Unit 1 Lessons 1 & 2 Quiz



Box-and-Whisker PlotsA box-and-whisker plot is a convenient way to display the five-number summary. To draw a box-and-whisker plot: Mark the minimum, maximum, median, Q1, and Q3 above the numbers on your number line.Draw a box that represents the middle 50% of the data by drawing a box from Q1 to Q3. The length of the box represents the interquartile range (IQR).Draw a vertical line segment inside the box to show the median.20701039941500Draw “whiskers” to represent the lowest 25% (by connecting Q1 to the minimum value) and highest 25% (by connecting Q3 to the maximum value) of the data.SeptemberHighAverageLow878675797768551071625211635955126964601382726414786857158168571670635517635650187560481971605120735843217760462275645323817466The data set on the right lists the high, average, and low temperatures in Farmington, CT from September 8 to September 23, 2011. Complete the table, using your calculator. (Suggestion: enter the data in L1, L2, and L3)MinQ1MedQ3MaxIQRSxHighAvg.LowThe statistics for the high temperatures are displayed in a box-and-whisker plot below.1905017018000Draw box-and-whisker plots below for the average and low temperatures. Box-and-Whisker Plots on the Calculator33369256921500Use the calculator to make the three box & whisker plots for the temperature data fromproblem 1. You may display them side by side if you use L1 in StatPlot 1, L2 in StatPlot 2, and L3 in StatPlot 3 and turn all plots on. Select either of the two icons for Box & Whiskers shown to the right.Indicate what values you used in the Window menu:Xmin = _____________ Xmax = _____________ Xscl = ________________Ymin = _____________ Ymax = _____________ Yscl = ________________Now change the values of Ymin and Ymax. Does this affect the way the box-and-whisker plots are displayed? Explain.320357514160500Match the box-and-whisker plots on the right to the descriptions they match. WWhich plot has the greatest range? WWhich plot has the greatest IQR? WWhich plot has the greatest Q1? WWhich plot has the greatest median?WWhich plot has the greatest Q3? The following set of data lists the top 18 New York Yankees Salaries for 2011. Find the five-number summary, the range, and the interquartile range. Then make a box-and-whisker plot.RKPlayerSalary (millions)1Alex Rodriguez32.02CC Sabathia24.33Mark Teixeira23.14A.J. Burnett16.55Mariano Rivera14.96Derek Jeter14.77Jorge Posada13.18Robinson Cano10.09Nick Swisher9.1RKPlayerSalary (millions)10Rafael Soriano9.011Curtis Granderson8.312Russell Martin4.013Phil Hughes2.714Eric Chavez1.5Andruw Jones1.5Freddy Garcia1.517Boone Logan1.218Bartolo Colon0.9(Source: )Five Number Summary:Michael Jackson’s Thriller is the top-selling album of all time, with 110 million albums sold world-wide. The next 24 top-selling albums are below.AlbumAlbums sold(millions)Thriller, Michael Jackson110Back in Black, AC/DC49The Dark Side of the Moon, Pink Floyd45The Bodyguard, Whitney Houston44Bat Out of Hell, Meatloaf43Eagles: Their Greatest Hits, 1971–197542Dirty Dancing, Various Artists42Millennium, Back Street Boys40Saturday Night Fever , Bee Gees40Rumours, Fleetwood Mac40Come On Over, Shania Twain40Led Zeppelin IV37Jagged Little Pill, Alanis Morisette33 AlbumAlbums sold (millions)Sgt. Pepper, The Beatles32Falling Into You, Celine Dion32Music Box, Mariah Carey32Dangerous, Michael Jackson321, The Beatles31Let’s Talk About Love, Celine Dion31Goodbye Yellow Brick Road, Elton John31Spirits Having Flown, Bee Gees30Born in the U.S.A., Bruce Springsteen30Brothers in Arms, Dire Straits30Immaculate Conception, Madonna30Bad, Michael Jackson30Enter all of the data into L1. Using the 1-Var Stats command, find the five-number summary, the range, and the interquartile range, mean and standard deviation of the albums sold.With ThrillerminQ1medianQ3maxrangeIQRmeanSxAlbums sold (millions)Apply the 1.5 times IQR rule to find the fences for this set of data. Upper fence = ____________________Lower fence = ______________________According to the 1.5 times IQR rule, can Thriller be considered an outlier? Explain.Enter the data without Thriller in L2. Using the 1-Var Stats command, find the five-number summary, the range, and the interquartile range, mean and standard deviation of the albums sold for the data without Thriller.Without ThrillerminQ1medianQ3maxrangeIQRmeanSxAlbums sold (millions)Compare the charts made in parts (a) and (d). Which statistics were most affected when the Thriller’s albums sold was removed from the list?Which statistics were least affected when Thriller’s albums sold was removed from the list?Statisticians often prefer a statistic that is not affected by outliers. Which measure of spread do you think they prefer? The range or the IQR? pare the values for the mean and standard deviation (Sx) for the data with and without the Thriller album. Describe how the outlier affected the mean and standard deviation of the data set. Now make a box & whiskers plot on your calculator using the album data from problem 7. Turn off all plots except for one and use the data in L1 (all albums including Thriller). Adjust the values in the Window menu so that the entire plot shows.First select the icon “Box and Whiskers Showing Outliers.” Make a sketch of what you see in the space below. Remember to scale your graph.Then select the icon “Box and Whiskers without Outliers.” Make a sketch of what you see in the space below. Remember to scale your graph.When there is an outlier, what is the effect of changing the box-and-whisker display on the length of the whiskers?Now have the calculator make a histogram for the albums sold data. Make a sketch of what you see in the space below.How can you tell from the histogram that there is an outlier in this set of data?Make up a data set with ten values, listed in order, which could have the box-and-whisker plot shown below.16160759652000 Write a story (context) to go along with your data in (9). ................
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