Mean, Median & Mode
Learn three different ways to find the "average" of a data set, understand what each measure tells you, and choose the right one for different situations.
The Three Measures of Centre
In statistics, a measure of centre is a single value that represents a typical value in a data set. There are three common measures: mean, median, and mode.
Mean
The arithmetic average. Add all values, then divide by how many values there are.
Median
The middle value when data is arranged in order. If even number of values, average the middle two.
Mode
The value that appears most often. A data set can have no mode, one mode, or more than one mode.
Working Through an Example
Here are the weekly pocket money amounts for 7 students (in dollars):
Mean
Sum: 5+8+8+10+12+15+16 = 74
Count: 7 values
Mean = 74 ÷ 7 ≈ $10.57
Median
Already ordered: 5, 8, 8, 10, 12, 15, 16
7 values → 4th value is middle
Median = $10
Mode
$8 appears twice, all others appear once.
Mode = $8
Which Measure Should You Use?
| Measure | Best When... | Example |
|---|---|---|
| Mean | Data is fairly spread evenly, no extreme outliers. | Average test score for a class. |
| Median | There are extreme values (outliers) that skew the mean. | House prices (one very expensive house skews mean). |
| Mode | You want to know the most popular or common item. | Most popular shoe size sold in a shop. |
Key Vocabulary
Mean
The sum of all values divided by the number of values. Also called the arithmetic average.
Median
The middle value when data is sorted in order from smallest to largest.
Mode
The value that occurs most frequently in a data set. A set can have no mode or multiple modes.
Outlier
A data value that is much larger or smaller than the other values. Outliers affect the mean more than the median.
Worked Examples
Find the mean of: 4, 7, 9, 6, 4
Step 1: Add all values: 4 + 7 + 9 + 6 + 4 = 30
Step 2: Count the values: 5
Step 3: Mean = 30 ÷ 5 = 6
Answer: Mean = 6
Find the median of: 12, 5, 18, 9, 3, 15
Step 1: Sort in order: 3, 5, 9, 12, 15, 18
Step 2: Even number of values (6), so average the middle two (3rd and 4th):
(9 + 12) ÷ 2 = 21 ÷ 2 = 10.5
Answer: Median = 10.5
A shop sold these shirt sizes in one day: S, M, L, M, XL, S, M, L, M. What is the mode?
Tally: S(2), M(4), L(2), XL(1)
M appears 4 times — more than any other size.
Answer: The mode is M (Medium).
Knowledge Check
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Key Concepts Summary
- ●Mean: add all values then divide by the count of values.
- ●Median: the middle value when data is in order; average the middle two if there is an even count.
- ●Mode: the most frequently occurring value; a set may have no mode or multiple modes.
- ●Outliers (extreme values) affect the mean more than the median or mode.
- ●Always sort data into order before finding the median.