Question

The following table show the ages of the patients admitted in a hospital during a year:

Age (in years):	5−15	15−25	25−35	35−45	45−55	55−65
Number of patients:	6	11	21	23	14	5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer 1

Age (in years)	5−15	15−25	25−35	35−45	45−55	55−65
Number of patients	6	11	21	23	14	5

Here, the maximum frequency is 23 so the modal class is 35−45.

Therefore,

Thus, the mode of the ages of the patients is 36.8 years.

Calculation for mean.

Age (in years)	Mid-Values(x)	Number of patients(f)	fx
5−15	10	6	60
15−25	20	11	220
25−35	30	21	630
35−45	40	23	920
45−55	50	14	700
55−65	60	5	300

Mean = $\frac{\sum _{}fx}{\sum _{}f}=\frac{2830}{80}=35.37$

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.