Text begins When it’s unique, the mode is the value that appears the most often in a data set and it can be used as a measure of central tendency, like the median and mean. But sometimes, there is no mode or there is more than one mode. There is no mode when all observed values
appear the same number of times in a data set. There is more than one mode when the highest frequency was observed for more than one value in a data set. In both of these cases, the mode can’t be used to locate the centre of the distribution. The mode can be used to summarize categorical variables, while the mean and median can be calculated only for numeric variables. This is the main advantage of the mode as a measure of central tendency. It’s also useful for discrete variables and for
continuous variables when they are expressed as intervals. Here are some examples of calculation of the mode for discrete variables. Example 1 – Number of points during a hockey tournamentDuring a hockey tournament, Audrey scored 7, 5, 0, 7, 8, 5, 5, 4, 1 and 5 points in 10 games. After summarizing the data in a frequency table, you can easily see that the mode is 5 because this value appears the most often in the data set (4 times). The mode can be considered a measure of central tendency for this data set because it’s unique.
Table 4.4.3.1
Example 2 – Number of points in 12 basketball gamesDuring Marco’s 12-game basketball season, he scored 14, 14, 15, 16, 14, 16, 16, 18, 14, 16, 16 and 14 points. After summarizing the data in a frequency table, you can see that there are two modes in this data set: 14 and 16. Both values appear 5 times in the data set and 5 is the highest frequency observed. The mode can’t be used a measure of central tendency because there is more than one mode. It’s a bimodal distribution.
Table 4.4.3.2
Example 3 – Number of touchdowns scored during football seasonThe following data set represents the number of touchdowns scored by Jerome in his high-school football season: 0, 0, 1, 0, 0, 2, 3, 1, 0, 1, 2, 3, 1, 0. Let’s compare the mean, median and mode.
Table 4.4.3.3
Therefore, the median is equal to 1. Once the data has been summarized in a frequency table, you can see that the mode is 0 because it is the value that appears the most often (6 times).
Table 4.4.3.4
In summary, in this example, the mean is 1, the median is 1 and the mode is 0. The mode is not used as much for continuous variables because with this type of variable, it is likely that no value will appear more than once. For example, if you ask 20 people their personal income in the previous year, it’s possible that many will have amounts of income that are very close, but that you will never get exactly the same value for two people. In such case, it is useful to group the values in mutually exclusive intervals and to visualize the results with a histogram to identify the modal-class interval. Example 4 – Height of people in the arena during a basketball gameWe are interested in the height of the people present in the arena during a basketball game. Table 4.4.3.5 presents the number of people for 20-centimetre intervals of height.
Table 4.4.3.5
Chart 4.4.3.1 shows this data set as a histogram. Data table for Chart 4.4.3.1Data illustrated in this chart are the data from table 4.4.3.5. Looking at the table and histogram, you can easily identify the modal-class interval, 160 to 179 centimetres, whose frequency is 480. You can also see that as the height decreases from this interval, the frequency also decreases for the interval 140 to 159 centimetres (363) and it continues to decrease for 120 to 139 centimetres (168), before starting to increase until the height reaches 80 to 99 centimetres (230). For categorical or discrete variables, multiple modes are values that reach the same frequency: the highest one observed. For continuous variables, all peaks of the distribution can be considered modes even if they don’t have the same frequency. The distribution for this example is bimodal, with a major mode corresponding to the modal-class interval 160 to 179 centimetres and a minor mode corresponding to the modal-class interval 80 to 99 centimetres. The modal class shouldn’t be used as a measure of central tendency, but finding two modes gives us an indication that there could be two distinct groups in the data that should be analyzed separately. Report a problem on this page Is something not working? Is there information outdated? Can't find what you're looking for? Please contact us and let us know how we can help you. Privacy notice Date modified: 2021-09-02Which measure of central tendency is the value that appears most often in a set of data?The mode of a set of data is simply the value that appears most frequently in the set. If two or more values appear with the same frequency, each is a mode.
What is the most commonly used measure of central tendency?It is the most commonly used measure of central tendency because it includes all the observation in a given data and in comparison to other measures of central tendency, arithmetic mean has very simple application.
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