Box plot maker
Box plot
Median 41
The middle half of the data runs from 35 to 47, an interquartile range of 12.
- Lower quartile
- 35
- Upper quartile
- 47
- Interquartile range
- 12
Working
- In order: 12, 31, 35, 38, 40, 41, 42, 45, 47, 52, 55 (11 values).
- Median at (n + 1) ÷ 2 = 6: the 6th value, 41. Lower quartile at (n + 1) ÷ 4 = 3: the 3rd value, 35. Upper quartile at 3(n + 1) ÷ 4 = 9: the 9th value, 47.
- Interquartile range = 47 − 35 = 12. 1.5 × IQR = 18.
- Outlier limits: below 35 − 18 = 17 or above 47 + 18 = 65. Outlier: 12, marked with a cross; the whiskers stop at the last values inside the limits, 31 and 55.
Your result
Median 41. The middle half of the data runs from 35 to 47, an interquartile range of 12. One value is an outlier: 12.
Practise box plots
Your mock plan, in three taps
A box plot shows five numbers: the lowest value, lower quartile, median, upper quartile and highest value; any value more than 1.5 × IQR beyond a quartile is an outlier.
Questions people ask
How do you find the quartiles for a box plot?
Order the data. With n values the lower quartile is the (n + 1) ÷ 4th value and the upper quartile the 3(n + 1) ÷ 4th. With 15 values they are the 4th and 12th, and the median is the 8th.
How do you know if a value is an outlier?
Work out 1.5 × the interquartile range. Anything more than that below the lower quartile or above the upper quartile is an outlier. GCSE Statistics also counts a value more than 3 standard deviations from the mean.
How do I compare two box plots?
Compare an average and a spread, in context. Say which has the higher median, so is higher on average, and which has the smaller interquartile range, so is more consistent. Use the numbers from both plots.
Where do the whiskers go when there is an outlier?
The outlier is marked with a cross on its own, and the whisker stops at the largest (or smallest) value that is not an outlier.
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How we work this out
What it does
Enter your data to draw a box plot, with the quartiles, interquartile range and outliers worked out step by step.
5 to 60 values in a data set, and an optional second data set drawn on the same scale.
Method
- Put the values in order; the median is at (n + 1) ÷ 2, the lower quartile at (n + 1) ÷ 4 and the upper quartile at 3(n + 1) ÷ 4.
- Interquartile range = upper quartile − lower quartile.
- An outlier is below lower quartile − 1.5 × IQR or above upper quartile + 1.5 × IQR. It is drawn as a cross and the whisker stops at the last value inside the limits.