Question

Consider the following table:

Class interval	10 – 14	14 – 18	18 – 22	22 – 26	26 – 30
Frequency	5	11	16	25	19

The mode of the above data is ______.

Options

• 23.5

• 24

• 24.4

• 25

Answer 1

The mode of the above data is 24.4.

Explanation:

The maximum frequency is 25 and the modal class is 22 – 26.

∴ x_k = 22, f_k = 25, f_{k – 1} = 16, f_{k + 1} = 19 and h = 4.

∴ Mode = `x_k + h · {((f_k - f_(k - 1)))/((2f_k - f_(k - 1) - f_(k + 1)))}`

= `{22 + 4 xx ((25 - 16))/((50 - 16 - 19))}`

= `(22 + 4 xx 9/15)`

= `(22 + 12/5)`

= (22 + 2.4)

= 24.4