How these statistics are calculated
The mean is the arithmetic average. The median is the middle value once the numbers are sorted (or the average of the middle two, for an even count). The mode is the most frequently occurring value. Quartiles split the sorted data into quarters using the exclusion method: find the overall median (Q2), then Q1 and Q3 are the medians of the lower and upper halves, excluding the middle value itself when the count is odd.
- xᵢ — each entered value
- n — count of values entered
- Q2 — the overall median
More detail
Why quartiles can differ by method
This calculator uses the exclusion method (also called Moore & McCabe's method): the overall median splits the sorted list in half, and when the count is odd, that middle value is left out of both halves before their own medians are taken. Other conventions — the inclusion method (also known as Tukey's hinges), or linear interpolation (as in Excel's QUARTILE.INC/EXC) — keep or weight the middle value differently and can give slightly different Q1/Q3 for the same data. If you're matching a textbook or spreadsheet answer, check which method it uses.
Reading the mode
If every value you enter is unique, there is no most-frequent value — this calculator then reports "no mode" rather than listing every entry. If two or more values are tied for the highest frequency, all of them are shown (a multimodal dataset).
Choosing mean vs. median. The mean is pulled toward extreme values (like the 100 in {1, 2, 3, 4, 100}, which drags the mean to 22 while the median stays at 3). When your data has outliers or is skewed, the median usually describes the "typical" value better than the mean.
Frequently asked questions
What are the mean, median, and mode of 6, 7, 8, 8, 10, 10, 11, 13, 15?
Sum is 88 over 9 values, so the mean ≈ 9.7778. The median (5th value once sorted) is 10. Both 8 and 10 appear twice, more than any other value, so the mode is multimodal: 8 and 10. These are the calculator's default values above.
How are Q1 and Q3 calculated here?
By the exclusion method: sort the values, find the overall median (Q2), then take the median of everything below Q2 as Q1 and the median of everything above Q2 as Q3 — excluding Q2 itself from both halves when the count is odd. For the default dataset above, Q1 = 7.5 and Q3 = 12.
What if two values are tied for the mode?
This calculator lists every value tied for the highest frequency, in ascending order — for example the default dataset above shows mode = 8, 10 because both occur twice while every other value occurs once.
Why does it show "—" for Q1 and Q3?
Quartiles need at least 2 values to define a lower and upper half. With only 1 value entered, the mean, median, and mode still show (all equal to that single value), but Q1/Q3 show "—".
What happens if every value I enter is different?
The mode field then reads "no mode" instead of listing values — a mode requires at least one value to repeat more often than the rest.