Math's: Measures of Central Tendency: Mode and Calculation of Mode
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Mode- Meaning
The word ‘Mode’ means ‘Fashion’ in French language. In statistics, the observation that occurs most frequently in the data is called mode of the data. Mode is denoted by .
Calculation of Mode
Ungrouped Series
In an ungrouped series, we look at the frequencies of all the observations. The observation which occurs most frequently is mode.
Example (i)- Find the mode of the following data-
3, 7, 6, 5, 3, 8, 7, 2, 7, 8, 1
Solution- Arrange the series in ascending or descending order-
1, 3, 3, 5, 6, 7, 7, 7, 8, 8
Since, 7 has the highest frequency, 7 is mode.
Example- (ii) Find the mode of the following data
Size | 4 | 7 | 11 | 17 | 24 |
Frequency | 3 | 10 | 14 | 21 | 13 |
Solution- Since in the above series, the highest frequency is 21 which corresponds to 17. Thus, mode is 17.
Grouped Series
In a grouped series, we first locate the class interval having the maximum frequency. The class having the maximum frequency is the modal class. Then the values corresponding to the modal class is substituted in the following formula to find the mode.
Where, :lower limit of the modal class; : frequency of the modal class; : frequency of the class preceding the modal class; : frequency of the class succeeding the modal; : Size of the modal class.
Example- Find mode from the following data
Class Interval | 10-20 | 20-40 | 40-60 | 60-80 | 80-100 |
Frequency | 4 | 7 | 12 | 20 | 11 |
Solution
Class Interval | Frequency | |
10-20 | 4 | |
20-40 | 7 | |
40-60 | 12 | |
60-80 | 20 | |
80-100 | 11 |