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

Age (in years)	Number of patients
5-15	6
15-25	11
25-35	12
35-45	23
45-55	14
55-65	5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Mode: The class which have highest frequency.
In this case, class interval 35-45 is the modal class.
Now, Lower limit of modal class, l = 35, h = 10, f1 = 23, f0 = 21, f2 = 14
We know that,
Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) * h
= 35 + ((23 - 21) / (2(23) - 21 - 14)) * 10
= 35 + (2 / 11) * 10
= 35 + 1.818
Mode = 36.8
Lets take assumed mean, A as 30
Class interval = 10
∴ ui = (xi - A) / h = (xi - 30) / 10
̄x = A + h Σ(fiui) / Σfi
= 30 + 10 * 43 / 80
= 30 + 5.375
= 35.375 ≈ 35.37
Hence, Mode = 36.8 years, Mean = 35.37 years.
Maximum number of patients admitted in the hospital are of age group 36.8 years, while on an average the age of a patient admitted to the hospital is 35.37 years.