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Unit 2

Unit 2. Section 2-3. 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

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Unit 2

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

  4. Section 2-3 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.

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

  6. Section 2-3

  7. Section 2-3

  8. Section 2-3 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.

  9. Section 2-3 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.

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

  11. Section 2-3

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

  13. Section 2-3 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.

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

  15. Section 2-3

  16. Section 2-3 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.

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