Mean Median Mode Calculator

The three measures of central tendency in one place. Type a list of numbers, or switch to grouped data and enter class intervals with their frequencies, as in Class 10 and Class 11 statistics.

Data type
Separate numbers with commas or spaces.
Results update as you type.

Mean · Median · Mode

6.22222 · 6 · 8

of 9 numbers

Mean
6.22222222256 ÷ 9
Median
6the 5th value
Mode
8appears 3 times
Range
63 to 9
Count and sum
9 and 56
Geometric mean
5.871565178
Harmonic mean
5.500848896

About this calculator

For grouped data the calculator builds the full working table with mid-points, f × x and cumulative frequency, and applies the textbook formulas for the median and mode.

How to use it

  1. Choose a list of numbers or grouped data.
  2. Enter the numbers, or the class intervals and frequencies.
  3. Read the three measures and the working table.

The formula

Grouped data: mean = Σfx ÷ Σf; median = l + ((N/2 − cf) ÷ f) × h; mode = l + ((f₁ − f₀) ÷ (2f₁ − f₀ − f₂)) × h
l
lower limit of the median or modal class
cf
cumulative frequency of the class before
f, f₁
frequency of the median or modal class
f₀, f₂
frequencies of the classes before and after the modal class
h
class width

Worked example

Classes 0-10 to 40-50 with frequencies 5, 8, 15, 7, 5

  1. N = 40 and Σfx = 990, so the mean is 24.75.
  2. N/2 = 20 falls in 20–30: median = 20 + ((20 − 13) ÷ 15) × 10 = 24.67.
  3. The modal class is 20–30: mode = 20 + (7 ÷ 15) × 10 = 24.67.

What the result means

The mean uses every value but is pulled by extreme ones; the median is the middle and resists outliers; the mode is the most common value.

For a symmetric distribution the three are close. When the mean is well above the median, the data are skewed to the right, as incomes usually are.

Assumptions

  • Grouped values are assumed to be spread evenly within each class.
  • Inclusive classes such as 10-19, 20-29 are converted to boundaries 9.5–19.5 and so on, as textbooks do.

Limitations

  • Grouped results are estimates; the exact values need the raw data.
  • The mode formula needs a single modal class with lower frequencies on both sides.

Frequently asked questions

What is the difference between mean, median and mode?

The mean is the total divided by the count, the median is the middle value after sorting, and the mode is the value that appears most often.

How do I find the median of grouped data?

Find N/2, locate the class where the cumulative frequency first reaches it, then use median = l + ((N/2 − cf) ÷ f) × h.

What if two values are equally common?

The data are bimodal and both are modes. The calculator lists all of them.

What is the empirical relation?

For moderately skewed data, mode ≈ 3 × median − 2 × mean. The calculator shows this as a check.

Last reviewed on 6 October 2026. Found a mistake? Tell us.