Question

Find the mode of the following distribution:

Class interval	10 – 14	14 – 18	18 – 22	22 – 26	26 – 30	30 – 34	34 – 38	38 – 42
Frequency	8	6	11	20	25	22	10	4

Answer 1

As the class 26 – 30 has the maximum frequency, it is the modal class.
Now, `x_k = 26, h = 4, f_k = 25, f_k-1 = 20, f_k+1 = 22`
∴ Mode, `M_0 = x_k + {ℎ ×((fk− fk−1))/((2fk− fk−1−fk+1))}`

= `26+{4xx ((25-20))/((2xx25-20-22))}`

= `26+{4xx5/8}`

= (26 + 2.5)
= 28.5