Statistics
Enter your numbers — from a measurement, a survey or a die — and get the most important statistics with explanations.
Your numbers
Separate the numbers with semicolons, spaces or line breaks. A decimal comma also works: 3,5 is read as 3.5.
9 numbers read
Answer
Mean
7.44
Median
7
Mode
7
Quantity
9
Sum
67
Smallest · largest
2 · 12
Range
10
Quartiles (lower · median · upper)
5.5 · 7 · 10
Interquartile range
4.5
Quartiles by the counting method: the lower quartile is the median of the lower half, the upper quartile of the upper half. If the count is odd, the middle number is left out. Source: Schacks noter, Matematik C, ch. 5 «Ugrupperet statistik» (2024). Spreadsheets and GeoGebra may give slightly different numbers — they calculate quartiles differently.
More statistics: standard deviation, outliers (extreme values)
Standard deviation, population (divide by n)
2.91
Standard deviation, sample (divide by n − 1)
3.09
Outliers (more than 1.5 interquartile ranges outside the quartiles)
none
Minimum 2 · Lower quartile 5.5 · Median 7 · Upper quartile 10 · Maximum 12
How to work it out
- 1Sorted: 2; 4; 7; 7; 7; 8; 10; 10; 12The median and quartiles are counted from the smallest number, so the numbers must be put in order first.
- 2Mean = 67 / 9 = 7.44The sum shared out evenly over all the numbers.
- 3Median = the middle number = 7Half of the numbers are below the median and half above. A single very large number does not move it — but it does move the mean.
- 4Lower quartile = the median of 2; 4; 7; 7 = 5.5The count is odd, so the middle number (the median) is not included in either half.
- 5Upper quartile = the median of 8; 10; 10; 12 = 10
- 6Interquartile range = 10 − 5.5 = 4.5This is how wide the middle half of the numbers is — the box in the box plot.
- 7Range = 12 − 2 = 10The distance from the smallest to the largest number.
The formula
mean = the sum / the count
Also called the average.
median = the middle number
Sort the numbers first. If there is an even number of them, take the average of the two middle ones.
mode = the most frequent number
There can be several modes — or none, if all numbers occur equally often.
range = largest − smallest
interquartile range = upper quartile − lower quartile
The lower quartile is the median of the lower half, the upper quartile the median of the upper half.
σ = √( Σ(x − x̄)² / n )
Standard deviation for a population: everyone you want to say something about is included.
s = √( Σ(x − x̄)² / (n − 1) )
Standard deviation for a sample: slightly larger, because a sample typically spreads less than the whole group.
In depth: more numbers and “what if”
What if one number was left out?
| Mean | Median | |
|---|---|---|
| All the numbers | 7.44 | 7 |
| Without the largest (12) | 6.88 | 7 |
| Without the smallest (2) | 8.13 | 7.5 |
Frequency table
| Value | Frequency | Frequency | Cumulative frequency |
|---|---|---|---|
| 2 | 1 | 11.1 % | 11.1 % |
| 4 | 1 | 11.1 % | 22.2 % |
| 7 | 3 | 33.3 % | 55.6 % |
| 8 | 1 | 11.1 % | 66.7 % |
| 10 | 2 | 22.2 % | 88.9 % |
| 12 | 1 | 11.1 % | 100 % |
Relative frequency = frequency / count. Cumulative frequency = the relative frequencies added up to and including that value — this percentage is less than or equal to it.