A.P. Statistics

1. A.P. Statistics Presentation 1-4 Histograms

2. Histograms • Topics in this lesson: • Histogram Basics • Relative Frequency Histograms • Creating Histograms on the TI 83+/84+ Calculator • Manipulating Histograms • Histograms with StatCrunch

3. Histogram Basics • The most significant variable in constructing a histogram is the bin or class width. Follow the link below. • http://davidmlane.com/hyperstat/A28364.html • Only read the histogram page, do not proceed to the next section.

4. Histogram Basics The height of this bin is at approximately 18 which means there are 18 observations between 140 and 160. These numbers on the vertical axis are all counts which makes this a frequency histogram. This bin ranges from 140 to 160.

5. Relative Frequency Histograms • There are also relative frequency histograms as well. • The difference is instead of each vertical bar's height representing the frequency of data in the bin, the vertical height represents the proportion of data values that fall into that bin (thus relative).

6. Relative Frequency Histograms • Consider the data: • Cost per ounce of various shampoos (in cents) • The frequency histogram would look like:

7. Relative Frequency Histograms • The relative frequency histogram would look like: • The frequency histogram would look like: • Notice the difference in the vertical scales! • The frequency histogram shows how many of the shampoos costs fall in the interval. • The relative frequency histogram shows the proportion (which you could convert to a percentage) of shampoos whose price fall in the interval.

8. Creating Histograms on the TI 83+/84+ Calculator • To create a histogram on the calculator you first need to enter data into your stat/list editor. Enter the following data into your list. • The data represents the poverty rates in the eastern United States in 1999. • Enter just the Poverty number into “L1” on the calculator.

9. Creating Histograms on the TI 83+/84+ Calculator • To create a histogram on the calculator you first need to enter data into your stat/list editor. Enter the following data into your list. • The data represents the poverty rates in the eastern United States in 1999. • Enter just the Poverty number into “L1” on the calculator.

10. Creating Histograms on the TI 83+/84+ Calculator • If you need help entering the data, try going to the following site: • http://www.prenhall.com/divisions/esm/app/calculator/medialib/Technology/Documents/TI-83/desc_pages/list-edit.html

11. Creating Histograms on the TI 83+/84+ • Then, to create the histogram, go to stat plot (2nd ? Y=) and choose plot 1. • Turn the plot on, choose the miniature histogram (by hitting enter while the cursor is over it), choose L1 for the xlist and 1 for the freq (frequency; 1 since each number appears in the list once). • Then use the zoom button and choose option 9:ZoomStat. If you need help, try the following site (you will need to scroll down a bit to find the histogram information): • http://www.prenhall.com/divisions/esm/app/calculator/medialib/Technology/Documents/TI-83/desc_pages/stat-plot.html • If at any time you have difficulty operating the calculator, be sure to come to the chat during office hours, post in the discussion board, or e-mail me.

12. Histogram Applet • The most significant variable in constructing a histogram is the bin or class width. • Follow the link at the end of this item and use the histogram applet there to assist you in completing assignment 1.4. • http://www.shodor.org/interactivate/activities/histogram/index.html

13. Constructing the Histogram with StatCrunch • In completing assignments, you may need to submit histograms within your electronic documents. • Feel free to use StatCrunch for this but be sure you are able to construct a histogram on your calculator. • Be sure you know how to construct both frequency AND relative frequency histograms. • http://www.statcrunch.com