A box and whisker plot displays the distribution of a dataset by dividing it into quartiles. The plot consists of a box that represents the interquartile range (IQR) and whiskers that extend to the minimum and maximum values of the data.
When Mr. Wilson creates box and whisker plots for each data set, he would observe the following characteristics:
1. Overlap in the data: The overlap in the box part of the plot indicates that there are common values between the two data sets. These common values fall within the 2nd and 3rd quartiles.
2. Overlap within the 1st and 3rd quartiles: If there is overlap within the 1st and 3rd quartiles, it suggests that the middle 50% of values in the two data sets are similar or have some degree of overlap.
3. Variability: The length of the whiskers in the box and whisker plot is an indicator of the variability of the data. A longer whisker suggests greater variability in the data set. Therefore, the data set with the longest whiskers would have the most variability.
In summary, by examining the overlap in the data, overlap within the 1st and 3rd quartiles, and the length of the whiskers, Mr. Wilson can determine the characteristics and variability of each data set using box and whisker plots.
If Mr. Wilson were to make a box-and-whisker plot of each data set, explain the characteristics he should see. (Is there overlap in the data? Is there overlap within the 1st and 3rd quartiles? Does the information shown in the box-and-whisker plots indicate which data set has the most variability?)
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