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

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

For mode:

Here, highest frequency is 23.

So, the modal class = 35-45

Mode is given by

Where,

L = Lower class limit of the modal class = 35

h = class interval of the modal class = 10

f₁ = frequency of the modal class = 23

f₀ = frequency of the class preceding the modal class = 21

f₂ = frequency of the class succeeding the modal class = 14

Substituting values in the formula of mode,

⇒

⇒ Mode = 35 + 20/11

⇒ Mode = 36.8

For mean:

Let’s draw a table showing midpoints and frequencies.

Mean is given by

⇒ Mean = 2830/80

⇒ Mean = 35.37

Thus, mode is 36.8 and mean is 35.37.

The mode shows maximum number of patients admitted in the hospital is of age 36.8 years approximately and mean shows that on an average, number of patients admitted is of age 35.37 years.