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 No. of students: 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.

Question

Philoid · Accepted Answer

We may compute class marks (x_i) as per the relation

X_i=

Now, let assumed mean (A) = 30

Age(in years)	No. of patients(f_i)	Class marks (x_i)	d_i=x_i-30	f_id_i
5-15	6	10	-20	-120
15-25	11	20	-10	-110
25-35	21	30	0	0
35-45	23	40	10	230
45-55	14	50	20	180
55-65	5	60	30	150
Total	80			430

∑f_i=80, ∑f_id_i=430

Mean=

= 30 + = 30+ 5.375

=35.38

It represents that on an average the age of patients admitted was 35.38 years. As we can observe that the maximum class frequency 23 belonging to class interval 35-45.

So, modal class= 35-45

Lower limit (l) of modal class =35

Frequency (f₁) of the modal class=23

h=10,

Frequency (f₀)of class preceding the modal class=21

Frequency (f₂) of class succeeding the modal class =14

Now,

=

=35 + 1.81 =36.8years

Age (in years):	5-15	15-25	25-35	35-45	45-55	55-65
No. of students:	6	11	21	23	14	5

The following table shows the ages of the patients admitted in a hospital during a year:Age (in years):5-1515-2525-3535-4545-5555-65No. of students:6112123145Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

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

No. of students:

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.