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Mean, median, mode and range calculator

11 values

Mean of 11 values

44.27

Median
42
Range
25
Inter-quartile range
13

Working

  1. In order: 35, 35, 38, 39, 41, 42, 44, 47, 51, 55, 60 (11 values).
  2. Mean = total ÷ number of values = 487 ÷ 11 = 44.27.
  3. Median = the middle value, at position (n + 1) ÷ 2 = 6: value 6, so 42.
  4. Mode = the most common value: 35 (2 times each).
  5. Range = largest − smallest = 60 − 35 = 25.
  6. Lower quartile at position (n + 1) ÷ 4 = 3: value 3, so 38.
  7. Upper quartile at position 3(n + 1) ÷ 4 = 9: value 9, so 51.
  8. Inter-quartile range = upper quartile − lower quartile = 51 − 38 = 13.

Your result

44.27. The median is 42, the range is 25 and the inter-quartile range is 13; the mode is 35.

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For 11 values in order, the median is the 6th value and the quartiles are the 3rd and 9th values: the inter-quartile range is the upper quartile minus the lower.

Questions people ask

How do you find the median?

Put the values in order and find the middle one, at position (n + 1) ÷ 2. With 11 values it is the 6th; with 10 values it is halfway between the 5th and 6th.

How do you work out the interquartile range?

Put the values in order. The lower quartile is at position (n + 1) ÷ 4 and the upper quartile at 3(n + 1) ÷ 4. Take the lower quartile from the upper. With 11 values the quartiles are the 3rd and 9th values.

Why use the interquartile range instead of the range?

The range uses only the two most extreme values, so one odd reading can stretch it. The inter-quartile range covers the middle half of the data and ignores the extremes, so it shows how spread out the typical values are.

Which average should I use for fieldwork data?

The mean uses every value but is pulled by extremes; the median is the middle value and is not. The mode suits categories, such as the most common land use. If your data has a few very large or very small readings, the median is usually the fairer summary.

Keep going

How we work this out

What it does

Enter a set of numbers to get the mean, median, mode, range, quartiles and inter-quartile range, with each step shown.

Averages and spread for 3 to 60 values: mean, median, mode, range, lower and upper quartiles and the inter-quartile range.

Method

  1. The values are put in order first.
  2. Mean = total ÷ number of values.
  3. Median = the value at position (n + 1) ÷ 2.
  4. Mode = the value or values that appear most often; there is no mode if every value is different.
  5. Range = largest − smallest.
  6. Lower quartile at position (n + 1) ÷ 4, upper quartile at 3(n + 1) ÷ 4; inter-quartile range = upper − lower.