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How to create a Histogram for Discrete Data

 

Example: The manager of a Wendy’s fast-food restaurant is interested in studying the typical number of customers who arrive during the lunch hour. The data in table below represent the number of customers who arrive at Wendy’s for 40 randomly selected 15-minute intervals of time during lunch.   

                               

To create a histogram of this example, you have two choices: 1): enter all the individual data points from the table below into one column

 

                  

 

Or 2): enter the data values into one column and the frequencies into another column using the below table. For this example, we will use the table.

 

 

To create this histogram, you must enter information into List1 (L1) and List2 (L2) on your calculator. You will enter the “number of customers” into L1 and the frequencies into L2. Press STAT and the Statistics Menu will appear.

 

 

Press ENTER and lists L1, L2, and L3 will appear.

 

 

If the lists already contain data, you should clear them before beginning this example. Move your cursor so that the List name (L1, L2, or L3) of the list that contains data is highlighted.

 

 

Press CLEAR ENTER. Repeat this process until all three lists are empty.

 

 

To enter the data values into L1, move your cursor so that it is positioned in the 1st position in L1. Type in the first value, 1, and press ENTER or use the blue down arrow. Enter the next value, 2. Continue this process until all 11 data values are entered into L1. Now use the blue up arrow to scroll to the top of L1. As you scroll through the data, check it. If a data point is incorrect, simply move the cursor to highlight it and type in the correct value. When you have moved to the 1st value in L1, use the right arrow to move to the first position in L2. Enter the frequencies into L2.

 

 

Before graphing the histogram make sure that there are no functions in the Y-registers. To do this, press Y= key. If there are any functions stored in any of the Y-values, simply move the cursor to the line that contains a function and press CLEAR. Now you are ready to graph the histogram. Press 2nd

 (located above the Y= key.)

 

 

Select Plot 1 by pressing ENTER.

 

 

Notice that Plot 1 is highlighted. On the next line, notice that the cursor is flashing on ON or OFF. Position the cursor on ON and press ENTER to select it. The next two lines on the screen show the different types of graphs. Move your cursor to the symbol for histogram (3rd item in the 1st line of Type) and press ENTER.

 

 

The next line is Xlist. Use the blue down arrow to move to this line. On this line, you tell the calculator where the data values are stored. In most graphing situations, the data are entered into L1 so L1 is the default option. Notice that the cursor is flashing on L1. Push ENTER to select L1. The last line is the frequency line. On this line, 1 is the default. The cursor should be flashing on 1. Change 1 to L2 by pressing 2nd . (Note: L2 is found above the 2 key.)

 

 

To view a histogram of the data, press ZOOM.

 

 

There are several options in the Zoom Menu. Using the blue down arrow, scroll down to option 9, ZoomStat, and press ENTER. A histogram should appear on the screen.

 

 

This histogram is not exactly the same as the ones on pg. 69 of your textbook. You can adjust the histogram so that it does look exactly like the one in your text. Press Window and set Xmin to 1, Xmax to 12(this one extra data value is needed to complete the last bar of the histogram), and Xscl equal to 1, which is the difference between successive data values in the frequency distribution. Note: In many cases it is not necessary to change the values for Ymin, Yman, or Yscl. What you must do is to check these values and make sure that Ymin is a small negative value (a value between -5 and -1 would be good) and Ymax must bwe larger than the largest frequency value in you dataset. You never need to adjust Yscl.

 

 

Press GRAPH .

 

 

Notice the blue TRACE key. If you press it, a flashing cursor, *, will appear at the top of the 1st bar of the histogram.

 

 

Notice the information at the bottom of the screen. Min is the actual data value for the first bar of the histogram. In this example, the first data value is 1. We do not actually need to use the Max value in this example. “n=1” tells us that there is only one data point in the dataset that has a value of 1. You can use the blue right arrow to move through each of the bars. For example, if you move to the 5th bar in the histogram, you will see that the data value for that bar is 5 and that there are 7 data points in the dataset that have a value of 5.

Now that you have completed this example, turn Plot 1 OFF. Using 2nd , select Plot1 by pressing ENTER and highlighting OFF. Press 2nd . (Note: Turning Plot 1 OFF is optional. You can leave it ON but leaving it ON will effect other graphing operations of the calculator.)