Part II



STATISTICAL PLOTS

Statisticians, engineers, businessmen, and many other professionals use statistical plots in their everyday responsibilities. These plots are used to visually illustrate countless examples, some of which might include company growth, finances, product distribution, and many others. A plot is nothing more than a diagram that exhibits a relationship of multiple quantities. In this exploration, you will examine three important plots: The Circle Graph, The Bar Graph, and The Box and Whisker Plot. You will look at these plots, and determine how they were created, what information can be obtained from each plot, and how to create a similar data plot.

Circle Graphs

The following chart is a circle graph (Pie Chart). We can use this tool to show the distribution of non-overlapping parts and how they relate to the whole. For example, Pie Charts can be used very effectively in showing a companies budget. Each part of the budget would be represented by a slice of the pie, and all of the slices would add up to 100% of the budget. Use the data from the graph to fill in the chart below.

[pic]

|Cause |Percentages |Actual # of Fires |Central Angle |

|Cooking |22% |264 |79o |

|Electrical | | |94o |

|Unknown | |216 | |

|Children | | | |

|Open Flames | | | |

|Smoking | | | |

|Arson | | | |

|Total | |1200 | |

1. How do you figure out the actual number of fires?

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2. How do you figure out the central angle?

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3. How does the percentage of fires relate to the central angle?

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Now that you have read a circle graph, it’s your turn to create one. Here is a chart of data. Find the percentages of each data value. Then find the angle of for the circle plot. Graph the circle plot.

Active Duty Military Personnel from the United States Worldwide

|Location |Number of Troops |% |Central Angles |

|US, US Territories, and special locations |1,397,083 | | |

|Middle East |166,249 | | |

|East Asia Pacific |99,022 | | |

|North Africa, South Asia |11,490 | | |

|Sub-Saharan Africa |6,864 | | |

|Other Western Hemisphere |17,758 | | |

|Total | | | |

Now use the percentages and the central angles in the above table to draw and label the Circle Graph:

BAR GRAPH

What percentage was the highest (list group and percentage)?

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What part of the central angle does it represent?

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Approximately, what location(s) make up ¾ of the pie chart?

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Bar Graph

Another way to organize data is by creating a bar graph. When making a bar graph, the bars can either be vertical or horizontal. The choice of the bar direction is really dependant on which way the plot can be read the easiest. Remember: The goal in using statistical plots is to represent data in the clearest way and make it the easiest to understand. This type of plot can be very useful in showing change over time. For example the following example shows the change in rainfall over a year’s time.

|Average Rainfall in Erie, PA |

|Month |J |

|Washington |57 |

|J. Adams |61 |

|Jefferson |57 |

|Madison |57 |

|Monroe |58 |

|J.Q. Adams |57 |

|Jackson |61 |

|Van Buren |54 |

|W.H. Harrison |68 |

|Tyler |51 |

|Polk |49 |

Five Major Values:

____________

____________

____________

____________

____________

Create the Box and Whisker Plot in the box below. Make sure to give the plot a title, label it and provide a number line below it.

Why do you think the data had to be ranked?

________________________________________________________________________

________________________________________________________________________

The 5 values that are needed to create the box and whisker plot, all have special names.

Minimum Smallest Value in the data set

1st Quartile The data value that is in the middle of the 1st half

Median (2nd Quartile) The data value in the middle of the data set

3rd Quartile The data value that is in the middle of the 2nd half

Maximum Largest value in the data set

By looking at the 3 quartiles, it can be seen that they divide the data into four equal parts (like a quarter is ¼ of a dollar). When looking at a box and whisker plot the length of box part can be calculated by subtracting the 1st Quartile (Q1) from the 3rd Quartile (Q3). This value is referred to as the Interquartile Range (IQR).

That is: IQR = Q3 – Q1

What is the IQR for the box plot you created? _____________

1. What are some important things to remember when creating a box-and-whisker plot?

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2. What does each quartile represent?

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3. In what situations would you the box-and-whisker plot be a good fit?

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Integrating Technology

The TI-83 graphing calculator has the ability to create statistical plots based on a list of data. For this part of the exercise you will create and compare two box and whisker plots using the TI-83.

