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Percentiles and percentile scores

5 November, 2024 by

Percentiles / kth percentile

The kth percentile (or kth centile) gives the value where k percent of the values in the distribution are at or below this level. So if the 10th percentile for height was 1.50m then this would mean that 10% of the population being examined had a height or 1.50m or less, and 90% had a height of 1.50m or more. The percentiles are expressed in the same units as the distribution or measurements.

Specific cases of percentiles are the 25th percentile which is known as the lower quartile, the 50th percentile which is known as the median, and the 75th percentile which is known as the upper quartile. When all values are listed in order, the median is the middle value – half of the values are the median or below and half the values are the median or above. For instance, the median age of three people aged 30, 28 and 32 years is 30 years as 30 is the middle value when these are placed in order of magnitude (28, 30 and 32). If there was another person aged 70 years included, then the median would be 31 years which is the average or mean of the middle two values (30 and 32) when all values were placed in order (28, 30, 32 and 70). Similarly, the lower quartile, upper quartile and percentiles illustrate the value at which a certain percentage of the values are equal to or below that value. As the median is in the middle, it measures a ‘typical’ value, but the most common measurement of a ‘typical value’ is the average or mean, but also the mode (most common value) can also be used.

The percentiles are particularly useful to examine the spread or variability within a distribution or set of values when the distribution is skewed (where a small number of values have particularly high values or a small number of values have particularly low values).

Percentile scores

The percentile scores or percentile ranks are slightly different, but related. These are expressed as a percentage, and give the rank of a particular case relative to all cases expressed as a percentage. A common use is in relation to academic scores, for example, a particular pupil had a test score that was in the top 10% of their class. The Index of Multiple Deprivation is often divided into percentage scores. For the Index of Multiple Deprivation 2019, Hull was ranked 4th out of 317 local authorities in terms of deprivation, and this means that it is in the bottom 2% (4/317 is 1.3%). There are 2% of local authorities in England when the Index of Multiple Deprivation 2019 was produced that were as equally deprived or more deprived compared to Hull. Similarly for other measures, the percentile scores can be calculated to give an indication of the rank. The Index of Multiple Deprivation 2019 was produced for lower geographical levels, and is originally produced at lower layer super output area levels (2011 lower layer super output area following the 2011 Census), and the Access to Healthy Assets and Hazards index has also been produced for lower layer super output area levels (2011 lower layer super output area following the 2021 Census). Thus areas of Hull can be ranked out of all lower layer super output area levels in England, and a specific area can be deemed to be in the bottom 10% of areas of England or the top 25% of areas of England, etc. Following population changes in the 2021 Census, a small number of the lower layer super output area levels were changed, and there are 33,755 lower layer super output areas in England based on the 2021 lower layer super output areas following the 2021 Census. All Hull’s 168 lower layer super output areas can be ranked out of 33,755 in relation to England, but this would be not as easy to interpret as percentages. So these ranks have been converted into percentile scores to denote where each of Hull’s lower layer super output areas sit in relation to all lower layer super output areas in England for the different indicators measured within the Access to Healthy Assets and Hazards index. Thus if a geographical area in Hull had a percentile score of 50 this would mean that half of areas in England had a value equal to this or lower, and half of areas in England had a value equal to this or higher. If another geographical area in Hull had a percentile score of 12 this would mean that 12% of areas in England had a value equal to this or lower, and 88% of areas in England had a value equal to this or higher.

 

Also see Median, Mean (or Average) or Mode.

Also see Lower Layer Super Output Areas, Index of Multiple Deprivation, and Access to Healthy Assets and Hazards Index.

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