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The average of ten numbers is 7. If 21 is added to each number, then the average of the new set of numbers will be:
19
31
28
7
28
When a constant value k is added to every observation in a data set, the mean (average) of the new data set increases by exactly k.
Average of 10 numbers = 7, and 21 is added to each of these numbers.
AveragenewтАЛ=AverageoldтАЛ+k
When a constant value k is added to every observation in a data set, the mean (average) of the new data set increases by exactly k.
Students often try to calculate the sum of 10 numbers, add 21 to each individually, find the new total, and then divide by 10, which is time-consuming and prone to calculation errors.
Identify initial state
We are given that the average of 10 numbers is 7.
AverageoldтАЛ=7
Apply transformation rule
Adding a constant k=21 to every number in the set increases the overall average by that same constant.
AveragenewтАЛ=AverageoldтАЛ+21
Calculate result
Substitute the given average into the formula.
AveragenewтАЛ=7+21=28
C is correct because adding a constant value of 21 to each of the 10 numbers increases their average by 21, resulting in 7 + 21 = 28.
This property also holds true for subtraction, multiplication, and division: if you multiply every term by c, the mean is multiplied by c.
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