Chapter 13 · Question 4

State the formula for mode of grouped data and define the terms.

Answer

Mode

=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h

, where

l

is lower limit of modal class,

h

is class size,

f_1

modal class frequency,

f_0

preceding frequency, and

f_2

succeeding frequency.

Find the modal class first: the class with highest frequency. Then use the formula.

For grouped data, identify the class with maximum frequency as the modal class. If its lower limit is

l

, class size

h

, frequency

f_1

, preceding class frequency

f_0

, and succeeding class frequency

f_2

, then mode is

l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h

.

Mode $=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$ , where $l$ is lower limit of modal class, $h$ is class size, $f_1$ modal class frequency, $f_0$ preceding frequency, and $f_2$ succeeding frequency.