The mode, or modal class, is a measure of central tendency that allows for a quick analysis of the most popular data value, or the most popular group of data, in a distribution.
-
The mode (Mod) is the value with the highest frequency in a data distribution.
-
The modal class is the interval of values with the highest frequency in a data distribution that has been grouped into classes.
The mode corresponds to the data value which is the most frequent. To find it, it is necessary to determine the value that is repeated most often in a distribution.
Given the following distribution:
|60,| |65,| |67,| |70,| |70,| |72,| |\boldsymbol{\color{#3b87cd}{78}},| |\boldsymbol{\color{#3b87cd}{78}},| |\boldsymbol{\color{#3b87cd}{78}},| |84,| |88,| |88,| |90,| |95|
|78| is the mode because it is the data value that is repeated most often (|3| times).
A distribution can have more than one mode.
Given the following distribution:
|60,| |65,| |67,| |70,| |70,| |72,| |\boldsymbol{\color{#3b87cd}{78}},| |\boldsymbol{\color{#3b87cd}{78}},| |\boldsymbol{\color{#3b87cd}{78}},| |84,| |\boldsymbol{\color{#fa7921}{88}},| |\boldsymbol{\color{#fa7921}{88}},| |\boldsymbol{\color{#fa7921}{88}},| |95|
The data value |\boldsymbol{\color{#3b87cd}{78}}| appears |3| times, as does the data value |\boldsymbol{\color{#fa7921}{88}}.| Therefore, the distribution has |2| modes: |78| and |88.|
To make it easier to identify the mode, a condensed data table is very useful.
Here is a condensed data table showing the number of animals adopted by |48| families:
| Number of animals | Frequency |
|---|---|
| |0| | |12| |
| |\boldsymbol{\color{#3b87cd}{1}}| | |\boldsymbol{\color{#3b87cd}{17}}| |
| |2| | |10| |
| |3| | |6| |
| |4| | |3| |
| Total | |\boldsymbol{48}| |
The Mode corresponds to 1 animal which is the value with the highest frequency of occurrence |(17).| In other words, amongst the families surveyed, the number of animals that is repeated most often is 1 pet.
When data has been grouped into classes (intervals), the mode is instead called a modal class. The method of determining the modal class is the same as for determining the mode.
Here is the age distribution of people in the neighbourhood who take karate classes.
| Age (years) | Frequency |
|---|---|
| |[0,5[| | |5| |
| |\boldsymbol{\color{#3b87cd}{[5,10[}}| | |\boldsymbol{\color{#3b87cd}{17}}| |
| |[10,15[| | |10| |
| |[15,20]| | |8| |
The modal class is |[5,10[,| since this is the group of data with the highest frequency |(17).| In other words, the age group that is most represented among the participants of the karate class is the 5 to 10 year olds.
The mode of the data can only be estimated by calculating the middle of the modal class.
||\text{Mode}\approx\dfrac{5 + 10}{2} = 7.5 \ \text{years}||