Question

The mean of 10 number is 14. Three of the number have a mean of 4. The remaining seven number are 15,18,5,m,34and 14. Find
I) the sum of the remaining seven number,
ii) the value of m

Answer 1

Complete Question :-

The mean of 10 number is 14. Three of the number have a mean of 4. The remaining seven number are 15, 18, 5, m, 34, 21 and 14. Find :

i) the sum of the remaining seven number

ii) the value of m

Answer :-

i) Sum of remaining 7 numbers is 128

ii) Value of m is 21

Explanation :-

i)

Mean of 10 numbers = 14

Number of observations = 10

We know that

Mean = Sum of observations/Number of observations

So Sum of 10 numbers = Mean * Number of observations = 14 * 10 = 140

Mean of three numbers = 4

Number of observations = 3

So sum of 3 numbers = Mean * Number of observations = 4 * 3 = 12

Sum of remaining 7 numbers = Sum of 10 numbers - Sum of 3 numbers = 140 - 12 = 128

ii)

Given

Remaining 7 numbers are 15, 18, 5, m, 34, 14

Sum of remaining 7 numbers = 128

⇒ 15 + 18 + 5 + m + 34 + 14 + 21 = 128

⇒ 107 + m = 128

⇒ m = 128 - 107

⇒ m = 21