Types of Range (Edexcel GCSE Statistics)

Range & Interquartile Range (IQR)

What is the range of a data set?

• The range of a data set is the difference between the largest and smallest values in the data set

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  • If the data has units (seconds, cm, etc.), then the range has the same units as the values in the data set

• The range is a measure of dispersion (i.e. a measure of spread)

  • An average for a data set tells you what a 'typical' data value is

  • The range tells you how spread out the data is around that average

    • A small range means all the data values are close to the average

    • A large range means that some of the data values are far from the average

What is the interquartile range (IQR) of a data set?

• The interquartile range (IQR) of a data set is the difference between the upper quartile (UQ) and lower quartile (LQ) of the data set

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  • The IQR has the same units as the values in the data set (seconds, cm, etc.)

• The interquartile range is also a measure of dispersion (i.e. of spread)

  • Half of the data values in a data set are between the LQ and UQ

    • This 'middle half' of the data set may be thought of as the 'most typical' half of the data

    • The IQR tells you how spread out the values in that middle half are

• The largest and smallest values in a data set do not affect the interquartile range

  • This makes the IQR a better measure of spread for data sets with extreme values (i.e. extremely large or extremely small)

    • Such 'untypical' values can cause the range of a data set to be large

    • The range would then give a misleading idea about how spread out most of the data really is