2. Objectives Organize discrete data in tables Construct histograms of discrete data Organize continuous data in tables Construct histograms of continuous data Draw Stem and Leaf plots Draw dot plots Identify the shape of a distribution

3. Organize Discrete Data in Tables The values of a discrete variable are used to create categories of data. This means we can tally how many of each are in a category, allowing us to create frequency and relative frequency tables and graphs.

4. Construct Histograms of Discrete Data  Histograms are constructed by drawing rectangles for each class of data.  The height of each rectangle is the frequency or relative frequency of the class.  The width of each rectangle is the same and they touch each other.  This is accomplished in Excel by either using the “Analysis” pack (which we do not have) or by creating a separate data chart from which to draw the graph.

5. Examples of HistogramsExamples of Histograms Number of Arrivals at Wendy’s 76664 566114 27124 65537 22975 62657 68265 46985 Raw Data # Customers Tally/Fre quency Relative Frequency 11.025 26.15 31.025 44.1 57.175 611.275 75.125 82.05 92 1000 111.025

6. Organize Continuous Data in Tables  Since raw, continuous data does not have natural categories for histograms, they must be created.  These categories are called “classes” and are intervals of numbers.  Each class has an upper and lower limit  The width of the class is the difference between the consecutive lower class limit and should be the same between all classes  One exception: open ended classes (ex: ages under 1 year, or under 55 years)  The intervals used to define the classes should not overlap  Otherwise data could be placed in more than one category

7. Organize Continuous Data in Tables  How to choose class width:  Needs to fit the data  Might need to fit the research question  Too few classes reduces data down to something not as usable  Too many classes makes it difficult to see similarities and trends in the data.  How to construct Histogram:  Tally the number of data occurrences for each class  Calculate relative frequency

8. Construct Histograms of Continuous Data  Done just like bar charts of discrete data or qualitative data…

9. Draw Stem and Leaf PlotDraw Stem and Leaf Plot  Stem and Leaf plots divide data according to the decimal system.  Stems can be integers in the ones or tens place, or even other places, if you note it properly in the chart legend.  Can be drawn with Excel  Represents actual data, but gives the appearance of a histogram of sorts.  Can determine frequency within classes.

10. Different Types of Stem and Leaf Plots

11. Draw Dot PlotsDraw Dot Plots  Dot plot  Is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed

12. The Shape of DistributionsThe Shape of Distributions  We have different ways of classifying shapes  Uniform (symmetric)  Bell-Shaped (symmetric)  Skewed Right  Tail to the right  Skewed Left  Tail to the left http://rchsbowman.wordpress.com/2010/08/30/statistics-notes-the-shape-of- distributions/

13. Assignment  Pg 87 – 96: 7, 8, 9, 11, 13, 15, 17, 19, 23, 30 (to be completed in MS Excel)