Q1. Find the mean of 4, 6, 8, 10, 12.
Sum = 4 + 6 + 8 + 10 + 12 = 40
Number of values = 5
Mean = 40 / 5 = 8
Statistics — Class 10
Three ways to describe "the middle" of data. Paste your numbers to get the mean, median and mode, then learn the grouped-data methods.
MeanThe average: sum of observations ÷ number of observations. For grouped data, mean = Σfᵢxᵢ / Σfᵢ.
MedianThe middle value when the data is arranged in order (or Σf/2-th value for grouped data).
ModeThe value that occurs most often. For grouped data, mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)]×h.
Empirical relationMode = 3 × Median − 2 × Mean (a handy approximate link).
Mean · Median · Mode calculator Interactive
Enter a list of numbers (comma separated) to get the mean, median, mode and range.
Mean—
Median—
Mode—
Range—
Numericals practice Interactive
Empirical-relation problems with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Mean (grouped) | x̄ = Σfᵢxᵢ / Σfᵢ |
| Median (grouped) | l + [(n/2 − cf)/f]×h |
| Mode (grouped) | l + [(f₁−f₀)/(2f₁−f₀−f₂)]×h |
| Empirical relation | Mode = 3·Median − 2·Mean |
Common mistakes & exam wins
- Always arrange the data in order before finding the median.
- For an even number of values the median is the average of the two middle ones.
- A data set can have no mode, one mode, or more than one mode.
- Remember the link: Mode = 3·Median − 2·Mean.
Frequently asked questions
What is the difference between mean, median and mode?
Mean is the average, median is the middle value, and mode is the most frequently occurring value.
What is the empirical relationship between them?
Mode = 3 × Median − 2 × Mean.
How do you find the median of grouped data?
Median = l + [(n/2 − cf)/f] × h, where l is the lower limit of the median class.