(A) Given observations are = 4, 6, x, 8, 10, 13

Mean =

Now, given mean = 8

Sum of the observations = 4 + 6 + x + 8 + 10 + 13 = 8 × 6

⇒ 41 + x = 48

∴ x = 48 – 41 = 7

So, x = 7

The given statement is true.

(B) Given array = 59, 62, 65, x, x + 2, 72, 85, 99

n = 8 (even)

Median = 1/2 [value of (n/2)th term + value of (n/2 + 1)th term]

= 1/2 [value of 4th term + value of 5th term]

Median =

Given median = 67

67 = 2x + 2 = 67 × 2

2x + 2 = 134

2x = 134 – 2

X = = 66

So, x = 66

The given statement is true

(C) Given,

Observations are = 1, 3, 5, 7, 5, 2, 7, 5, 9, 3, p, 11

Mode = 5

Value of p = 7

We know that mode is the item which has highest frequency and in given statement 5 is the mode. If p = 7 then it will become the number with highest frequency. It means p can’t be equals to 7 as mode is 5.

So, the given statement is false.

(D) Given;

Mean of 10 observations = 15

Mean of 15 observations = 18

Mean of all 25 observation = 16.8

Now the sum of the observations;

Sum of 10 observations = 10 × 15 = 150

Sum of 15 observation = 15 × 18 = 270

Sum of 25 observation = Sum of 10 observations + Sum of 15 observations

Mean of 25 observations =

⇒ Mean =

⇒ Mean = 420/25

∴Mean = 16.8

So, the given statement is true.