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The mean of 5 observations is 20. If each observation is increased by 5, what will be the new mean?
25
20
30
22
25
When every observation in a dataset is increased, decreased, multiplied, or divided by a constant c, the mean changes by the exact same operation directly without recalculating the sum.
Number of observations n=5, mean of observations x=20, and each observation is increased by 5
xnewтАЛ=x+c
When every observation in a dataset is increased, decreased, multiplied, or divided by a constant c, the mean changes by the exact same operation directly without recalculating the sum.
Students often unnecessarily recalculate the total sum by multiplying 5├Ч20=100, adding 5 to each observation to get a new sum of 125, and then dividing by 5, which wastes valuable exam time.
Identify Given Data
We are given that the number of observations n=5 and their mean is x=20.
n=5,x=20
Understand the Property of Mean
If each observation in a dataset is increased by a constant c, the new mean is equal to the old mean plus that constant c. Here, c=5.
c=5
Calculate the New Mean
Applying the property, the new mean becomes xnewтАЛ=20+5=25.
xnewтАЛ=20+5=25
A is correct because increasing each of the 5 observations by 5 increases the overall mean by 5, resulting in a new mean of 25.
Similar property-based shortcuts apply to median, mode, and standard deviation when data points are scaled or shifted uniformly in statistics problems.
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