Final answer:
The interquartile range (IQR) represents the spread of the middle 50 percent of a data set and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). It also helps in identifying potential outliers in the data.
Step-by-step explanation:
The interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the middle 50 percent of a data set. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). To elaborate:
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- First Quartile (Q1): This is the median of the lower half of the data set, not including the median if the number of data points is odd.
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- Third Quartile (Q3): This is the median of the upper half of the data set, not including the median if the number of data points is odd.
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- The IQR is found by the formula IQR = Q3 - Q1.
If, for example, Q1 is 2 and Q3 is 9, the IQR is calculated as 9 minus 2, resulting in an IQR of 7.
In addition to providing insight into the spread of the central portion of the data set, the IQR can also be used to identify potential outliers. These are values that fall more than 1.5 times the IQR above Q3 or below Q1.