Mean / Median / Mode
Also known as: average, arithmetic mean, central tendency, median vs mean, summary statistics
Mean, median, and mode are three measures of central tendency -- each describing what a 'typical' value in a dataset looks like from a different angle.
The mean (average) divides the total by the count; the median is the middle value when all data is sorted in order; the mode is the value that appears most frequently. Each measure is most appropriate in different situations: the mean is useful for symmetrical distributions without extreme outliers; the median is more representative when the data is skewed or has outliers; the mode is most useful for categorical data. Choosing the wrong measure can produce misleading summaries of data.
Mean / Median / Mode, explained at three levels
At home
Mean (average): add all the numbers and divide by how many there are. If five friends scored 70, 80, 85, 90, and 90 on a test, the mean is (70+80+85+90+90)/5 = 83. Median: sort the numbers and take the middle one. Sorted: 70, 80, 85, 90, 90 -- the middle is 85. Mode: the value that appears most often. In this set, 90 appears twice (the others appear once) so the mode is 90. The mean can be pulled up or down by extreme values; the median stays near the center regardless; the mode shows what the most common value is.
At work
Household income in Canada illustrates when to use each measure: in 2023 median household income was approximately $68,000 while mean household income was higher -- because a small number of very wealthy households pull the mean upward. The median is the more representative figure for a 'typical' household. If a government report cited mean income and a union was negotiating wages, using mean income would make everyone seem better-off than most people actually are. When data has extreme values (outliers), the median usually better represents the 'typical' experience than the mean.
At home
Skewed distributions and choosing the right measure: in a right-skewed distribution (a long tail to the right, with a few very large values -- like income or house prices), the mean is pulled toward the tail and is higher than what most people experience. The median sits near where most people are. In a left-skewed distribution (a few very small values), the mean is pulled downward. For symmetrical, bell-shaped distributions (like height in a population), mean and median are approximately equal and both are appropriate. As a rule of thumb: when extreme values exist or the distribution is skewed, use the median; when the distribution is roughly symmetrical and no extreme outliers exist, the mean is appropriate.
At work
Mode in business contexts: mode is most useful when you need to know the most common category or value. What is the most common order value? What is the most frequently purchased product? What is the most common customer support issue type? Mode is appropriate for discrete and categorical data (product categories, geographic regions, support types) where calculating a mean or median is nonsensical (what is the average product category?). For continuous numerical data (revenue, age, time on page), mode is rarely the most informative measure.
At home
The bimodal distribution and mode's analytical value: a bimodal distribution has two prominent peaks (two modes), which a single mean or median completely obscures. Website session times might be bimodal: most users spend either under 30 seconds (bounced, didn't find what they wanted) or over 3 minutes (engaged, reading content). The mean session time (say, 90 seconds) accurately represents neither group and might look 'fine' while hiding a serious problem. Visualizing distributions (histograms, density plots) before choosing summary statistics reveals bimodality and other structures that summary statistics miss.
At work
Geometric mean for growth rates: the arithmetic mean is misleading for percentage changes and growth rates. If a stock increases 50% one year and decreases 33% the next, the arithmetic mean is (50% + (-33%))/2 = 8.5%, but the actual return over two years is zero: $100 becomes $150 then back to $100. The geometric mean correctly represents growth: ((1+0.50)*(1-0.33))^(1/2) - 1 = 0%. Compound annual growth rate (CAGR) is a geometric mean applied to growth. When reporting average growth rates or returns across periods, the geometric mean is almost always more appropriate than the arithmetic mean.
Real-world examples
At home
Lena was comparing cities to potentially move to, looking at average home prices. She noticed one city reporting an 'average home price' of $850,000 -- much higher than she expected. When she found the median home price was $620,000, she realized a small number of luxury properties had pulled the mean up significantly. The median better represented what a typical home actually cost in that city. She used median prices in her comparison to get a more realistic picture of what she could expect to pay.
At work
Marcus ran an e-commerce business. His average order value (mean) was $87. During a planning meeting, he learned the median order value was only $52. The discrepancy meant a small number of high-value orders ($500+) were pulling the mean up significantly. His typical customer order was much closer to $52. He restructured his upsell strategy to focus on increasing median order value (getting the typical customer to spend more) rather than optimizing for the mean, which was distorted by outlier large orders.
How it compares
| feature | Mean | Median | Mode |
|---|---|---|---|
| Definition | Sum of all values divided by the count | Middle value when data is sorted | Most frequently occurring value |
| Affected by outliers | Yes -- extreme values pull it significantly | No -- middle value is unaffected by extremes | No -- based only on frequency, not value |
| Best for | Symmetrical data without extreme outliers | Skewed data or data with extreme outliers | Categorical data or finding the most common value |
| Common examples | Test score averages, temperature averages | Income, house prices, age | Most common product, most frequent support issue |
Mean, median, and mode each describe central tendency differently. Median is usually most representative for skewed data (income, prices); mean is appropriate for symmetrical data; mode identifies the most common value for categorical or discrete data.
For analysts
When reviewing client data presentations or research, checking whether the right central tendency measure was used is a quick high-value audit. Salary and compensation data should use median (means are distorted by executive pay); customer spending data should use median when there are high spenders in the mix; satisfaction scores should use mean (for symmetrically distributed Likert scales) or median (if there is a bimodal satisfaction split). Anytime you see a report citing 'average' for income, compensation, or price data, ask whether they mean mean or median -- the two can tell very different stories about the same dataset.
History & origin
Measures of central tendency have been calculated throughout human history for purposes ranging from census data to astronomical observations. The term 'average' (arithmetic mean) was used in the 14th century in the context of maritime law (averaging losses from ship cargo). Francis Galton promoted the median in the 1880s for describing skewed biological data. The mode was formalized in statistical practice in the late 19th century. The practical importance of choosing the right measure became widely understood as statistics entered business, public policy, and medicine -- government reporting of household income (median rather than mean, to avoid distortion by billionaires) and average salary (median, for the same reason) became standard for representing typical economic situations rather than totals distorted by extremes.