The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value if discarded number is
A. 98
B. 99
C. 100
D. 101
Answers
Given: The mean of a set of seven numbers is 81
Total number of observations = 7
Mean = sum of all the observations/total number of observations
81 = sum of seven number/7
Sum of seven numbers = 81 × 7
Sum of seven numbers = 567
Also, new mean = sum of all the observations/total number of observations
78 = sum of six number/6
sum of six number = 78 × 6
sum of six number = 468
Discarded number = Sum of seven numbers - Sum of six numbers
= 567 - 468
= 99
Hence, the value of discarded number is 99
Option (B) 99 is correct.
Extra information :
Mean:
The mean of a number of observations is the sum of the values of all the observations divided by the total number of observations.
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Given:
- The mean of a set of seven numbers is 81
- Total number of observations = 7
we know that formula
Mean = sum of all the observations/total number of observations
81 = sum of seven number/7
Sum of seven numbers = 81 × 7
Sum of seven numbers = 567
Also, new mean = sum of all the observations/total number of observations
78 = sum of six number/6
sum of six number = 78 × 6
sum of six number = 468
Now,
Discarded number = Sum of seven numbers - Sum of six numbers
= 567 - 468
= 99
Hence, the value of discarded number is 99
Option (B) 99