Mean, median, and mode are the three most common ways to describe the center of a dataset. The steps are straightforward, but small details (like sorting or handling outliers) matter a lot.
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These are all measures of central tendency, but they behave differently when a dataset has outliers (extreme values).
Write values from smallest to largest. Sorting is essential for the median.
Add all values, then divide by n.
If n is odd, pick the middle value. If n is even, average the two middle values.
Count how often each value appears. The most frequent value is the mode. (There can be none or more than one.)
Data: 2, 5, 5, 7, 9
Mean
(2 + 5 + 5 + 7 + 9) / 5 = 28 / 5 = 5.6
Median
Middle value = 5
Mode
Most frequent = 5
Notice how the mean (5.6) doesn’t have to be one of the data values.
Data: 3, 4, 7, 10
Mean
(3 + 4 + 7 + 10) / 4 = 24 / 4 = 6
Median
(4 + 7) / 2 = 5.5
Mode
No repeats → no mode
For even n, the median is the average of the two middle values. That’s why sorting is non-negotiable.
Use the mean when:
The data is fairly balanced and outliers are not a big factor (it uses every value).
Use the median when:
The data is skewed or has outliers (median is resistant). Example: incomes or house prices.
Use the mode when:
You need the most common value (especially for categories or discrete options): shoe sizes, survey answers, etc.
If you want more practice problems and visuals (including how outliers pull the mean), Khan Academy’s lessons on summarizing quantitative data are a solid companion.
Median uses position. If the list isn’t sorted, the “middle” is meaningless.
Mean divides by how many values there are — not the largest value.
If no value repeats, the dataset has no mode (and that’s okay).
Outliers can drag the mean. In skewed data, median often tells the story better.
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