As mentioned earlier, the median is the 50 percentile or the 2 quartile (Q ). Percentiles and quartiles are both quantiles—values that divide data into equal groups each containing the same percentage of the total data. Percentiles divide the data into 100 parts, while quartiles do so into four (25%, 50%, 75%, and 100%).
Since quantiles neatly divide up our data, and we know how much of the data goes in each section, they are a perfect candidate for helping us quantify the spread of our data. One common measure for this is the interquartile range (IQR), which is the distance between the 3 and 1 quartiles:
The IQR gives us the spread of data around the median and quantifies how much dispersion we have in the middle 50% of our distribution. It can also be useful when checking the data for outliers. In addition, the IQR can be used to calculate a unitless measure of dispersion, which we will discuss next.
Just like we had the coefficient of variation when using the mean as our measure of central tendency, we have the quartile coefficient of dispersion when using the median as our measure of center. This statistic is also unitless, so it can be used to compare datasets. It is calculated by dividing the semiquartile range (half the IQR) by the midhinge (midpoint between the first and third quartiles):
In the next post we will look at how we can use measures of central tendency and dispersion to summarize our data.
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