Quick reference
Three types of average
Central tendency describes where the centre of a dataset lies. Three measures are used depending on the nature of the data and the question being asked.
The arithmetic mean is the sum of all values divided by the count. It is what most people mean by average and is appropriate for symmetric, roughly normally distributed data without extreme outliers.
The median is the middle value when the dataset is sorted in order. Half the values are above it and half below. It is resistant to outliers and is preferred for skewed distributions such as income, house prices, and waiting times.
The mode is the most frequently occurring value. It is the only average that makes sense for categorical (non-numerical) data, such as the most common blood type in a population or the most frequently purchased product in a store.
Using the wrong measure of average produces misleading conclusions. Reporting the mean salary in a company where a small number of executives earn many times the median salary overstates what a typical employee earns.
Arithmetic mean
Worked examples — all three averages
Sum = 12 + 15 + 18 + 22 + 13 = 80. Count = 5. Mean = 80 / 5 = 16. Each value contributes equally to the mean regardless of its position in the dataset. The mean does not have to be a value that actually appears in the dataset.
With 5 values (odd count), the median is the middle value at position (5+1)/2 = 3. The third value in the sorted list is 15. Two values are below (12 and 13) and two are above (18 and 22).
With 6 values (even count), the median is the mean of the two middle values at positions 3 and 4. Those values are 15 and 18. Median = (15 + 18) / 2 = 16,5. The median does not have to be a value that exists in the dataset.
The mean of 55.000 is far above what any typical employee earns because the single high salary of 150.000 pulls it upward. The median of 32.000 accurately represents the typical salary. This is exactly why official salary statistics use the median rather than the mean. The median is said to be resistant to outliers.
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Weighted average
A weighted average assigns different levels of importance to different values. The standard mean treats every value equally. In many real situations, values should not contribute equally.
Example: a student's final grade is composed of coursework (40% weight) scoring 65, a midterm exam (20% weight) scoring 72, and a final exam (40% weight) scoring 80.
Weighted mean = (65 x 0,40) + (72 x 0,20) + (80 x 0,40) = 26 + 14,4 + 32 = 72,4.
Simple mean = (65 + 72 + 80) / 3 = 72,3. In this case the two are nearly identical because the weights are balanced, but when weights are unequal the difference can be substantial.
Weighted averages are used for: portfolio returns (weighted by position size), GPA calculations (weighted by credit hours), price indices (weighted by quantity sold), and any scenario where different observations carry different significance.
When to use which average
| Situation | Best measure | Reason |
|---|---|---|
| Symmetric data, no extreme outliers | Mean | Uses all data points efficiently |
| Skewed data (income, house prices) | Median | Not distorted by extreme values |
| Categorical data (colours, types) | Mode | Only meaningful average for categories |
| Values with different importance | Weighted mean | Reflects the varying significance |
| Small dataset with potential outliers | Median | Mean is unreliable with few values |
| Comparing population averages | Median | Standard for demographic reporting |
How outliers affect each measure
An outlier is a value far from the other values in a dataset. Understanding how each average responds to outliers determines which is appropriate for a given dataset.
The mean is highly sensitive to outliers. Adding a single extreme value can shift the mean dramatically. In the salary example above, one salary of 150.000 in a dataset of mostly 28.000 to 35.000 values doubles the mean. This is not wrong mathematically — the mean is calculated correctly — but it misrepresents the typical case.
The median is resistant to outliers. Changing the extreme value from 150.000 to 1.500.000 does not change the median at all. The median depends only on the ordering of values, not their magnitude.
The mode is not affected by outliers unless the outlier happens to be the most frequent value. In most continuous numerical datasets, there is no mode because no value repeats exactly.
In practice: use the mean when data is roughly symmetric and there are no extreme values. Use the median when the distribution is skewed or when outliers are present and you want to represent the typical case. Report both when the comparison between them is itself informative — a large gap between mean and median signals skewness in the data.
Common mistakes
Methodology
Arithmetic mean: sum of all values divided by count. Median: middle value of sorted dataset, or mean of two middle values for even-count datasets. Mode: most frequently occurring value. Weighted mean: sum of (value multiplied by weight) divided by sum of weights. All formulas follow standard statistical definitions.
These definitions apply to descriptive statistics for finite datasets. Population parameters use the same formulas applied to all members of a population rather than a sample.
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Frequently asked questions
Formula based on standard mathematical and financial methods. Results are for informational purposes. Last reviewed May 2026. Version 1.