What is an Interquartile Range?
The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie. That’s why it’s preferred over many other measures of spread (i.e. the average or median) when reporting things like school performance or SAT scores.
The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles.
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.
- Q1 is the "middle" value in the first half of the rank-ordered data set.
- Q2 is the median value in the set.
- Q3 is the "middle" value in the second half of the rank-ordered data set.
The 75th and 25th percentiles
As you know, the median is a measure of the central tendency of the data but says nothing about how the data is distributed in the two arms on either side of the median. Quartiles help us measure this.
Thus if the first quartile is far away from the median while the third quartile is closer to it, it means that the data points that are smaller than the median are spread far apart while the data points that are greater than the median are closely packed together.
Another way of understanding quartiles is by thinking of those as medians of either of the two sets of data points differentiated by the median. In this case, the first quartile is the median of the data that is smaller than the full median while the third quartile is the median of the data that is larger than the full median. Here full median is used in the context of the median of the entire set of data.
It should be noted that a quartile is not limited to discrete variables but also applies equally well to continuous variables. In this case, you will need to know the data distribution to figure out the quartiles. If the distribution is symmetric, like a normal distribution, then the first and third quartiles are equidistant from the median in either direction.
Source: Explorable
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