1.3 Box & Whisker Plots

Transcription

1 1.3 Box & Whisker Plots Box and Whisker Plots or box plots, are useful for showing the distribution of values in a data set. The box plot below is an example. A box plot is constructed from the five-number summary of the data, which includes the minimum value, maximum value, median, lower quartile, and upper quartile. When a set of data is ordered from least to greatest, the lower quartile is the median of the values to the left of the median. The upper quartile is the median of the values to the right of the median.

2 The box plot below shows how the five-number summary corresponds to the features of the box plot. The five-number summary divides a data distribution into four parts. About what percent of the data values fall in each of the following intervals? before the median after the median in the box (between upper and lower quartiles) before the upper quartile after the upper quartile before the lower quartile after the lower quartile between the median and the upper quartile between the median and the lower quartile What do you think the term quartile means?

3 You can compare distributions by displaying two or more box plots on the same scale. Many people consider both quality and price when deciding which products to buy. The box plots above show the distributions of per-serving prices for natural peanut butters and regular peanut butters. In the Peanut Butter Comparisons table (page 6 from your book), refer to the column that gives the price per serving. A. 1. Calculate the five-number summary for the prices of the natural peanut butters. 2. Calculate the five-number summary for the prices of the regular peanut butters. 3. Which box plot above represents the distribution of prices for natural peanut butters and which represents the distribution of prices for regular peanut butters? 4. How do the prices of the natural peanut butters compare with the prices of the regular peanut butters? Explain how you can make this comparison using box plo

4 B. Refer to the plots below and the plots in Question A. 1. Suppose price is the only factor a buyer considers. Is natural peanut butter or regular peanut butter a better choice? Explain. 2. Suppose quality is the only factor a buyer considers. Is natural peanut butter or regular peanut butter a better choice? C. In a box plot, the length of the box represents the difference between the upper and lower quartiles. The difference is called the interquartile range (IQR). 1. What is the IQR for the quality ratings for natural peanut butters? What does it tell you? 2. What is the IQR for the quality ratings for regular peanut butters? What does it tell you?

5 D. Values in a data set that are much greater or much less than most of the other values are called outliers. To decide whether a value is an outlier, first find the IQR. Outliers are data values that are either: greater than 1.5 times the IQR added to the upper quartile, or less than 1.5 times the IQR subtracted from the lower quartile 1. What are the outliers in the quality ratings for the natural peanut butters? 2. What are the outliers in the ratings for the regular peanut butters? 3. On a box plot, outliers are sometimes indicated with asterisks (*). The box plots in Question B and the box plots below show the same data distributions. a. In the Question B plots, the whiskers extend to the minimum and maximum values. What values do the whiskers in the plots above extend to? b. Describe how you would construct a box plot if you wanted to show the outliers in the distribution.

6 E. 1. Make a pair of box plots to compare the quality ratings for creamy and chunky peanut butters (information can be found on page 6). 2. What is the IQR for each distribution? Use the IQR to determine whether there are any outliers. 3. Based on quality ratings, are creamy peanut butters or chunky peanut butters a better choice? Explain.