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Mode is the value that occurs with the greatest number of frequency. For example- if the given set of values are 2, 3, 2, 4, 5, 2, 3, 1, 6 the mode here would be 2 which appears thrice. However, when there are 2 or more values appearing with same frequencies then the mode is said to be ill-defined. Such series is called as bi-modal or multi-modal.
Mode is an appropriate measure than average and median under certain circumstances. For instance, while studying the income earned by the workers in a company, mode reflects the wages earned by a large number of workers. Average income of the workers, on the other hand, may be much higher just because few employees in higher positions are earning a very high level of income.
Majority votes are considered in decision making where mode is applied to see the choice preferred by a large number of people.
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Example 1:
Calculate the mode from the data given below showing the marks obtained by 10 students.
75, 80, 82, 76, 82, 74, 75, 79, 82, 70
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Solution:
The mode here is 82 as it appears with the highest frequency.
Example 2:
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Calculate the mode for the data pertaining to the size of shoes.
Solution:
The mode here is 6 as it has the highest frequency.
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3. Continuous Series:
Mode for a data in the form of a continuous series is calculated using the formula
Example 3:
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Calculate the mode from the data given below pertaining to the marks obtained by the students in a test.
Solution:
By observation, it is known that the modal class is 40 – 50 as this class has the highest frequency.
Calculation of Mode – Grouping Method:
Ascertaining the mode by mere observation can be erroneous when there is a very low frequency preceding or succeeding the highest frequency. In such cases, a grouping table and an analysis table is prepared to ascertain the modal class. A grouping table consists of six columns. The maximum frequency is marked in the first column.
The frequencies are grouped in two’s in the second column. In the third column, the first frequency is left out and the remaining frequencies are grouped in two’s. In the fourth column, the frequencies are grouped in three’s. In the fifth column, the first frequency is left out and the remaining frequencies are grouped in three’s. In the sixth column, the first two frequencies are left out and the remaining frequencies are grouped in three’s. In each of these columns the maximum value is observed.
The analysis table is prepared taking the column numbers on the left and the probable values of mode on the right. The probable values of mode are those values against which the frequencies are the highest in the grouping table. The values are entered by means of a bar in the analysis table. The column total is then taken and the one which has the maximum value is the modal value.
Example 4:
Calculate the value of mode for the following data:
The modal value is 25 as it has the maximum total of 5 bars.
1. It can be easily observed from the data.
2. It is easy to compute.
3. It is unaffected by extreme values.
4. Mode can be determined even if the distribution has open end class.
5. It can also be determined easily by graphic method.
6. It is easy to understand.
1. Mode is ill-defined when there are distributions with two modes.
2. It is not based on all the values.
3. It cannot be accurate when there are sampling fluctuations.
4. When mode is computed through different methods, the value may differ in each of the methods.
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