Question

Find the mode of the following distribution given below.
`{:("Class Interval",f),(" "0-19,12),(" "20-39,20),(" "40-59,23),(" "60-79,22),(" "80-99,13):}`

Answer 1

Correct Answer - 54.5

Answer 2

Class Interval	Exclusive Class Intervals	Frequency
0 - 19	0 - 19.5	12
20 - 39	19.5 - 39.5	20 (f0)
40 - 59	39.5 - 59.5 (l)	23 (f1)
60 - 79	59.5 - 79.5	22 (f2)
80 - 99	79.5 - 99.5	13

39.5 - 59.5 is the model class interval.

Mode = \(l + \left(\frac {f_1 - f_0}{2f_1 - f_0-f_2}\right) \times h\)

\(= 39.5 + \left(\frac {23 - 20}{2\times 23 - 20 -22}\right) \times 20\)

\(= 39.5 + \left(\frac 3{46 - 20 - 22}\right) \times 20\)

\(= 39.5 + \frac 34 \times 20 \)

\(= 39.5 + 15\)

\(= 54.5\)