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The average of 70 values is 40. If each value is multiplied by 20, what will be the changed average?
800
60
90
1400
800
When each value in a data set is multiplied, divided, added, or subtracted by a constant, the average of the data set changes by the exact same operation.
Number of values = 70, Average of 70 values = 40, Each value is multiplied by 20
New┬аAverage=Original┬аAverage├ЧMultiplier
When each value in a data set is multiplied, divided, added, or subtracted by a constant, the average of the data set changes by the exact same operation.
Many students waste time by multiplying 70 and 40 to find the total sum (2800), multiplying the sum by 20, and then dividing by 70 again. The average scales directly by the factor.
Understand the Property of Averages
If each observation in a data set is multiplied by a constant k, the new average also gets multiplied by k.
New┬аAverage=Original┬аAverage├Чk
Identify Given Values
We are given that the original average is 40 and the multiplier k is 20.
Original┬аAverage=40,k=20
Calculate the Changed Average
Applying the property directly: New┬аAverage=40├Ч20=800.
New┬аAverage=40├Ч20=800
A is correct because when each value in a set is multiplied by 20, the average is also multiplied by 20, giving 40├Ч20=800.
This same linear property applies to addition, subtraction, and division: adding c to each value increases the average by c, while subtracting c decreases it by c.
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