The value which has a higher frequency than others in its neighborhood is called mode. The important characteristic of mode is that, it is easy to compute and may be applied to qualitative as well as quantitative data. It is generally used when the data is of qualitative nature where the addition (for mean) or arrangement (for median) of values is not possible. Since mode is defined as the most repeated value of the data therefore a distribution may have more than one mode or it may have no mode.
Data having One Mode
If a data contains only one value with higher frequency than others in its neighborhood, then this value would be considered as the mode of data. If the distribution has only one mode, it is called Uni-modal distribution. This can be explained with the help of following problem.
Problem: Following are the marks (out of 10) obtained by a student in ten quizzes: 4, 5, 5, 6, 6, 6, 6, 8, 9, 9, Find the mode.
In the above problem the frequency of 4 is 1 (student secured 4 marks only in one quiz). Similarly the frequencies of 5, 6, 8, and 9 are 2, 4, 1, and 2. Since the frequency of 6 is higher than its neighbors (Five and Eight) therefore 6 is the mode.
Data having more than one Mode
If a data have two or more most repeated values then all the values are considered mode. If the distribution has two modes, it is called Bi-modal distribution, if the distribution has more than two modes it is called Multi-modal distribution.
Problem: Following are the number of employees per organization in 21 organizations: 22, 23, 27, 27, 27, 28, 28, 28, 28, 30, 30, 35, 35, 35, 35, 35, 36, 36, 36, 36, and 40. Find the mode.
Now we have two modes 28 and 35. Modal value 28 has frequency of 4 which is higher than the frequencies of neighbor values (frequency of 27 = 3 and 30 =2). Similarly the frequency of 35 is 5 which is higher than the frequency 2 of 30 and 4 of 36. Here we should note that that 28 and 36 both occur with frequency 4, but 36 is not mode because it is not the most frequent around its adjacent values.
Data having no Mode
If all values of the data are distinct, mode will not exist. This can be explained with the help of following problem.
Problem: Following are the number of road accidents per month for one year: 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, and 20. Find the mode.
It has no mode, because there is no observation that occurs with highest frequency.
Mode of Grouped Data
In case of grouped data, mode is the value of x against which maximum frequency occurs. The concept of calculating a mode of grouped data can be explained with the help of following problem.
Problem: For the data given below in table, find the mode.
52 is mode because it occurs with the highest frequency.
Mode of Frequency Distribution
In a frequency distribution mode is that value of the variable for which the frequency curve takes maximum height. A frequency distribution with one mode is called unimodal while frequency distribution with two modes is called a bimodal frequency distribution. For a frequency distribution mode can be obtained by using the formula.
Problem: Table below shows the frequency distribution of the number of years with their last employer of 24 persons who retired from their jobs. Calculate the mode.