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The mean of 10 observations is 15. If each observation is increased by 3, what will be the new mean?
15
18
20
25
18
When each observation in a data set is increased/decreased by a constant k, the mean of the data set also increases/decreases by the same constant k. Simply add 3 to the original mean.
Number of observations n = 10, Mean of original observations = 15, Constant increase for each observation = 3.
MeannewтАЛ=MeanoldтАЛ+k
When each observation in a data set is increased/decreased by a constant k, the mean of the data set also increases/decreases by the same constant k. Simply add 3 to the original mean.
Students often spend time calculating the sum of observations (10 * 15 = 150), adding 3 to each (150 + 30 = 180), and dividing by 10, which is unnecessary and time-consuming.
Identify original mean property
The original mean is given as 15. The property of mean states that if every observation xiтАЛ is replaced by xiтАЛ+k, the new mean is Mean+k.
MeanoldтАЛ=15,k=3
Apply the addition constant
Since every observation is increased by 3, the mean increases directly by the same value.
MeannewтАЛ=15+3
Calculate the final value
Performing the addition yields the result for the new mean.
MeannewтАЛ=18
B is correct because adding a constant value to all observations in a dataset increases the mean by exactly that same constant value, resulting in 15 + 3 = 18.
This property also applies to subtraction, multiplication, and division: if you multiply every term by k, the new mean becomes Meanimesk.
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