The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14^th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)

Question

Question

This question was previously asked in

SSC CGL 2020 Tier-I Official Paper 1 (Held On : 13 Aug 2021 Shift 1)

Answer 1

Given:

Average of 28 numbers = 77

Average of first 14 numbers = 74

Average of last 15 numbers = 84

Formula used:

Average = Sum of observations ÷ No of observations

Calculation:

Value of 14th number = (Sum of first 14 numbers + Sum of last 15 numbers) - Sum of 28 numbers

⇒ 14th Number = (14 × 74 + 15 × 84 - 28 × 77)

⇒ 1036 + 1260 - 2156 = 140

Average of remaining 27 numbers = (Sum of 28 numbers - 14th number) ÷ 27

⇒ (2156 - 140) ÷ 27 = 2016 ÷ 27

⇒ 74.66 or 74.7

∴ The required result = 74.7
Alternate Method

Average of 28 numbers = 77

Average of first 14 numbers = 74

Average of last 15 numbers = 84

Deviation on first 14 numbers = 74 - 77 = - 3 × 14 = - 42

Deviation on last 15 numbers = 84 - 77 = 7 × 15 = 105

14th number = 77 - 42 + 105 = 140

∴ Average of remaining 27 numbers = (28 × 77 - 140) ÷ 27 = 74.7