Mode
The mode is the most repeated value in a distribution.
It is represented by M_{o}_{.}
It is possible to find the mode for categorical and quantitative variables.
Examples
Find the mode of the following distribution:
2, 3, 3, 4, 4, 4, 5, 5 M_{o}= 4
If a group has two or more scores with the same frequency and that frequency is the maximum, the distribution is bimodal or multimodal, that is to say, it has several modes.
1, 1, 1, 4, 4, 5, 5, 5, 7, 8, 9, 9, 9M_{o}= 1, 5, 9
When the scores of a group all have the same frequency, there is no mode.
2, 2, 3, 3, 6, 6, 9, 9
If two adjacent values are the maximum frequency, the average of the two adjacent scores is the mode.
0, 1, 3, 3, 5, 5, 7, 8 Mo = 4
Calculation of the Mode for Grouped Data
1. All Classes Have the Same Width.
L_{i} is the lower limit of the modal class.
f_{i} is the absolute frequency of the modal class.
f_{i--1} is the absolute frequency immediately below the modal class.
f_{i-+1} is the absolute frequency immediately after the modal class.
a_{i} is the width of the class containing the modal class.
Example
Calculate the mode of a statistical distribution given by the following table:
f_{i} | |
---|---|
[60, 63) | 5 |
[63, 66) | 18 |
[66, 69) | 42 |
[69, 72) | 27 |
[72, 75) | 8 |
100 |
2. The Classes Have Different Widths.
First, find the heights.
The modal class is the one with the greatest height.
Example
The following table shows the scores of a group of 50 students. Calculate the mode.
f_{i} | h_{i} | |
---|---|---|
[0, 5) | 15 | 3 |
[5, 7) | 20 | 10 |
[7, 9) | 12 | 6 |
[9, 10) | 3 | 3 |
50 |