Types of Range (Edexcel GCSE Statistics)

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

• 

• 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

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

• 

• 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

An interpercentile range is the difference between two percentiles for the data set

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

It is necessary to specify which percentiles are to be used

• e.g. the 30^th to 80^th interpercentile range

  • this would be 80^th percentile minus 30^th percentile

• or the 2.5^th to 97.5^th interpercentile range

  • this would be 97.5^th percentile minus 2.5^th percentile

• Note that the 25^th to 75^th interpercentile range is the same as the interquartile range

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

• Like the interquartile range it is not affected by the most extreme values in the data set

• You can choose the percentiles to focus on the part of the data set you are most interested in

An interdecile range is the difference between two deciles for the data set

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

It is necessary to specify which deciles are to be used

• e.g. the 1^st to 9^th interdecile range

  • this would be 9^th decile minus 1st decile

• or the 4^th to 8^th interdecile range

  • this would be 8^th decile minus 4^th decile

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

• Like the interquartile range it is not affected by the most extreme values in the data set

• You can choose the deciles to focus on the part of the data set you are most interested in

Remember the relationship between deciles and percentiles

• The 1^st decile is the same as the 10^th percentile

• The 2^nd decile is the same as the 20^th percentile

• etc.