Mode of a data set
The mode of a data set is the value that occurs most frequently. In other words, you are looking for the value with the highest frequency.
The following data set gives the number of hours kids spend on homework every night.
2 3 4 1 0.5 2
Looking at the data, I see that the number 2 occurs most frequently. The remaining values occur only once.
Therefore, 2 is the mode of this data set.
A data set can have no mode, 1 mode, or more than 1 mode.
The data set about number of hours kids spend on homework each night has only 1 mode.
When a data set has only 1 mode, the data set is called unimodal.
Data set with no mode
The income of 7 families selected randomly are
25411 35100 47852 20000 60000 1000000 15000
Every value occur only once, so this data set has no mode.
Data set with 2 modes
The prices of a popular smartphone at 10 online stores are
600 750 740 500 750 630 610 590 630 800
750 occurs twice and 630 also occurs twice.
Therefore, the two modes of this data set are 750 and 630.
When a data set has 2 modes, the data set is called bimodal.
For example, take a look at this data set showing the number of TVs owned by 8 families selected randomly.
2 1 4 2 0 2 3 1
2 occurs three times and 1 occurs two times.
However, this set does not have 2 modes.
Since we are looking for the value with the highest frequency, then 1 cannot be a mode.
1 does not have the highest frequency. Since 2 has the highest frequency, then 2 is the only mode.
Data set with 3 modes
The data set below shows the number of times 9 people selected randomly go to the movie theater.
0 1 6 4 1 2 5 2 4
A close examination of this data set reveals that this set has 3 modes.
The modes are 1, 2, and 4 each occurring 2 times.
When a data set has more than 2 modes, the data set is called multimodal.
The mode can also be found for a set of qualitative data.
The data set below lists the type of book read in 1990.
Science fiction Drama Romance Cookbooks Romance Drama
Romance Comics History Science fiction Math Fantasy
Romance has the highest frequency, so romance is the mode.
The main advantage of the mode is that we can use it to find the mode for both quantitative and qualitative data.