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.

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