Correct Answer - Option 1 : 31
Given:
The average of 8 consecutive even numbers in ascending order = 17
Formula used:
Sum of the observations/Number of observations
Calculation:
Let the 8 consecutive even numbers be (2a – 6), (2a – 4), (2a – 2), 2a, (2a +2), (2a + 4), (2a + 6) and (2a + 8)
Sum of 8 consecutive even numbers = (2a – 6) + (2a – 4) + (2a – 2) + 2a, (2a +2) + (2a + 4) + (2a + 6) + (2a + 8)
⇒ 16a + (-12 +20)
⇒ 16a + 8
Average sum of 8 consecutive even numbers = (16a + 8)/8 = 17
⇒ 8(2a + 1)/8 = 17
⇒ 2a + 1 = 17
⇒ 2a = (17 – 1)
⇒ 2a = 16
Now, putting the value in last three three numbers
⇒ (2a + 4) = (16 + 4) = 20
⇒ (2a + 6) = (16 + 6) = 22
⇒ (2a + 8) = (16 + 8) = 24
Again,
Sum of last three numbers, 36 and 53 = (20 + 22 + 24 + 36 + 53)
⇒ 155
Average of sum of last three numbers, 36 and 53 = (155/5)
⇒ 31
∴ The average of the last three numbers, 36 and 53 is 31