Sample Survey 1

The number of hours of television watched per day by a sample of 28 teenagers:

2 4 1 5 7 2 5 4 4 2 3 6 4 3

5 2 0 3 5 9 4 5 2 1 3 6 7 2

Sample Survey 2

The number of hours of television watched per day by a sample of 28 adults, 20 to 30 years of age:

3 5 0 2 4 3 4 1 2 1 3 4 1 2

5 4 1 1 3 2 4 3 2 3 0 1 2 6

1. Enter the data for the first plot using the List editor

a. [pic]

2. If L1 (List 1) is not empty, clear L1

a. [pic]

3. Enter data from Sample Survey 1

a. Enter data value [pic] (there should be 28 values)

4. Repeat 2 and 3, placing the data for Sample Survey 2 in L2.

5. Graph the plot of Survey 1

a. [pic]

b. Plot 1: on

c. Type: select the box and whisker plot by hitting the right arrow 4 times

d. Xlist: [pic]

e. Freq:1

f. [pic]

6. Find the 5 major values of the box-and whisker plot

a. [pic] (Then use the left and right arrows to find values)

Survey 1

minX _____ Q1______ Med_______ Q3________ maxX_____

7. Graph the plot of Survey 2

a. [pic]

b. Plot 2: on

c. Type: select the box and whisker plot by hitting the right arrow 4 times

d. Xlist: [pic]

e. Freq:1

f. [pic]

8. Find the 5 major values of the box-and whisker plot

a. [pic] ([to switch between plots, use the up and down arrows] Then use the left and right arrows to find values)

Survey 2

minX _____ Q1______ Med_______ Q3________ maxX_____

What survey has the highest median? __________

What sample is the largest IRQ (Q3 – Q1)? __________

Which survey group had the largest number __________

of hours of TV watched?

Who watches more TV, teenagers (Survey 1), __________

or adults ages 20 – 30 (survey 2)?

Why do we use statistical plots?

________________________________________________________________________________________________________________________________________________

What are the advantages to using the graphing calculator to create box and whisker plots?

__________________________________________________________________________________________________________________________

Using the TI-83 to make a Bar Graph

STEP ONE:

Enter data points in L1 – [STAT] [EDIT] [1].

Move the cursor on the label L1 then [CLEAR] [ENTER]. This will erase the current list. Now, enter the values.

STEP TWO:

Program bar graph in the Stat Plot Screen

Make sure all plots are turned off in [Y=]

Then, [2nd] [STAT PLOT] [1] [ENTER] to turn on plot 1.

Select the bar graph icon. (Make sure the cursor changes to a solid box indicating you have selected the bar graph).

For the X list: type L1

For the Freq: type 1 (since each number occurs once in the list)

STEP THREE:

Set up the bar width and data ranges on the Window screen. This part is tricky. Note: The TI-83 sets up the bars into classes. For example, a bar graph with x min at 0 and x max at 12 with 6 bars and a width of 2 would have 6 classes where each class would represent data points from 0-2, 2-4, 4-6, 6-8, 8-10, 10-12.

Go into [WINDOW]

X min = this number must be smaller then the smallest data point in the set

X max = this number must be larger then the largest data point in the set

X scl = this is the bar width

Y min = 0 (since no frequency is less than zero)

Y max = make this number fairly large, you may have to play around with it to get a good graph

Y scl = this number represents how far apart you want the dots to be vertically

STEP FOUR:

Look at the graph [GRAPH]

Make changes to the [WINDOW] for a better fit if needed

Use [TRACE] to see the value of the bars.

Using the TI-83 to make a Box-and-Whisker Plot

STEP ONE:

Enter data points in L1 – [STAT] [EDIT] [1].

Move the cursor on the label L1 then [CLEAR] [ENTER]. This will erase the current list. Now, enter the values.

STEP TWO:

Program bar graph in the Stat Plot Screen

Make sure all plots are turned off in [Y=]

Then, [2nd] [STAT PLOT] [1] [ENTER] to turn on plot 1.

Select the box-and-whisker plot. This is the second icon in the second row. (Make sure the cursor changes to a solid box indicating you have selected the bar graph).

For the X list: type L1

STEP THREE:

Set up the bar width and data ranges on the Window screen.

Go into [WINDOW]

Ignore all setting except X scl =1 and Y scl = 0.

Then go to [ZOOM] [ZOOM STAT]

This will display the box-and-whisker plot.

Use the [TRACE] feature to view least value, lower quartile, median, upper quartile and greatest value.

Using the TI-73 to make a Pie Chart

STEP ONE:

In [MODE], make sure the first entries in each row are highlighted.

Make sure all graphs and plots are turned off.

Go to 2nd [FORMAT] and make sure the first entries in each row are highlighted.

STEP TWO:

Go to [LIST] and scroll over until you get to a blank list.

Press 2nd [TEXT] and name the lists (ex. location, number of troops). Arrow to each letter and press [ENTER]. Then, press 2nd [TEXT] to name the elements in each list you just created (ex. US, Middle East). Make sure to use “ “ around the name to tell TI-73 that this is a category list. Use the marks for the first entry only.

STEP THREE:

To draw a circle graph, go to 2nd [PLOT], Press 1:Plot 1, Press [GRAPH] then [TRACE] and arrow around. (Use 2nd [STAT] to find the list names.

To see percentages, follow the directions above but set option to Percent instead of Number.

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