Hot Coffee! Box Plots Work in groups of two. Turn in one activity per group. Person to whom the activity will be returned: _____________________ Other group member: _____________________ I. A good travel mug should keep coffee warm awhile. To compare how well coffee mugs do this, a statistics student fills each of four different brand coffee mugs with water heated to 180 F, covers them, and measures the temperature drop after 45 minutes. He does this 10 times per mug. The temperature decreases are in the table below. Water Temperature Drops from 180 F for Four Travel Mugs Brand A Brand B Brand C Brand D

22 12 29 26

15 15 22 15

23 17 32 27

24 17 22 31

19 25 24 25

22 15 44 25

22 13 27 26

15 14 28 27

23 12 33 28

21 18 16 28

Use the instructions from your book to get the quartiles. Then draw and label a nice big box plot of the temperature drops for Brand A in the space below.

Now use your calculator to get the quartiles for Brand A. Pres STAT and select Edit. Put the data for Brand A into a list. Then press STAT, arrow to CALC, and select 1-Var Stats. Enter the list name and press Enter. Are the quartiles from your calculator the same as the quartiles you calculated by hand? Yes

No

Now let’s use Minitab to make box plots. Enter these data into a Minitab worksheet by putting the Brand A temperature drops in the first column, Brand B temperature drops in the second column, etc. Be sure to label the columns `Brand A’, `Brand B’, etc. Once the data are entered, make a boxplot for the temperature drops for each brand by clicking Graph – Boxplot – Multiple Y’s – Simple – OK. Select columns c1 – c4 for the graph variables and click OK. The Minitab box plot for Brand A differs from the one you made by hand. The quartiles are not the same! Why is this so, and is it okay?

__________________________________________________________ __________________________________________________________

__________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ Which brand has the largest spread or variation? _____________ Which brand has the smallest range? _____________ Which brand has the largest interquartile range (IQR)? _____________ Which brand has the smallest interquartile range (IQR)? _____________ Which brand keeps coffee the warmest after 45 minutes? _____________ Which brand has the smallest median temperature decrease? _____________ Give two possible causes for the outlier in the Brand B data.

__________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ II.

III.

Match each brand with one of the four distribution descriptions below: Brand A

left-skewed, median at about 22 F

Brand B

fairly symmetric with a large spread

Brand C

median at about 26 F, Q1 = 25 F

Brand D

fairly symmetric with an outlier at about 25 F

Make up your own data sets E and F such that E has a larger range than F, but F has a larger standard deviation than E. They don’t have to have many data values.