Mode

The mode is the most repeated value in a distribution.

It is represented by Mo.

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 Mo= 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, 9Mo= 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.

Mode for Grouped Data Formula

Li is the lower limit of the modal class.

fi is the absolute frequency of the modal class.

fi--1 is the absolute frequency immediately below the modal class.

fi-+1 is the absolute frequency immediately after the modal class.

ai is the width of the class containing the modal class.

Example

Calculate the mode of a statistical distribution given by the following table:

  fi
[60, 63) 5
[63, 66) 18
[66, 69) 42
[69, 72) 27
[72, 75) 8
  100

Mode Calculations

Mode Calculations


2. The Classes Have Different Widths.

First, find the heights.

Mode Height Formula

The modal class is the one with the greatest height.

Statistical Mode Formula

Example

The following table shows the scores of a group of 50 students. Calculate the mode.

  fi hi
[0, 5) 15 3
[5, 7) 20 10
[7, 9) 12 6
[9, 10) 3 3
  50  

Mode Calculations

Mode Calculations