Question

Compute the mode from the following data:

Class interval	1 – 5	6 – 10	11 – 15	16 – 20	21 – 25	26 – 30	31 – 35	36 – 40	41 – 45	46 – 50
Frequency	3	8	13	18	28	20	13	8	6	4

Answer 1

Clearly, we have to find the mode of the data. The given data is an inclusive series. So, we will convert it to an exclusive form as given below:

Class interval	0.5 – 5.5	5.5 – 10.5	10.5 – 15.5	15.5 – 20.5	20.5 – 25.5	25.5 – 30.5	30.5 – 35.5	35.5 – 40.5	40.5 – 45.5	45.5 – 50.5
Frequency	3	8	13	18	28	20	13	8	6	4

As the class 20.5 – 25.5 has the maximum frequency, it is the modal class.
Now, `x_k = 20.5, h = 5, f_k = 28, f_k-1 = 18, f_k+1 = 20`
∴ Mode, `M_0 = x_k + {ℎ × ((f_k− f_k−1))/((2f_k− f_k−1−f_k+1))}`
`= 20.5 + {5 × ((28−18))/((2×28−18−20))}`
`= 20.5 + {5× 10/18}`
= (20.5 + 2.78)

= 23.28
Hence, mode = 23.28