Tuesday, May 17, 2016

Daily Regents: Box-and-Whisker Plot

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

June 2014, Questions 32

32. Robin collected data on the number of hours she watched television on Sunday through Thursday nights for a period of 3 weeks. The data are shown in the table below.
Using an appropriate scale on the number line below, construct a box plot for the 15 values.

You have two choices.

First, you can put the data into order and then find the Five-Number Summary: the minimum, Q1, median, Q3, and maximum.

The numbers in order are: 1. 1.5, 1.5, 2, 2, 2.5, 2.5, 3, 3, 3, 3.5, 4, 4, 4.5, 5.
The median is the middle number. There are 15 numbers and the 8th is the middle. That is 3
Q1 is the middle of the lower seven numbers. The 4th number is 2.
Q3 is the middle of the upper seven numbers. The 11th number is 4.
The minimum is the 1st (lowest) number, 1. The maximum is the last (highest) number, 5.

So the Five-Number Summary, and the numbers that will be used to make the Box-and-Whisker Plot, are 1, 2, 3, 4, and 5. (Note: It will NOT always work out so nicely.)

Make a scale on the number line. There is enough room to number it from 0 to 5, counting by 1/2. (That is, every two spaces is 1.) You could use a scale of 1, if you like, but your graph will be smaller than mine. That's okay.

Put a point above each number in our Five-Number Summary: 1, 2, 3, 4, 5.
Draw a box around the middle three with a line through the median.
Draw whiskers connecting the first two points and the last two points.
You're done.

The second method is to use the Graphing Calculator. Take a look at the 10 figures in the diagram below. Don't let the 10 screens frighten you.

If you use this method, make sure you copy some of the information onto the test so you will get points for showing work. In particular, the Five-Number Summary would be good.

To use the calculator, press the STAT key. You should see Figure 1. You need to EDIT a List -- fill it with the data that you will be using. Press (1). Figure 2 shows some of the data that was entered into the first list, L1. Enter all 15 numbers. Now you are ready to plot you graph.

Press STAT again. When you get the menu, hit the right arrow to get to the CALC menu. See 1-Var Stats? That's what we want: 1 variable statistics. Press Enter twice.

You will get a scrollable screen of information. Scroll down to see the Five-Number Summary (Figure 6).

Press 2nd and Y= to get to the STAT PLOT screen (Figure 7) and press ENTER to bring you to the Plot page (Figure 8). Make sure that ON is highlighted, and arrow over to the icon that looks like a box-and-whisker plot and press ENTER.

If you press Graph, your graph won't appear because the window is formatted from -10 to 10 on the x-axis. You need to adjust this. Press ZOOM and then press 9: ZoomStat. Your box-and-whisker plot will appear. Put the graph on the paper, using the points that the 1-Var Stats function gave you.

Any questions?

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.

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