Question

Compute the mode from the following data:

Age (in years)	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35
No of patients	6	11	18	24	17	13	5

Answer 1

As the class 15 – 20 has the maximum frequency, it is the modal class.
Now, `x_k= 15, h = 5, f_k = 24, f_k-1 = 18, f_k+1 = 17`

∴ Mode, `M_0 = x_k + {ℎ ×((f_k− f_k−1))/((2f_k− f_k−1−f_k+1))}`
`= 15 + {5 × ((24−18))/((2×24−18−17))}`
`= 15 + {5 × 6/13}`
= (15 + 2.3)
= 17.3
Hence, mode = 17.3 years