Mean, median, and mode are the three measures of central tendency in statistics. They each describe the center of a dataset in a different way — and knowing when to use each one is just as important as knowing how to compute them. This guide walks you through all three with clear formulas, step-by-step examples, and real-life contexts.
The Three Measures at a Glance
The arithmetic average. Add all values, divide by how many there are. Sensitive to outliers.
The value in the exact center when data is sorted. Resistant to outliers. Best for skewed data.
The value that appears most often. A dataset can have no mode, one mode, or multiple modes.
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How to Compute the Mean
The mean (also called the arithmetic mean or average) is the most familiar measure of central tendency. It is calculated by adding all values in a dataset and dividing by the count of values.
Where x̄ = mean, Σx = sum of all values, n = count of values
Add all values together
Sum every number in the dataset. Order does not matter for this step.
Count how many values there are
Count the total number of values in the dataset — this is n.
Divide the sum by the count
Sum ÷ n = mean. The result may not be a whole number even if all the original values are integers.
Mean — Worked Example
Consider incomes: ₱25,000 / ₱28,000 / ₱30,000 / ₱27,000 / ₱500,000
Mean = ₱610,000 ÷ 5 = ₱122,000 — but four out of five people earn around ₱28,000. The one outlier (₱500,000) pulled the mean up dramatically. In cases like this, the median is a more representative measure.
How to Compute the Median
The median is the middle value of a dataset when arranged in order from smallest to largest. Half the values are below the median and half are above it.
Even count: median = average of the two middle values at positions n÷2 and (n÷2)+1
Sort all values in ascending order
Arrange every number from smallest to largest. This is the most critical step — the median is meaningless unless the data is sorted first.
Find the middle position
If n is odd: the median is the value at position (n+1) ÷ 2.
If n is even: the median is the average of the values at positions n÷2 and (n÷2)+1.
Read or average the middle value(s)
For an odd dataset, the median is exactly one value. For an even dataset, add the two middle values and divide by 2.
Median — Worked Example (Odd Count)
Median — Worked Example (Even Count)
How to Compute the Mode
The mode is the value that appears most frequently in a dataset. Unlike mean and median, mode can be used with non-numerical data (like colors or categories) and a dataset can have more than one mode.
Unimodal — one value appears most often
Bimodal — two values tie for most frequent
Multimodal — three or more values tie
Count the frequency of each value
Tally how many times each distinct value appears in the dataset. A frequency table makes this easier for large datasets.
Find the highest frequency
Identify the maximum count. If all values appear the same number of times, there is no mode.
Identify all values with that frequency
If only one value has the highest frequency, that is the mode. If multiple values share the highest frequency, all of them are modes.
Mode — Worked Example (Unimodal)
Mode — Worked Example (Bimodal)
Mode — Worked Example (No Mode)
Worked Example: All Three Together
Let's compute mean, median, and mode for the same dataset.
When to Use Each Measure
| Situation | Best Measure | Why |
|---|---|---|
| Symmetric data, no outliers | Mean | Uses all data values — most informative when data is balanced |
| Skewed data or outliers present | Median | Not affected by extreme values — more representative of the center |
| Categorical / non-numeric data | Mode | Only measure that works with categories (e.g. most popular color) |
| Income, house prices, wealth | Median | A few very high values distort the mean significantly |
| Exam scores (no extreme outliers) | Mean | Gives the overall class performance level |
| Most popular shoe size or product | Mode | You want to know the most common value, not the average |
Grouped Data — Finding the Mean
When data is presented in a frequency table (grouped data), the mean is computed using weighted averages:
Practice Problems
| Dataset | Mean | Median | Mode |
|---|---|---|---|
| 2, 4, 4, 6, 8 | 4.8 | 4 | 4 |
| 10, 20, 20, 40, 50, 50 | 31.67 | 30 | 20 & 50 |
| 5, 5, 5, 5, 5 | 5 | 5 | 5 |
| 1, 2, 3, 100 | 26.5 | 2.5 | None |
| 7, 3, 3, 7, 7, 3 | 5 | 5 | 3 & 7 |
1. Mean: Sum ÷ Count — best for symmetric data without outliers
2. Median: Middle of sorted data — best for skewed data and outlier resistance
3. Mode: Most frequent value — only measure that works for categorical data
4. Even-count median = average of the two middle values
5. A dataset can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal)
6. For grouped data, use weighted mean: Σ(value × freq) ÷ Σ(freq)
7. When in doubt about which to use — check for outliers first
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