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(7) 2. The next two questions will ask you to draw and describe box plots. For these box plots, please do not make any attempt to identify outliers or to plot outliers separately (i.e. have the box plot be a visualization of the five number summary for the data set). (a) Draw a box plot for a data set that shows skewness to the right. Explain generally what it means for a data set to be skewed to the right, and briefly describe how you selected values for the five number summary to depict skewness to the right. 12 (b) Where, roughly, would you expect the mean to be located on the boxplot you drew in part (a)? [2] (c) Draw a box plot for a data set where the median is 10, the inter-quartile range is 4, and whose histogram would be symmetrical and approximately bell-shaped. [2] (d) Suppose every data value in the data set from part (c) was duplicated (i.e. if the original data set was the three numbers 1,4,7, after duplication the set would be the six numbers 1,1,4,4,7,7). How would you expect the shape of your boxplot to change? Justify your answer with reference to the definitions of the values included in the five-number summary. (7) 2. The next two questions will ask you to draw and describe box plots. For these box plots, please do not make any attempt to identify outliers or to plot outliers separately (i.e. have the box plot be a visualization of the five number summary for the data set). (a) Draw a box plot for a data set that shows skewness to the right. Explain generally what it means for a data set to be skewed to the right, and briefly describe how you selected values for the five number summary to depict skewness to the right. 12 (b) Where, roughly, would you expect the mean to be located on the boxplot you drew in part (a)? [2] (c) Draw a box plot for a data set where the median is 10, the inter-quartile range is 4, and whose histogram would be symmetrical and approximately bell-shaped. [2] (d) Suppose every data value in the data set from part (c) was duplicated (i.e. if the original data set was the three numbers 1,4,7, after duplication the set would be the six numbers 1,1,4,4,7,7). How would you expect the shape of your boxplot to change? Justify your answer with reference to the definitions of the values included in the five-number summary