Chapter 14: Statistics and Probability

(D) 38

Explanation:

Let a,b,c,d and e are five numbers

Average of a data = sum of total observations / total number of observations

According to the question,

Mean = 30

(a +b+ c+ d+e)/5 = 30

⇒ (a +b+ c+ d+e) = 150 …(1)

Let the number excluded be a

Then,

New mean = (b+ c+ d+e)/4 = 28

⇒ (b+ c+ d+e) = 112

Substituting this in equation (1),

⇒a + 112 = 150

⇒ a = 150 – 112

= 38

Therefore, excluded number = 38

Hence, option (D) is the correct answer.

(C)

Explanation:

We know that,

Average of a data = sum of total observations / total number of observations

According to the question

(x + x+3 + x+5 + x+7 + x+10)/5 = 9

(5x +15)/5 = 9

x + 3 = 9

x = 6

Now, the terms become

6, 6 + 3, 6 + 5, 6 + 7, 6 + 10 = 6, 9, 11, 13, 16

So, the mean of the last three observations = ( 11 + 13 + 16)/3

= 40/3

=

Hence, option (C) is the correct answer.