Statistics Assignment Page 1 of 2 Working with Box-and-Whisker Plots 1. The data below shows the number of raisins in each of 14 boxes (1/2 oz.) of three

different brands of raisins: (8 points)

Sun Tyrant: 25, 28, 25, 28, 29, 24, 28, 24, 24, 28, 30, 24, 22, 27 Sun Acrid: 29, 31, 29, 26, 28, 22, 25, 29, 29, 27, 28, 23, 26, 29 Laminatekist: 25, 26, 26, 26, 26, 28, 27, 26, 25, 28, 24, 28, 27, 25

A. Compute the median, lower and upper quartiles, and interquartile range for

each data set. NOTE: We are using the following definitions in this Assignment and course: when there's an odd number of observations in a group, the median is the middle number. When there's an even number of observations in a group, the median is (n+1)/2. The Interquartile Range, IQR, is Q3 – Q1, where Q3 is the median number of the top 50% and Q1 is the median of the bottom 50% of scores. (We are not using fences.)

B. Construct three different modified box-and-whisker plots and place them on

the same horizontal axis, labeling the axes, and labeling Q1, Q3, the median and the mean on the boxes.

C. What conclusions can you make about the shape of the distributions by looking

at the three box plots? Are the distributions symmetric or skewed in one direction? Justify your answer.

D. For which brand are you more likely to end up with a box with a fewer raisins?

Justify your answer. 2. Here is a set of data of college GPAs from a sample of students who completed an AP

course in statistics in their senior year at a fictional high school: (9 points)

3.8, 3.8, 3.9, 3.9, 3.5, 3.5, 3.0, 3.5, 3.8, 4.0, 3.5, 2.5, 2.4, 1.9, 4.0, 3.8, 3.7, 3.5, 3.9, 3.2

A. Construct a histogram of the GPA data using a class width of 0.3, and a

minimum x-value of 1.9, and be sure to label both axes. B. Construct a modified box-and-whisker plot using the GPA data and report the

values of the five-number summary, labeling the axes, and labeling Q1, Q3, the median and the mean on the boxes.

C. Describe the shape of the distribution of GPAs in terms of symmetry (is it

skewed?) and outliers. Use evidence from the two types of plots to support your answer.

Statistics Assignment Page 2 of 2 Working with Box-and-Whisker Plots 3. The Houses of Parliament in Ghyronmia (a hypothetical small country) have two political

parties: the Purple Party and the Chartreuse Party. Twenty different “tax cut” bills came up in the most recent Parliamentary session. If senators voted yes, they were in support of a tax cut. The number of times (out of a possible 20) each senator voted yes is shown below: (8 points)

Number of times senators from each party voted yes to a tax cut bill: Purple: 17, 18, 20, 15, 12, 15, 17, 19, 20, 17, 20, 18, 15, 9, 14, 16, 17, 14, 3, 15 Chartreuse: 11, 13, 12, 9, 17, 11, 10, 14, 7, 8, 8, 11, 12, 12, 13, 12, 14, 10, 10, 10

A. Construct modified box-and-whisker plots for each data set on the same

horizontal axis. Please indicate the values of Q1, median, and Q3 on the different plots.

B. Compute the IQR for each data set. C. Compare the shapes of the two distributions (skew and outliers) and the

amount of variation in the distributions. What do these plots tell you about the policies of Chartreuse and Purples in this particular state during this particular legislative session? What do the outliers tell you about the behavior of a few of the senators?

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