Statistics Lecture Notes

Subsection The Shape of a Distribution

One reason for going through the trouble of displaying data in a histogram is to determine the basic shape of your data. The four most common shapes are:

Subsection Create Histograms and Frequency Distributions from Data Using the TI-84 Plus

The TI-84 Plus calculator can generate histograms and frequency distributions from raw data. Normally, one would first sort their data, separate it into classes to create a frequency distribution and then plot the frequency distribution with vertical bars to generate a histogram. However, when we use the calculator, we will first generate the histogram and then read off the frequencies from the height of each bar to create the frequency distribution.

The data below was generated by asking each student from a statistics class to give their height in inches.

To create a histogram of the height data above do the following:

1. Enter the data in the above table into list 1. This can be done by pressing stat, 1 and then using the cursor to select list 1.

2. Press 2nd, y= to enter the STAT PLOTS menu. (Make sure Plot2 and Plot3 are OFF by pressing 4 (PlotsOff) if necessary.) Choose Plot1 by pressing 1.

   

3. Make your screen match the image below:

   

4. Press zoom, 9. This will cause the calculator to bin the data according to its internal algorithm and display the histogram.

   

   You can press trace and move the cursor to check the class/bin limits the calculator chose.

5. Press window and modify Xmin, Xmax, Xscl, Ymin and Ymax to match the screen below. Setting Xscl to 2 changes the class/bin width to 2 (inches).

   

6. Press graph to display the new histogram.

   

   You can use the trace and cursor keys to check the lower and upper class limits for each class as well as the count or frequency. The screenshot above indicates that the class of heights between 62 and 64 inches contains 7 individuals.

7. If you use the trace feature to determine the frequency for each bar (class) you can generate a frequency distribution. On the TI-84 Plus calculator, instead of using the classes we instead enter the class midpoints in list 2 and the frequencies in list 3.

   Height	Freq.
   60–<62	1
   62–<64	7
   64–<66	1
   66–<68	2
   68–<70	6
   70–<72	5
   72–<74	1
   74–<76	0
   76–<78	0
   78–<80	1
   Sum:	24

   

8. Next, we can have the TI-84 Plus calculator generate relative frequencies for us. Let's store the relative frequencies in list 4. Go to stat, 1 and edit list 4. Cursor to the list 4 header, i.e. cursor up until the header is highlighted (shaded black) and press the following:

   2nd3÷2ndstat,

   choose CALC and then press the following keys:

   52nd3)enter

   

   
   The resulting frequency and relative frequency distributions are reproduced here.

   Height	Freq.	Rel. Freq.
   60–<62	1	.04167
   62–<64	7	.29167
   64–<66	1	.04167
   66–<68	2	.08333
   68–<70	6	.25000
   70–<72	5	.20833
   72–<74	1	.04167
   74–<76	0	.00000
   76–<78	0	.00000
   78–<80	1	.04167
   Sum:	24	1.00000

Subsection Creating Histograms from Frequency Distributions Using the TI-84 Plus

Perhaps you don't have access to raw data, but you do have a frequency distribution of the data, then you can still create a histogram of the data.

In this section, we will continue using the height data in table Table 2.2.3. Further, we will assume you have the same list data generated in that example in lists 2,3 and 4 of your calculator.

To create a histogram from a frequency distribution:

1. Go to STAT PLOTS by pressing 2nd y= and choosing Plot1. Assuming you have the class midpoints in list 2 and the frequencies in list 3, we can generate a histogram by filling out the Plot1 menu to look like below:

   

2. If you have not changed any settings in window, then you can just press graph to generate the histogram. If you have changed window settings use ZoomStat by pressing zoom 9.