Mode
- Sometimes, you may be interested in knowing the most typical value of a series or the value around which maximum concentration of items occurs.
- For example, a manufacturer would like to know the size of shoes that has maximum demand or style of the shirt that is more frequently demanded.
- Here, Mode is the most appropriate measure. The word mode has been derived from the French word “la Mode” which signifies the most fashionable values of a distribution, because it is repeated the highest number of times in the series.
- Mode is the most frequently observed data value. It is denoted by Mo.
Computation of Mode
Discrete SeriesConsider the data set 1, 2, 3, 4, 4, 5. The mode for this data is 4 because 4 occurs most frequently (twice) in the data.
Example 10
Look at the following discrete series:
Variable 10 20 30 40 50
Frequency 2 8 20 10 5
Here, as you can see the maximum frequency is 20, the value of mode is 30. In this case, as there is a unique value of mode, the data is unimodal. But, the mode is not necessarily unique, unlike arithmetic mean and median. You can have data with two modes (bi-modal) or more than two modes (multi-modal).
It may be possible that there may be no mode if no value appears more frequent than any other value in the distribution. For example, in a series 1, 1, 2, 2, 3, 3, 4, 4, there is no mode.
Unimodal Data Bimodal Data
Continuous SeriesIn case of continuous frequency distribution, modal class is the class with largest frequency. Mode can be calculated by using the formula:
Where L = lower limit of the modal class
D1= difference between the frequency of the modal class and the frequency of the class preceding the modal class (ignoring signs).
D2 = difference between the frequency of the modal class and the frequency of the class succeeding the modal class (ignoring signs). h = class interval of the distribution. You may note that in case of continuous series, class intervals should be equal and series should be exclusive to calculate the mode. If mid points are given, class intervals are to be obtained.
Example 11
Calculate the value of modal worker family's monthly income from the following data:
Income (in '000 Rs) |
Number of families |
Below 50 Below 45 Below 40 Below 35 Below 30 Below 25 Below 20 Below 15 |
97 95 90 80 60 30 12 4 |
Table 5.7
Grouping Table
Table 5.8
Analysis Table As you can see this is a case of cumulative frequency distribution. In order to calculate mode, you will have to covert it into an exclusive series.
In this example, the series is in the descending order. Grouping and Analysis table would be made to determine the modal class. The value of the mode lies in 25-30 class interval. By inspection also, it can be seen that this is a modal class. Now L = 25, D1 = (30 - 18) = 12, D2 = (30 - 20) = 10, h = 5 Using the formula, you can obtain the value of the mode as:
=
Activities
- A shoe company, making shoes for adults only, wants to know the most popular size of shoes. Which average will be most appropriate for it?
- Take a small survey in your class to know the student's preference for Chinese food using appropriate measure of central tendency. ? Can mode be located graphically?