Question

The average of 17 numbers is 15. If the average of the first nine numbers is 14 and that of the last 9 numbers is 16, then the middle number is:
1. 15
2. 14
3. 17
4. 16

Answer 1

Correct Answer - Option 1 : 15

Given:

Average of 17 number is 15.

Average of first 9 numbers is 14.

Average of last 9 numbers is 16.

Formula Used:

Average = Sum of all observations/Total number of observations

Calculation:

For all observations,

15 = Sum of all 17 observations/17

⇒ Sum of all 17 observations = 15 × 17

⇒ Sum of all 17 observations = 255

For first 9 numbers,

14 = Sum of first 9 numbers/9

⇒ Sum of first 9 numbers = 14 × 9

⇒ Sum of first 9 numbers = 126

For last 9 numbers,

16 = Sum of last 9 numbers/9

⇒ Sum of last 9 numbers = 16 × 9

⇒ Sum of last 9 numbers = 144

Sum of first 9 number + Sum of last 9 number,

⇒ Sum of total 18 numbers

I.e. Middle number is added twice

For middle number,

⇒ Sum of 18 numbers – Sum of 17 numbers

⇒ (126 + 144) – 255

⇒ 270 – 255

⇒ 15

∴ The middle number is 15.