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Identifying the Shape of a distribution and computing the Mean and the Median

 

Example: The following data represent the number of customers waiting for a table at 6:00 p.m. on Saturday for 40 consecutive Saturdays at Bobak’s Restaurant.

 

11

6

5

8

11

6

3

7

4

6

5

4

13

14

9

11

13

8

10

10

9

9

6

5

10

8

8

8

7

7

3

8

7

8

9

6

10

11

4

8

 

(a) Compute the mean and the median number of customers waiting.

 

(b) Identify the shape of the distribution based on the histogram drawn here, the arithmetic mean, and the median.

 

 

Press STAT and select 1: Edit. Clear L1 and enter the data into L1. Press STAT again and highlight CALC to view the Calc Menu. Select 1:1- Var Stats and press 2nd ENTER.

 

(a.) The first item is the sample mean, 7,875. To find the median, scroll down to the next page of output. The median is 8.

 

(b.) Before graphing the histogram, make sure that there are no functions in the Y-registers. To do this, press the 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. Position the cursor on ON and press ENTER to select it. On the next line, 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 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 us the default. The cursor should be flashing on 1.

 

 

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.

 

 

The distribution is Symmetric.