Statistics - Arithmetic Mode of Continous Series
When data is given based on ranges alongwith 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
${f_1}$ = 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
Thus Arithmetic Mode is 18.
