Presentation on theme: "More Graphs and Displays"— Presentation transcript:
1 More Graphs and Displays Section 2.2More Graphs and DisplaysStatisticsMrs. SpitzFall 2008
2 Objectives:How to graph quantitative data sets using stem-and-leaf plots and dot plotsHow to graph qualitative data using pie charts and Pareto chartsHow to graph paired data sets using scatter plots and time series charts.Assignment: pp #1-30
3 Graphing Quantitative Data Sets – don’t write this down. In Section 2.1, you learned several traditional ways to display quantitative data graphically. In this section, you will learn a newer way to display quantitative data called a stem-and-leaf plot. Stem-and-leaf plots are examples of exploratory data analysis (EDA), which was developed by John Tukey in 1977.
4 Graphing Quantitative Data Sets – don’t write this down. In a stem and leaf plot, each number is separated into a stem (the entry’s leftmost digits) and a leaf (the rightmost digit). A stem-and-leaf plot is similar to a histogram but has the advantage that the graph still contains the original data values. Another advantage is that it provides an easy way to sort data.
5 Stem-and-Leaf PlotLowest value is 67 and highest value is 125, so list stems from 6 to 12.StemLeafTo see complete display, go to next slide.6 |7 |8 |9 |10 |11 |12 |62Divide each data value into a stem and a leaf. The leaf is the rightmost significant digit. The stem consists of the digits to the left. The data shown represent the first line of the ‘minutes on phone’ data used earlier. The complete stem and leaf will be shown on the next slide.Divide each data value into a stem and a leaf. The leaf is the rightmost significant digit. The stem consists of the digits to the left. The data shown represent the first line of the ‘minutes on phone’ data used earlier. The complete stem and leaf will be shown on the next slide.2834
6 Stem-and-Leaf Plot Key: 6 | 7 means 67 6 | 7 7 | 1 8 8 | 2 5 6 7 7 6 | 77 | 1 88 |9 |10 |11 | 2 6 812 | 2 4 5Key: 6 | 7 means 67It is very important to use a key to explain the plot. 6|7 could mean 6700 or .067 for a different problem. A stem and leaf should not be used with data when values are very different such as 3, 34,900, 24 etc. The stem-and leaf has the advantage over a histogram of retaining the original values.Stress the importance of using a key to explain the plot. 6|7 could mean 6700 or .067 for a different problem. A stem and leaf should not be used with data when values are very different such as 3, 34,900, 24 etc. The stem-and leaf has the advantage over a histogram of retaining the original values.
7 Stem-and-Leaf with two lines per stem Key: 6 | 7 means 676 | 77 | 17 | 88 | 28 |9 | 29 |10 |10 |11 | 211 | 6 812 | 2 412 | 51st line digits2nd line digitsWith two lines per stem the data is more finely “chopped”. Class width is 5 times the leaf unit. All stems except possibly the first and last must have two lines even if one is blank. For this data set, the first line for the stem 6 can be blank because there are no data values from 60 to 64.1st line digits2nd line digitsWith two lines per stem the data is more finely “chopped”. Class width is 5 times the leaf unit. All stems except possibly the first and last must have two lines even if one is blank. For this data set, the first line for the stem 6 can be blank because there are no data values from 60 to 64.
8 Dot PlotsYou can also use a dot plot to graph quantitative data. In a dot plot, each data entry is plotted, using a point, above a horizontal axis. Like a stem-and-leaf plot, a dot plot allows you to see how data are distributed and determine specific data entries.
9 Dot PlotPhone66768696106116126minutesDot plots also allow you to retain original values.Dot plots also allow you to retain original values.
10 Graphing Qualitative Data Sets Pie charts provide a convenient way to present qualitative data graphically. A pie chart is a circle graph that shows relationships of parts to a whole.
11 NASA budget (billions of $) divided among 3 categories. Pie ChartUsed to describe parts of a wholeCentral Angle for each segmentNASA budget (billions of $) divided among 3 categories.Pie charts help visualize the relative proportion of each category. Find the relative frequency for each category and multiply it by 360 degrees to find the central angle.Pie charts help visualize the relative proportion of each category. Find the relative frequency for each category and multiply it by 360 degrees to find the central angle.Billions of $Human Space FlightTechnologyMission SupportConstruct a pie chart for the data.
12 Pie Chart Human Space Flight 5.7 143 Technology 5.9 149 Billions of $DegreesHuman Space Flight5.7143Technology5.9149Mission Support2.76814.3360TotalMissionSupport19%HumanSpace Flight40%NASA Budget(Billions of $)Technology41%
13 You will need a protractor and a compass. Take the part and divide it by the whole, and you will get a decimal. Multiply by 360 and you will get the number of degrees in that part of the circle. Do this until you have 360 degrees.Draw a circle. Starting from the middle of the circle, draw a line from the center of the circle to the side of the circle. This is your starting point for 0 degrees.Use your protractor to measure the number of degrees required, mark and draw another line from the center to the edge.Start at the edge of the next to begin measuring your next cut in the pie. Continue until you are done.Yes, you have to do a few by hand so you get the idea. Later, we will use Excel to create pie charts.
14 Pareto ChartAnother way to graph qualitative data is to use a Pareto chart. A Pareto chart is a vertical bar graph in which the height of each bar represents frequency or relative frequency. The bars are positioned in order of decreasing height with the tallest bar positioned at the left. Such positioning helps highlight important data and is used frequently in business.
15 Example Pareto ChartLast year, the retail industry lost $40.9 million in inventory shrinkage. The causes of the inventory shrinkage are administrative error ($7.8 million), employee theft ($15.6 million), shoplifting ($14.7 million), and vendor fraud ($2.9 million). If you were a retailer, which causes of inventory shrinkage would you address first? Construct a Pareto chart to show which causes would be addressed first.
17 Graphing Paired Data Sets If two data sets have the same number of entries, and each entry in the first data set corresponds to one entry in the second data set, the sets are called paired data sets. For instance, suppose, a data set contains the costs of an item and a second data set contains the sales amounts for the item at each cost. Because each cost corresponds to a sales amount, the data sets are paired. One way to graph paired data sets is to use a scatter plot, where the ordered pairs are graphed as points in a coordinate plane.
19 Time SeriesA data set that is composed of entries taken at regular intervals over a period of time is a time series. For instance, the amount of precipitation measured each day for one month is an example of a time series. You can use a time series chart to graph a time series.
20 Constructing a Time Series Chart The table lists a number of cellular telephone subscribers in millions, and a subscriber’s average local monthly bill for service, in dollars, for the years 1987 through Construct a time series chart for the number of cellular subscribers. What can you conclude?YearSubscribersAverage bill19871.296.8319882.198.0219893.589.3019905.380.9019917.672.74199211.068.68199316.061.48199424.156.21199533.851.00199644.047.70
21 Constructing a Time Series Chart Let the horizontal axis represent the years and the vertical axis represent the number of subscribers in millions. Then plot the paired data. From the graph, you can see the number of subscribers has been increasing since Recent years show greater increases.