When there is more than one value that occurs the most often in a data set the data set is quizlet?

Example 1 – Number of points during a hockey tournament

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
Number of games by the number of points scored
Table summary
This table displays the results of Number of games by the number of points scored. The information is grouped by Number of points scored (appearing as row headers), Frequency (number of games) (appearing as column headers).

Example 2 – Number of points in 12 basketball games

During 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
Number of games by the number of points scored
Table summary
This table displays the results of Number of games by the number of points scored. The information is grouped by Number of points scored (appearing as row headers), Frequency (number of games) (appearing as column headers).

Example 3 – Number of touchdowns scored during football season

The 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.
The sum of all values is 14 and there are 14 data points. This gives a mean of 1. Because the number of values is even, the median is average between the data point of rank 7 and the data point of rank 8, after arranging the data set in increasing order.

Table 4.4.3.3
Rank associated with each value of the number of touchdowns during football season
Table summary
This table displays the results of Rank associated with each value of the number of touchdowns during football season. The information is grouped by Rank (appearing as row headers), Number of touchdowns (appearing as column headers).

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
Number of games by the number of touchdowns
Table summary
This table displays the results of Number of games by the number of touchdowns. The information is grouped by Number of touchdowns (appearing as row headers), Frequency (appearing as column headers).

In summary, in this example, the mean is 1, the median is 1 and the mode is 0.

Example 4 – Height of people in the arena during a basketball game

We 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
Number of people by height intervals
Table summary
This table displays the results of Number of people by height intervals. The information is grouped by Height (in centimetres) (appearing as row headers), Frequency (number of people) (appearing as column headers).

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.