19 May 2026
Learning statistics is essential for understanding and interpreting complex datasets, though many students find it one of the more challenging areas of mathematics. Building on their foundational knowledge is key to helping them understand, and what better way than to start with some core components of statistics?
Mean, median, and mode are measures of central tendency used to determine the central or typical value of a dataset. These measures provide a single value that summarises a large dataset, allowing students to identify the overall trend or average and determine other key points when solving a maths problem.
Understanding the concepts of mean, median, and mode enables students to conduct effective data analysis, extracting vital information from statistical data to solve specific statistical problems.
The mean, or the average, is the central measure of a dataset. To find the mean, add all the values in the dataset, then divide the total by the number of values. For example, if five students had 7, 2, 10, 6, and 5 coins respectively, then the mean value would be:
Sum of coins: 7 + 2 + 10 +6 + 5 = 30
Mean value: 30 ÷ 5= 6
A common mistake many students make is forgetting to include certain values in a dataset, especially when they are zero. It is important to divide the sum by the correct number of values to calculate an accurate mean.
While the mean is useful, students must be careful with outliers, which are extreme values that are much smaller or larger than the other values. The mean is highly sensitive to outliers, as a single extreme value can significantly change the result.
The median is the middle number in a dataset when arranged in ascending order. For datasets with an odd number of values, the position of the median can be found using:
[n + 1] ÷ 2
Using the same coin example, finding the median starts with identifying that there are five students with coins. Let us arrange the values in ascending order:
2, 5 , 6, 7, 10
From there, we use the formula above to find the position of the median:
[5 + 1] ÷ 2 = 3
Thus, the median is in the 3rd position, corresponding to 6 coins.
The above example shows that when a dataset contains an odd number of values, the middle value is the median. If there is an even number of values, the median is the mean of the two middle values.
Additionally, unlike the mean, the median is not affected by outliers and can provide a more accurate representation of the dataset.
The mode is the value that occurs most frequently in a dataset. There is no calculation involved in finding the mode, as it only requires careful observation. For example, consider the following dataset:
2, 5 ,3, 2, 4, 6, 2, 7, 1, 2, 2, 3, 5, 2, 9, 2
From this dataset, you can determine that value 2 is the mode. If a dataset contains no numbers that occur more than once, then there is no mode. Additionally, a dataset can have more than one mode. That means, if a student finds two or more sets of values that appear an equal number of times and are the highest, the dataset has two modes.
2, 5 ,3, 2, 3, 6, 2, 3, 1, 2, 2, 3, 5, 2, 9, 3, 4, 3
In the above example, 2 and 3 are the modes.
Occasionally, you may be asked to determine the range of a dataset, along with its mean, median, or mode (or a combination of these). The range is the difference between the largest and smallest values in a dataset. To find the range, identify the largest and smallest values in the dataset, then subtract the minimum from the maximum. For example:
3, 4 ,6, 9, 10, 16
For the dataset above, the range is:
16 – 3 = 13
A larger range indicates that the data is more spread out.
Use this comparison chart to differentiate between the mean, median, and mode.
| Measures of central tendency | Mean | Median | Mode |
|---|---|---|---|
|
Definition |
Average of a dataset |
Middle value of a dataset |
Most frequent value in a dataset |
|
Purpose |
Finding the overall average in continuous data |
Finding the middle ground in skewed data |
Finding the most frequent value |
|
Formula |
Sum of values ÷ Total number of values
|
[n + 1] ÷ 2
(n = number of values) |
Count the most frequent value
|
|
Advantage |
Represents all data points in a dataset
|
Useful to analyse skewed data |
Highlights the most common value |
|
Outliers |
Affected by outliers
|
Not affected by outliers
|
Not affected by outliers
|
Is your child struggling with understanding statistical concepts? Matrix Math can provide personalised maths tuition to help students build a strong foundation, including how to find the mean, median, and mode of a dataset, as well as other mathematical concepts they find challenging. Contact us today to learn more about our teaching approach!
