# Range and Interquartile Range

### This simplest measure of variability is the distance between the lowest score and the highest score in a set of data, also known as the range.  Some researchers simply report the highest and lowest value as the range; others subtract the lowest score from the highest score to give a range statistic.  Thus we can interpret the range statistic is the maximum possible difference between scores in a set of data.  The larger the value of the range statistic, the more variability there is in the set of scores.

A critical weakness of the range statistic is that it is based on two (often extreme) scores and may not reflect the true variability of the distribution.  In other words, it reflects the maximum variability within the distribution, and not the average variability.

### Computing the Range

`Range = Maximum Score – Minimum Score`

The interquartile range (IQR) indicates the scores obtained by the middle 50% of participants.  That is, we ignore the lowest 25% and the highest 25%.  This middle section supplies us with a measure of variability that is resistant to the effects of extreme scores at either end.  To determine the interquartile range, you must first identify the 25th percentile and the 75th percentile.  A critical weakness of the IQR is that it is based on only half of your data.  When it is computed, potentially valuable information is thrown away.

### Computing the Interquartile Range

To obtain the Interquartile Range, follow these steps:

1. Order the scores from low to high.
2. Identify the median of the distribution (middle most score), and mark the scores below the median as a group and the scores above the median as a group.
3. Find the median of the lower half of the scores: That is the 25th Percentile.
4. Find the median of the upper half of the scores: that is the 75th Percentile.
5. Subtract the value of the score at the 25th Percentile from the value of the score at the 75th Percentile to obtain the Interquartile Range.

Note that certain measures of variability are commonly reported with certain measures of central tendency because they have similar restrictions as to which type of data with which they are appropriate.  The interquartile range is most often reported with the median.  Both are insensitive to extreme scores and work well with skewed distributions.

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