Calculate range and interquartile range

Range is the difference between the greatest and least values in an ordered data set, whereas the interquartile range (IQR), $Q_3-Q_1$ , measures the spread of the middle 50% between the lower and upper quartiles. The learner determines quartiles from data lists or box plots, calculates both measures with appropriate units, and interprets range as sensitive to extreme values while IQR is more resistant; standard deviation and inferential analysis are beyond this scope.

Detailed Explanation: Calculate range and interquartile range

To calculate the range and interquartile range (IQR):

Range: greatest value $-$ least value
IQR: $Q_3-Q_1$ , where $Q_1$ is the lower quartile and $Q_3$ is the upper quartile

Example

The times, in minutes, that 12 students took to complete a task were:

4,\ 6,\ 7,\ 8,\ 9,\ 10,\ 12,\ 13,\ 15,\ 16,\ 18,\ 25

The data is already in order from least to greatest.

1. Find the range

The greatest value is $25$ and the least value is $4$ .

\text{Range}=25-4=21

The range is $21$ minutes.

2. Find the quartiles

There are 12 values, so split the list into two equal halves:

Lower half: $4,6,7,8,9,10$
Upper half: $12,13,15,16,18,25$

The lower quartile, $Q_1$ , is the median of the lower half:

Q_1=\frac{7+8}{2}=7.5

The upper quartile, $Q_3$ , is the median of the upper half:

Q_3=\frac{15+16}{2}=15.5

3. Find the IQR

\text{IQR}=Q_3-Q_1

\text{IQR}=15.5-7.5=8

The IQR is $8$ minutes.

The range describes the spread from the very smallest to the very largest value, so it can be strongly affected by an extreme value such as $25$ . The IQR describes the spread of the middle $50\%$ of the data, so it is less affected by extreme values.

Learn by doing: Calculate range and interquartile range

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Statistics - Quartiles - Data Set (No Outliers) to Interquartile Range

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