AP StatsMr. Warren2011-2012

Company Cases Sold (Millions) Market Share (percent)

Coca Cola 4377.5 44.1

Pepsi-Cola 3119.5 31.4

Dr.Pepper/7-Up 1455.1 14.7

Cott Corp. 310 3.1

National Beverage 205 2.1

Royal Crown 115.4 1.2

Other 347.5 3.4

The table above displays the sales figures and market share achieved by several major soft drink companies in 1999.

How could we display this table graphically?

Steps to a Bar GraphStep 1: Label your axes and TITLE YOUR

GRAPH. Draw a set of axes. Label the horizontal axis

“Company” and the vertical axis “Cases Sold”. Title your graph

Step 2: Scale your axes. Use the counts in each category to help you

scale your vertical axis . Write the category names at equally spaced

intervals beneath the horizontal axis.Step 3: Draw a vertical bar above each

category name to the appropriate height.

How to Construct a Pie Chart:Use Technology!

When do we use a bar graph?To describe quantities of categorical data.

When do we use a pie chart?To describe percentages of a whole of

categorical data

The NPHS Varsity Football team scored the following number of points in their games for the past three years:50, 51, 23, 27, 10, 31, 17, 56, 30, 59, 26,

14, 41, 33, 19, 27, 20, 9, 23, 42, 15, 26, 14, 21, 19, 37, 28, 27, 21, 44

Create three graphical displays of this data: Dot Plot Stem Plot Histogram

Steps to Making a Dot PlotStep 1 Label your axis and TITLE YOUR

GRAPH. Draw a horizontal line and label it with the

variable. TITLE YOUR GRAPH

Step 2: Scale the axis based on the values of the variable.

Step 3: Mark a dot above the number on the horizontal axis corresponding to each data value.

Describe the DistributionShape – the data has a peak at 27 meaning

the most frequent score was 27 points, the data is skewed to the right.

Center – The median of the data is approximately 27, could also talk about the mean.

Spread – The data has a low value of 9 and a high value of 59 giving a range of 50.

Outliers – The data appears skewed right but there do not appear to be any outliers.

Shape Approximately Symmetric – right and left sides are approximately mirror

images Skewed Right – the right side of the distribution is stretched out, most of

the data is to the left scared away from the right side Skewed Left - the left side of the distribution is stretched out, most of

the data is to the right scared away from the left side Bi-Modal – Two points of high frequency, you would list both points of

high frequency Uniform – Data is approximately the same all the way across the

distribution Center

Mean Median

Spread Low Value to High Value Range of Inner Quartile Range Standard Deviation

Outliers Check for Outliers ( Hold tight, eyeball it for now!)

Steps to a Stem Plot Step 1: Separate each observation into a stem

consisting of all but the rightmost digit and a leaf, the final digit.

Step 2: Write the stems vertically in increasing order from top to bottom, and draw a vertical line to the right of the stems. Go through the data writing each leaf to the right of its stem and spacing the leaves equally.

Step 3: Write the stems again, and rearrange the leaves in increasing order out from the stem,

Step 4: TITLE YOUR GRAPH and add a key describing what the stems and leaves represent.

Describe the distribution:Any time we hear this phrase what do we

have to talk about? 1. 2. 3. 4.

Steps to Making Histograms Step 1: Divide the range of the data into

classes of equal width. Count the number of observations in each class.

Step 2: Label and scale your axes and title your graph.

Step 3 Draw a bar that represents the count in each class. The base of the bar should cover its class, and the bar height is the class count. Make sure the bars touch.

President Age President Age President Age

Washington 57 Lincoln 52 Hoover 54

J. Adams 61 A. Johnson 56 F.D. Roosevelt 51

Jefferson 57 Grant 46 Truman 60

Madison 57 Hayes 54 Eisenhower 61

Monroe 58 Garfield 49 Kennedy 43

J.Q. Adamas 57 Arthur 51 L.B. Johnson 55

Jackson 61 Cleveland 47 Nixon 56

Van Buren 54 B. Harrison 55 Ford 61

W.H. Harrison 68 Cleveland 55 Carter 52

Tyler 51 McKinley 54 Reagan 69

Polk 49 T.Roosevelt 42 G. Bush 64

Taylor 64 Taft 51 Clinton 46

Filmore 50 Wilson 56 G.W. Bush 54

Pierce 48 Harding 55 Obama 47

Buchanan 65 Coolidge 51

Presidential Age at Inauguration

Classes40 < president’s age at inauguration < 4545 < president’s age at inauguration < 5050 < president’s age at inauguration < 5555 < president’s age at inauguration < 6060 < president’s age at inauguration < 6565 < president’s age at inauguration < 70

Class Count

40 - 44 2

45 - 49 6

50 - 54 13

55 - 59 12

60 - 64 7

65 - 69 3

What is wrong with this graph? What is missing?

Now that we have fixed our histogram: Describe the distribution:

1. 2. 3.4.

Let’s do the histogram with your calculator now!

Step 1 Decide on class intervals and make a frequency table, just like a histogram. Add three columns to your frequency table: relative frequency, cumulative frequency, and relative cumulative frequency.

Class Frequency

Relative Frequency

Cumulative Frequency

Cumulative Relative Frequency

40 – 44 2 2/44 = .045 4.5%

2 2/44 = .045 4.5%

45 - 49 7 7/44 = .159 15.9%

9 9/44 = .205 20.5%

50 - 54 13 13/44 = 29.5 %

22 22/44 = .5 50%

55 - 59 12 12/44 = .273 27.3%

34 34/44 = .773 77.3%

60 - 64 7 7/44 = .205 20.5%

41 41/44 = .932 93.2%

65 - 69 3 3/44 = .068 6.8%

44 44/44 = 1.00 100%

Step 2: Label and scale your axes then title your graph. Horizontal axes, “Age at Inauguration”. Vertical axis “Relative Cumulative Frequency”

Step 3: Plot a point corresponding to the relative cumulative frequency in each class at the left endpoint of the of the next class interval. See Figure 1.12