1. Unit 2 Section 2-3

2. 2-3: Histograms, Frequency Polygons, and Ogives  Graphs are used to present data after it has been organized into frequency distributions.  The purpose of a graphs in statistics is to display data in pictorial form.  The three most commonly used graphs are:  Histograms  Frequency Polygons  Ogives (pronounced: o-jive)

3. The Histogram  Histogram – a graph that displays data using contiguous vertical bars of various heights to represent the frequencies of the classes. Section 2-3

4. How to Construct a Histogram  Draw and label the x and y axis  Remember x is the horizontal axis and y is the vertical.  Represent the frequency on the y axis and the class boundaries on the x axis.  Using the frequency as the heights, draw vertical bars for each class. Section 2-3

5. Activity: Construct a Histogram  Using the data on the following slide, construct a histogram to represent the data. Section 2-3

6. Class Limit Class Boundary TallyFrequencyCumulative Frequency 100-10499.5-104.5||22 105-109104.5-109.5||||||| | 810 110-114109.5-114.5||||||| ||||||| |||| 1828 115-119114.5-119.5||||||| |||||| 1341 120-124119.5-124.5|||||||748 125-129124.5-129.5|149 130-134129.5-134.51150 Section 2-3

8. The Frequency Polygon  Frequency Polygon – a graph that displays data by using lines that connect points plotted for the frequencies at the midpoints of the classes.  The frequencies are represented by the heights of the points. Section 2-3

9. How to Construct a Frequency Polygon  Find the midpoints of each class.  Add the upper and lower boundary, then divide by 2.  Draw and label the x and y axis  Label the x-axis with the midpoint of each class.  Determine a suitable scale for the frequencies.  Using the midpoints for the x values and the frequencies as the y values, plot the points.  Connect the adjacent points with line segments.  Draw a line back to the x axis at the beginning and end of the graph.  The line should connect at the same distance where the previous and next midpoint would be located. Section 2-3

10. Activity: Construct a Frequency Polygon  Using the data representing record high data for the 50 states, construct a frequency polygon to represent the data. Section 2-3

12. The Ogive  Ogive – a graph that represents the cumulative frequencies for the classes in a frequency distribution.  Also known as a cumulative frequency graph. Section 2-3

13. How to Construct an Ogive  Find the cumulative frequency of each class.  Draw and label the x and y axis  Label the x-axis with the class boundaries of each class.  Determine a suitable scale for the frequencies.  Plot the cumulative frequency at each upper class boundary.  Starting with the first upper class boundary, connect adjacent points. Then extend the graph to the first lower class boundary on the x axis. Section 2-3

14. Activity: Construct an Ogive  Using the data representing record high data for the 50 states, construct an Ogive to represent the data. Section 2-3

16. Relative Frequency Graph  Relative Frequency Graph – a graph that coverts the distributions from frequencies to proportions of frequencies.  To covert, divide the frequency by the overall cumulative frequency.  The sum of the relative frequencies will always equal 1. Section 2-3