Mode Calculator
The mode is the value that occurs most often in a data set. Unlike the mean and the median it requires no arithmetic; it is found simply by counting frequencies. That is why the mode is the only measure of central tendency available for categorical data that cannot be ordered (brand, color, occupation, blood type).
This calculator counts the data, builds the frequency table, and states separately whether the distribution has one mode (unimodal), two (bimodal), or more (multimodal). If no value repeats, the amodal case is reported explicitly. Mode, mean, and median are also shown together; the ordering of these three gives the first clue about the skewness of the distribution.
Mode formulas
Raw data: Mode = the value with the highest frequency
f(Mode) = max{f(x₁), f(x₂), …, f(xₖ)}
Grouped data: Mode = L + [Δ₁ / (Δ₁ + Δ₂)] · h
Δ₁ = f_mode − f_previous , Δ₂ = f_mode − f_next
L = lower bound of the modal class, h = class width
Empirical rule: Mode ≈ 3·Median − 2·x̄
Symmetric case: Mode = Median = x̄For raw data the mode is found by counting frequencies; like Excel's MODE.MULT, this calculator lists every peak value that shares the highest frequency.
How to Calculate
- Paste your data values into the box; commas, spaces, and line breaks are all accepted.
- If you are entering continuous measurements, choose a counting precision — without rounding, no value may repeat at all.
- Find the row with the highest frequency in the frequency table; the mode is the value in that row.
- Check the mode type: unimodal, bimodal, multimodal, or amodal is reported separately.
- Compare the mode with the mean and the median; the ordering of the three shows the direction of the skew.
- If the bar chart shows more than one peak, ask whether your data is made up of subgroups.
Worked Examples
A unimodal data set
Among 8 observations the value 7 appears 3 times and the value 9 appears twice; since the highest frequency is 3, the mode is 7 and the data is unimodal (the mode makes up 37.5% of the data). In the same data the mean is 8.75 and the median is 8; the mean exceeding the mode points to right skew. The Pearson estimate gives 3·8 − 2·8.75 = 6.50.
Number of values (n): 8 · Mode: 7.00 · Mode type: Unimodal (one mode)
Bimodal data
Because the values 12 and 15 each appear twice, the data is bimodal; the modes are 12 and 15. The mean is 14.13 and the median is 14.50. Two peaks suggest the data may come from two different subgroups rather than a single homogeneous population.
Number of values (n): 8 · Modes: 12.00 and 15.00 · Mode type: Bimodal (two modes)
Amodal data (no mode)
All five values appear exactly once, so the highest frequency is 1 and the data set has no mode. In this case the median (8) or the mean (8.20) should be reported as the measure of center; the mean and median being nearly equal indicates a nearly symmetric distribution.
Number of values (n): 5 · Mode: None · Mode type: No mode (amodal) — no value repeats