Question

. Find the mode age of the patients from the following distribution :
Age(in years) 6-15 16-25 26-35 36-45 46-55 56-65
No. of patients 6 11 21 23 14 5

Answer 1

Mode= l + (f1-f2/2f1-f0-f3)×h

=36 + (23-14/2×23-21-14)×9

=36 + (9/11)×9

=36 + (81/11)

=36 + 7.3

=43.3

Answer 2

The mode age of patients is 37.636 years.

Step-by-step explanation:

Given:

Age(in years)= 6-15 16-25 26-35 36-45 46-55 56-65

No. of patients= 6 11 21 23 14 5

To find:

Mode age of patients

Formula:

Mode= $l+(\frac{f_{1} -f_{0} }{2f_{1}-f_{0} -f_{2} } )h$

Solution:

First, we look at the modal class

The class that has the highest frequency is called the modal class

Here, the highest frequency is 23

∴The class corresponding to that which is 36-45 is the modal class

Now, l=lower limit of modal class=36

h=difference between the class limits=45-36

∴h=9

$f_{1}$=frequency of modal class=23

$f_{2}$=frequency of class succeding the modal class=14

$f_{0}$=frequency of class preceding the modal class=21

Let's put the values in the formula

mode= $l+(\frac{f_{1} -f_{0} }{2f_{1}-f_{0} -f_{2} } )h$

∴mode=36+$(\frac{23-21}{2(23)-21-14} )9$

∴mode=36+($\frac{2}{46-35} )9$

∴mode=36+$(\frac{2}{11}$)9

∴mode=36+$\frac{18}{11}$

∴mode=$\frac{396+18}{11}$

∴mode=$\frac{414}{11}$

∴mode=37.636 years.

Thus the mode age of patients is 37.636 years.