What is the Mode in Maths?
The mode in maths is the value that occurs most often in a data set.
So in the last 2, 2, 3, 3, 3, 4, 5, 6, 6, the modal number is 3 as it appears most often.
The mode in maths is one of the key ways to detect the average within a set of data. By finding the standard, we can understand the most common value. Moreover, it might tell us something significant about the data set and can be very useful. Although analyzing data can be complicated, learning about the simple concepts of mode, median, mean, and range are helpful.
You can remember what the mode means thanks to the first two letters, “M” and “O.” Remember that the mode is the number that appears Most Often.
The mode in maths is not to be confused with other averages, such as the median, mean, and range. These are similar concepts to managing data sets, but each concept does something different with a group of numbers.
More Than One Modal Number
While, in an ideal world, there would be one modal number for each data set, this is not always the case. Often, a collection of data will have more than one mode.
Let’s look at an example to illustrate this.
Example 1: Find the modal number(s) in this set of data…
3, 3, 8, 3, 10, 21, 9, 4, 7, 4, 12, 4
If you look closely at the data above, you can see that the number 3 and the number 4 appearing three times. However, the rest of the scores only appear once. Therefore, there must be two modal numbers for this set of data.
The modal numbers are 3 and 4.
When a data set has two modes, it is called ‘bimodal.’
Example 2: Find the modal number(s) in this set of data…
88, 70, 70, 21, 88, 70, 70, 88, 90, 90, 90, 88, 35, 10, 90
By analyzing this data set, you can see three numbers appear 4 times. These numbers are 88, 70, and 90. It means that there are 3 modes for this set of data.
The modal numbers are 88, 70, and 90.
It is called multimodal when a data set has more than two modes.
Modal Classes
In some instances, you will find that each value in a data set occurs the same number of times. Finding the mode won’t be very helpful when working with data like this. Instead, you can group the data into ‘modal classes, and you can then identify the mode of each of the individual classes. It will give you an understanding of the data set as a whole.
For example, find the mode of this set of data:
1, 4, 2, 7, 8, 9, 10, 17, 19, 20, 32, 34, 37, 40, 43
Now, you have to separate your data into appropriate groups. Again, it’s essential to ensure all your groups are of equal sizes so you can accurately compare them.
The groups for this set of data are as follows:
1 – 4: 3 values (1, 4, and 2)
7 – 10: 4 values (7, 8, 9, and 10)
17 – 20: 3 values (17, 19, and 20)
31 – 34: 2 values (32 and 34)
36 – 39: 1 values (37)
40 – 43: 2 values (40 and 43)
One class contains more values than the others: 7-10 has 4 values. It means that the modal class is 7-10.
This method of dividing data into different groups and figuring out the modal class is advantageous when dealing with a data set containing anomalies (outliers/irregularities) that could skew the results.
Still unsure about finding the modal class? Let’s try another example!
Find the mode in this set of data:
20, 22, 25, 26, 27, 28, 29, 33, 46, 50, 57, 58, 59, 61, 63, 72, 74, 75
The first step is to analyze the data closely and find appropriate groups for your numbers. Remember to make sure all of your groups are the same size!
For this set of data, the groups would be as follows:
20 – 24
25 – 29
30 – 34
46 – 50
55 – 59
60 – 64
71 – 75
Now that you have your groups, you can figure out how many values each has.
20 – 24: 2 values (20 and 22)
25 – 29: 5 values (25, 26, 27, 28, and 29)
30 – 34: 1 value (33)
46 – 50: 2 values (46 and 50)
55 – 59: 3 values (57, 58, and 59)
60 – 64: 2 values (61 and 63)
71 – 75: 3 values (72, 74, and 75)
It is clear that the group ’25 – 29’ has more values than any other group. Therefore, the modal class for this data set is 25 – 29.
Advantages and Disadvantages of the Mode
Finding the modal value in a data set can be a good way of understanding the data better. However, as a measurement method, the mode has several downsides. Let’s have a look at some of the key advantages and disadvantages of finding the mode:
Benefits of finding the mode:
- The mode is super simple and easy to understand.
- The mode is not affected by extremely large or small values in a set of data.
- The mode is easy to find in a group of data.
- The mode can be located on a graph.
Disadvantages of finding the mode:
- There must be repeated values in a data set to find the mode.
- It is hard to find the mode when the data set contains a small number of values.
- A set of data can have 1 mode, more than 1 mode, or no mode at all
What is the Mode in Maths? – Why is it Important?
In schools, this topic is essential when closely linked to the National Curriculum. For example, in Year 5, children must describe and interpret different data sets in context (ACMSP120). In Year 6, they must analyze secondary data presented in digital media and elsewhere (ACMSP148).
Understanding the mode in maths is also essential for children’s observation and analysis skills. After recording data, the mode requires children to observe, analyze, and present their findings. In the long run, this can inspire children to look at more numerical information in everyday life, such as statistics in the news. In addition, it is good preparation for other topics and subjects, like science lessons.
Learning about the mode in maths gives children a fantastic opportunity to do independent research tasks. Children can use the Internet, newspapers, or observe events from everyday life to find data sets to practice finding the mode. For example, what was the modal average of all the students that took a test? From a scientific experiment, what was the most common temperature recorded?
