The following table show the ages of the patients admitted in a hospital during a year:
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Here, the maximum frequency is 23 so the modal class is 35−45.
Therefore,
$l=35$
$h=10$
$f=23$
$f_{1}=21$
$f_{2}=14$
$\Rightarrow$ Mode $=l+\frac{f-f_{1}}{2 f-f_{1}-f_{2}} \times h$
$=35+\frac{2}{46-35} \times 10$
$=35+\frac{2}{11} \times 10$
$=35+\frac{20}{11}$
$=35+1.80$
Mode $=36.8$ years
Thus, the mode of the ages of the patients is 36.8 years.
Calculation for mean.
Mean $=\frac{\sum f x}{\sum f}=\frac{2830}{80}=35.37$
Thus, the mean age of the patients is 35.37 years.
The mean age of the patients is less than the modal age of the patients.
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