What is the mode of the data given below? [Give your answer correct to 2 decimal places.]

Age in years	15-25	25-35	35-45	45-55	55-65	65-75	75-85
No. of patients	14	32	39	38	10	36	22

Correct option is C

Formula Used:

In a grouped frequency distribution, the mode:

Mode = L +$$\left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$$​​

Where:

L = lower boundary of modal class

f₁ = frequency of modal class

f₀ = frequency of class before modal class

f₂ = frequency of class after modal class

h = class width

Solution:

From the table:

Highest frequency = 39 → Modal class = 35 – 45

L = 35

f₁ = 39

f₀ = 32 (frequency before 35 – 45)

f₂ = 38 (frequency after 35 – 45, i.e., 45 – 55)

h = 10 (class width)

Now, 

Mode = 35 + $$\left( \frac{39 - 32}{2(39) - 32 - 38} \right) \times 10$$​​

= 35 + $$\left( \frac{7}{78 - 70} \right) \times 10$$​​

= 35 + $$\left( \frac{7}{8} \right) \times 10$$​​

= 35 + 8.75 = 43.75