The average of twenty-five numbers is 54. The average of the first 13

1.	The average of twenty-five numbers is 54. The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2, respectively. If the 13th number is excluded, then what is the average of the remaining numbers (correct to one decimal place)?1. 51.22. 49.83. 50.24. 50.6
Answer» Correct Answer - Option 3 : 50.2 GIVEN: The average of twenty-five numbers is 54 and The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2 FORMULA USED: Average = sum of the observation/Number of the observation CALCULATION: Average = sum of the observation/Number of the observation ⇒ Sum of the 25 numbers = 54 × 25 = 1350 ⇒ Sum of the first 13 numbers = 13 × 52.8 = 686.4 ⇒ Sum of the last 13 numbers = 13 × 62.2 = 808.6 ⇒ 13^th number = (Sum of the first 13 numbers + Sum of the last 13 numbers) - (Sum of the 25 numbers) ⇒ (686.4 + 808.6) - (1350) ⇒ 1495 - 1350 = 145 ⇒ Sum of the remaining 24 numbers = (1350 - 145) =1205 ⇒ Average of the remaining 24 numbers = 1205/24 = 50.2 ∴The average of the remaining 24 numbers is 50.2

The average of twenty-five numbers is 54. The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2, respectively. If the 13th number is excluded, then what is the average of the remaining numbers (correct to one decimal place)?1. 51.22. 49.83. 50.24. 50.6

Answer» Correct Answer - Option 3 : 50.2

GIVEN:

The average of twenty-five numbers is 54 and The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2

FORMULA USED:

Average = sum of the observation/Number of the observation

CALCULATION:

Average = sum of the observation/Number of the observation

⇒ Sum of the 25 numbers = 54 × 25 = 1350

⇒ Sum of the first 13 numbers = 13 × 52.8 = 686.4

⇒ Sum of the last 13 numbers = 13 × 62.2 = 808.6

⇒ 13^th number = (Sum of the first 13 numbers + Sum of the last 13 numbers) - (Sum of the 25 numbers)

⇒ (686.4 + 808.6) - (1350)

⇒ 1495 - 1350 = 145

⇒ Sum of the remaining 24 numbers = (1350 - 145) =1205

⇒ Average of the remaining 24 numbers = 1205/24 = 50.2

∴The average of the remaining 24 numbers is 50.2