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The mean of 10 observations is 25. If each observation is multiplied by 3, what is the new mean?
25
75
50
100
75
If every observation in a data set is multiplied by a constant factor 'k', the mean of the data set also gets multiplied by the same constant factor 'k'.
Initial number of observations n = 10, initial mean = 25, multiplier = 3.
New┬аMean=Old┬аMean├Чk
If every observation in a data set is multiplied by a constant factor 'k', the mean of the data set also gets multiplied by the same constant factor 'k'.
Many students unnecessarily calculate the sum of observations (25├Ч10=250), multiply the sum by 3 (750), and then divide by 10, which is time-consuming.
Identify Initial Properties
The mean of a data set is the ratio of the sum of observations to the number of observations. Given Mean=25 and n=10.
x=25
Apply Property of Mean
When each observation xiтАЛ is transformed to kтЛЕxiтАЛ, the new mean becomes kтЛЕx.
New┬аMean=3├Ч25
Calculate Final Result
Multiplying the initial mean by the constant factor 3 yields the new mean.
New┬аMean=75
B is correct because multiplying each observation of a data set by a constant factor 'k' results in the new mean being the initial mean multiplied by 'k', which is 25├Ч3=75.
This property also applies to addition or subtraction: if you add a constant 'c' to every observation, the mean increases by 'c'. This is a vital shortcut in data interpretation sections of competitive exams.
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