 = 89+x
99 = 89+x
x = 99-89 = 10
Hence the 9th variate is 10.