What Is the Mode?The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set. Show
Key Takeaways
Understanding the ModeIn statistics, data can be distributed in various ways. The most often cited distribution is the classic normal (bell-curve) distribution. In this, and some other distributions, the mean (average) value falls at the midpoint, which is also the peak frequency of observed values. For such a distribution, the mean, median, and mode are all the same values. This means that this value is the average value, the middle value, and also the mode—the most frequently occurring value in the data. Mode is most useful as a measure of central tendency when examining categorical data, such as models of cars or flavors of soda, for which a mathematical average median value based on ordering can not be calculated. Examples of the ModeFor example, in the following list of numbers, 16 is the mode since it appears more times in the set than any other number:
A set of numbers can have more than one mode (this is known as bimodal if there are two modes) if there are multiple numbers that occur with equal frequency, and more times than the others in the set.
In the above example, both the number 3 and the number 16 are modes as they each occur three times and no other number occurs more often. If no number in a set of numbers occurs more than once, that set has no mode:
A set of numbers with two modes is bimodal, a set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal. When scientists or statisticians talk about the modal observation, they are referring to the most common observation. Advantages and Disadvantages of the ModeAdvantages:
Disadvantages:
How Do I Calculate the Mode?Calculating the mode is fairly straightforward. Place all numbers in a given set in order; this can be from lowest to highest or highest to lowest, and then count how many times each number appears in the set. The one that appears the most is the mode. What Is Mode in Statistics With an Example?The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set. What Is the Difference Between Mode and Mean?The mode is the number in a set of numbers that appears the most often. The mean of a set of numbers is the sum of all the numbers divided by the number of values in the set. The mean is also known as the average. 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. During 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 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 can have more than one value?Hence, out of the three measures of central tendency, only mode can have more than one value.
Which measures of central tendency are used for numeric data?The mean can be used for both continuous and discrete numeric data.
Which measure of central tendency may not exist for all numeric data sets?in this problem we have been asked which measure of central tendency may not exist for all numeric data sets. The options are mode mean and median. Now the answer to this question will be the mode. The mood may not exist for all numeric data sets.
Which measure of central tendency is not resistant to extreme values in a numeric data set?The median is not influenced by extreme values. The median is sensitive only to the value of the middle point or points; it is not sensitive to the values of all other points.
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Which measure of central tendency may have more than one value in a numeric data set?
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