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The mean of five observations is 20. If each observation is increased by 5, what is the new mean?
25
20
30
22
25
If every observation in a dataset is increased by a constant value 'k', the mean of the dataset also increases by the same value 'k'. Simply add the increment to the original mean.
Mean of five observations = 20, Number of observations = 5, Increase value for each observation = 5.
New┬аMean=Old┬аMean+k
If every observation in a dataset is increased by a constant value 'k', the mean of the dataset also increases by the same value 'k'. Simply add the increment to the original mean.
Many students waste time recalculating the sum of observations: (20 * 5 = 100), adding (5 * 5 = 25) to get 125, then dividing by 5. The property of mean invariance/translation is faster.
Identify original parameters
We are given the original mean of n=5 observations as MoldтАЛ=20.
MoldтАЛ=20
Apply the property of mean
When a constant k is added to each observation, the new mean MnewтАЛ is given by the relation MnewтАЛ=MoldтАЛ+k, where k=5.
MnewтАЛ=20+5
Calculate the final result
Performing the addition gives the new mean of the dataset.
MnewтАЛ=25
A is correct because when every observation in a data set is increased by a constant k, the mean increases by k, resulting in 20+5=25.
This property also holds for subtraction, multiplication, and division; if every value is multiplied by k, the new mean is M├Чk. This is a frequently tested property in Statistics questions across RRB and SSC exams.
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