Statistics · 5 min read
Mean vs Median vs Mode
Three summaries of the same list — and why they can disagree
Mean is the arithmetic average, median is the middle of the ordered list, and mode is the most frequent value. This tutorial walks through all three on 1, 2, 2, 3, 4, 5, then a playground that plots three markers on one sorted strip. It is a teaching sketch, not a full statistics package.
Written by the My Calculator Stack editorial team. About our methods
Mean, median, and mode are descriptive summaries, not a diagnosis of the data. Ties, even-length lists, and “no unique mode” are possible. Fees, weights, and missing values are omitted.
1.Three different questions
The mean asks for the balance point: sum divided by count. The median asks for the middle after you sort: half the list is at or below it, half at or above. The mode asks what repeats most. They often sit near each other on a symmetric list, and they split when a tail or a pile-up appears. None of them is “the” average in every sentence people say out loud — pick the one that matches the question.
2.The formulas
Mean: add every value, divide by n. Median: sort the list. If n is odd, take the middle entry. If n is even, average the two middle entries. Mode: count frequencies; the mode is every value that shares the highest count, but only if that count is at least 2. If every value appears once, there is no unique mode.
\[ \begin{aligned}\bar{x} &= \frac{1}{n}\sum x_i \\\mathrm{median} &= \text{middle of the ordered list} \\\mathrm{mode} &= \text{most frequent value(s)}\end{aligned} \]
3.Worked example
Take 1, 2, 2, 3, 4, 5 — the same defaults as the mean–median–mode calculator. Sorted, the list is already 1, 2, 2, 3, 4, 5. Mean: 17/6 ≈ 2.833. Median: n is even, so average the 3rd and 4th values, (2 + 3)/2 = 2.5. Mode: 2 appears twice and nothing appears more often, so the mode is 2. Same six numbers, three summaries.
\[ \bar{x}\approx 2.833,\ \mathrm{median}=2.5,\ \mathrm{mode}=2 \]
4.Three markers on one strip
Edit the six values. The chips show the sorted list; the strip below places mean, median, and mode as three markers on one number line. Stretch an outlier and watch the mean slide while the median and mode stay put. This is a teaching widget — no comma-separated paste box, no full calculator chrome. Open the mean–median–mode calculator when you want the standalone tool.
Inline playground
Tiny dataset
Sorted list
Mean
2.833
Median
2.5
Mode
2
mean 2.833 · median 2.5 · mode 2
Teaching sketch only — mean, median, and mode answer different questions. An outlier pulls the mean; the median and mode often stay put.
Open the full mean–median–mode calculator →5.Open the full calculator
The mean–median–mode calculator uses the same three summaries and the same 1, 2, 2, 3, 4, 5 example, with How it works and related statistics tools on one page. Browse other statistics calculators if you need an average or standard deviation next.
Try it yourself
Open the related calculator and put these formulas to work.