Measures of Central Tendency Explained — Mean, Median & Mode (JAMB/WAEC Maths)
Measures of central tendency describe the “center” or typical value of a data set, giving a single representative figure that summarizes the data as a whole.
This topic — covering mean, median, and mode, is one of the most fundamental in JAMB and WAEC Mathematics statistics questions, and it forms the basis for later topics like measures of dispersion. This lesson walks through all three measures with worked examples.
Quick takeaways
- The mean is the average of a data set, found by adding all values and dividing by the number of values.
- The median is the middle value of a data set when arranged in order, or the average of the two middle values if there’s an even number of data points.
- The mode is the value that occurs most frequently in a data set; a data set can have one mode, more than one mode, or no mode at all.
- The mean is sensitive to extreme values (outliers), while the median is not, which matters when choosing the most appropriate measure for a given data set.
- Exam questions frequently ask you to calculate all three from the same data set, or to identify which measure best represents a particular data set.
What is the mean, and how do you calculate it?
The mean, commonly called the average, is calculated by adding up all the values in a data set and dividing by the total number of values:
Mean = (Sum of all values) / (Number of values)
For example, the mean of 4, 8, 6, 10, and 2 is (4+8+6+10+2)/5 = 30/5 = 6. The mean is the most commonly used measure of central tendency, but it can be significantly affected by extremely high or low values (outliers) within the data set.
What is the median, and how do you calculate it?
The median is the middle value of a data set when all values are arranged in order from smallest to largest. To find it:
- Arrange the data in ascending order
- If there’s an odd number of values, the median is the single middle value
- If there’s an even number of values, the median is the average of the two middle values
For example, in the ordered set 2, 4, 6, 8, 10, the median is 6 (the middle value). In the ordered set 2, 4, 6, 8, the median is (4+6)/2 = 5. Unlike the mean, the median is not affected by extreme values, making it a more reliable measure when a data set contains outliers.
What is the mode, and how do you find it?
The mode is the value that appears most frequently in a data set. To find it, simply identify which value (or values) occurs more often than any other. A data set can be:
- Unimodal — having exactly one mode
- Bimodal — having exactly two modes (two values tied for most frequent)
- Multimodal — having more than two modes
- No mode — if every value occurs with the same frequency (e.g., each value appears exactly once)
Why do the mean, median, and mode sometimes give very different results?
Because each measure calculates the “center” of a data set differently, they can produce noticeably different values, especially when a data set contains outliers or is heavily skewed in one direction.
For example, in a data set of salaries where most people earn a similar amount but one person earns an extremely high salary, the mean would be pulled upward by that outlier, while the median would remain closer to what most people actually earn.
This is exactly why exam questions sometimes ask you to explain which measure is most appropriate for a given real-world scenario.
Common mistakes students make with measures of central tendency
- Forgetting to arrange data in order before finding the median
- Averaging the two middle values incorrectly when there’s an even number of data points
- Assuming every data set has exactly one mode, when some have none, and others have more than one
- Using the mean automatically without considering whether an outlier makes the median a more appropriate measure
Frequently asked questions
Q: What is the difference between mean, median, and mode? The mean is the average of all values, the median is the middle value when data is arranged in order, and the mode is the value that occurs most frequently in the data set.
Q: How do you find the median when there’s an even number of values? When there’s an even number of values, the median is calculated by averaging the two middle values after arranging the data in ascending order.
Q: Can a data set have more than one mode? Yes, a data set can be bimodal (two modes) or multimodal (more than two modes) if multiple values are tied for the highest frequency, and it can also have no mode if every value occurs equally often.
Q: Why might the median be a better measure than the mean for some data sets? The median is not affected by extreme values (outliers), making it a more reliable representation of the “typical” value when a data set contains unusually high or low figures that would otherwise skew the mean.
Ready to go further with data spread? Read our Measures of Dispersion lesson →
This is one topic from our full JAMB & WAEC Maths course — see everything covered →
