In a set of data, the quartiles are the values that divide the data into four equal parts. The median of a set of data separates the set in half. The median of the lower half of a set of data is the lower quartile (LQ) or Q1.
The median of the upper half of a set of data is the upper quartile (UQ) or Q3 .
The upper and lower quartiles can be used to find another measure of variation call the interquartile range.
The interquartile range is the range of the middle half of a set of data. It is the difference between the upper quartile and the lower quartile.
Interquartile range = Q3 – Q1 In the above example, the lower quartile is 52 and the upper quartile is 58.
The interquartile range is 58 – 52 or 6.
Data that is more than 1.5 times the value of the interquartile range beyond the quartiles are called outliers .
Semi-interquartile range is one-half the difference between the first and third quartiles. It is half the distance needed to cover half the scores. The semi-interquartile range is affected very little by extreme scores. This makes it a good measure of spread for skewed distributions. It is obtained by evaluating $ \frac {Q3 - Q2}{2} $.
The midquartile range is the numerical value midway between the first and third quartile. It is one-half the sum of the first and third quartiles. It is obtained by evaluating $ \frac {Q3 + Q2}{2} $.
(The median, midrange and midquartile are not always the same value, although they may be.)
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