Final answer:
The interquartile range (IQR) is the difference between the third and first quartile, representing the spread of the middle 50 percent of the data set. A larger IQR indicates greater variability among the middle values. Calculation of IQR is necessary to identify potential outliers in the data.
Step-by-step explanation:
The range of a data set is the difference between the maximum and the minimum value within the set. It is calculated as Range = maximum value − minimum value. The interquartile range (IQR), on the other hand, represents the spread of the middle 50 percent of the data. It is found by subtracting the first quartile (Q1) from the third quartile (Q3), hence IQR = Q3 − Q1. When comparing the spread of different data sets, a larger IQR indicates more variability in the middle 50 percent of the data set.
For example, if given the quartiles for a data set where Q3 = 70 and Q1 = 64.5, we would calculate the IQR by subtracting Q1 from Q3, which gives us IQR = 70 − 64.5 = 5.5. This indicates that the middle 50 percent of the data values are spread out over an interval of 5.5 units.
To determine potential outliers using the IQR, you can apply the rules that any value less than Q1 − 1.5 × IQR or greater than Q3 + 1.5 × IQR may be considered a potential outlier. These potential outliers indicate values that are significantly different from the rest of the data and may require further investigation.