AP Stats Mr. Warren

CompanyCases Sold (Millions)Market Share (percent) Coca Cola Pepsi-Cola Dr.Pepper/7-Up Cott Corp National Beverage Royal Crown Other 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 Graph  Step 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 Plot  Step 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 Distribution  Shape – 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.

 0 9       5 | 0 = 50 points scored in a game NPHS Football scores for 2008 – 2010

 Describe the distribution:  Any time we hear this phrase what do we have to talk about?

 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 Washington 57Lincoln 52Hoover 54 J. Adams 61A. Johnson 56F.D. Roosevelt 51 Jefferson 57Grant 46Truman 60 Madison 57Hayes 54Eisenhower 61 Monroe 58Garfield 49Kennedy 43 J.Q. Adamas 57Arthur 51L.B. Johnson 55 Jackson 61Cleveland 47Nixon 56 Van Buren 54B. Harrison 55Ford 61 W.H. Harrison 68Cleveland 55Carter 52 Tyler 51McKinley 54Reagan 69 Polk 49T.Roosevelt 42G. Bush 64 Taylor 64Taft 51Clinton 46 Filmore 50Wilson 56G.W. Bush 54 Pierce 48Harding 55Obama 47 Buchanan 65Coolidge 51 Presidential Age at Inauguration

 Classes  40 < president’s age at inauguration < 45  45 < president’s age at inauguration < 50  50 < president’s age at inauguration < 55  55 < president’s age at inauguration < 60  60 < president’s age at inauguration < 65  65 < president’s age at inauguration < 70

ClassCount

 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.

ClassFrequencyRelative Frequency Cumulative Frequency Cumulative Relative Frequency 40 – 442 2/44 = % /44 = % 99/44 = % /44 = 29.5 % 2222/44 =.5 50% /44 = % 34 34/44 = % /44 = % 41 41/44 = % /44 = % 44 44/44 = %

 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