Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

The following table shows 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 :


The class 35-45 has the maximum frequency, therefore, this is the modal class.

Here l = 35 , h = 10 , f1 = 23 , f0 = 21 , f2 =14

Now, let us substitute these values in the formula

\(Mode \ = \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)

\(= \ 35 \ + \ \frac{23 \ - \ 21}{2 \ × \ 23 \ - \ 21 \ - \ 14} \ × \ 10 \)

\(= \ 35 \ + \ \frac{2}{46 \ - \ 21 \ - \ 14} \ × \ 10 \)

\(= \ 35 \ + \ \frac{2}{11} \ × \ 10 \)

\(= \ 35 \ + \ 1.8 \ = \ 36.8 \)

Now, to calculate the Mean,

Class Interval Frequency ( \(f_i\) ) Mid-point ( \(x_i\) ) \( f_i x_i \)
5-15 6 10 60
15-25 11 20 220
25-35 21 30 630
35-45 23 40 920
45-55 14 50 700
55-65 5 60 300
\( \sum f_i \ = \ 80 \) \( \sum f_i x_i \ = \ 2830 \)

The formula for mean is :

\( \overline{x} \ = \ \frac{ \sum \ f_i x_i}{ \sum f_i} \)

\(= \ \frac{2830}{80} \ = \ 35.37 \) years

\(\therefore \) The mean of the given data = 35.37 years

NCERT solutions of related questions for Statistics

NCERT solutions of related chapters class 10 maths

NCERT solutions of related chapters class 10 science