Statistics - Continuous Series Arithmetic Mode

When data is given based on ranges along with their frequencies. Following is an example of continous series −

Items	0-5	5-10	10-20	20-30	30-40
Frequency	2	5	1	3	12

Formula

$M_o = {L} + \frac{f_1-f0}{2f_1-f_0-f_2} \times {i}$

Where −

${M_o}$ = Mode
${L}$ = Lower limit of modal class
${f_1}$ = Frquencey of modal class
${f_0}$ = Frquencey of pre-modal class
${f_2}$ = Frquencey of class succeeding modal class
${i}$ = Class interval.

In case there are two values of variable which have equal highest frequency, then the series is bi-modal and mode is said to be ill-defined. In such situations mode is calculated by the following formula −

Mode = 3 Median - 2 Mean

Arithmetic Mode can be used to describe qualitative phenomenon e.g. consumer preferences, brand preference etc. It is preferred as a measure of central tendency when the distribution is not normal because it is not affected by extreme values.

Example

Problem Statement −

Calculate the Arithmetic Mode from the following data −

Wages (in Rs.)	No.of workers
0-5	3
5-10	7
10-15	15
15-20	30
20-25	20
25-30	10
30-35	5

Solution −

Using following formula

$M_o = {L} + \frac{f_1-f0}{2f_1-f_0-f_2} \times {i}$

${L}$ = 15
${f_1}$ = 30
${f_0}$ = 15
${f_2}$ = 20
${i}$ = 5

Substituting the values, we get

$M_o = {15} + \frac{30-15}{2 \times 30-15-20} \times {5} \\[7pt] \, = {15+3} \\[7pt] \, = {18}$

Thus Arithmetic Mode is 18.

Calculator

Print Page