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Understanding Histograms, Frequency Polygons, and Ogives in Data Representation

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aimee
24 diapositives · 420 Views · Jul 19, 2014

This section covers the essential aspects of histograms, frequency polygons, and ogives. A histogram displays data through contiguous vertical bars, with the x-axis showing quantitative values in intervals and the y-axis representing frequency. A frequency polygon connects points plotted at class midpoints. The ogive graph illustrates cumulative frequencies. Instructions for constructing these graphs from raw data and frequency tables are included, along with homework exercises to reinforce learning.

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  1. Section 2-2 Histograms, Frequency Polygons Ogives

  2. Histograms • The histogram is a graph that displays data by using contiguous vertical bars of various heights to represent the frequencies of the classes. • the x-axis of a histogram represents quantitative i.e. numerical values that are organized in intervals.

  3. Frequency Histogram

  4. Side by side Histograms

  5. Side by side Histograms

  6. Bar graph • A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different heights. • The x-axis will display qualitative i.e. categorical data.

  7. Bar graph

  8. Histograms Please refer to the states temperatures data from section 2-2.

  9. Use your ruler and draw the x and y axes. Label each of the axes. Scale each axes carefully. Represent the class boundaries on the x axis. Represent the frequency on the y axis. Using the frequencies as the heights, draw vertical bars for each class.

  10. The Frequency Polygon The frequency polygon is a graph that displays the data by using lines to connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points.

  11. Frequency Polygon

  12. Frequency Polygon Superimposed on a Histogram

  13. Constructing a frequency polygon Step1: Find the midpoints of each class. Step 2: Draw the x and y axes. Label the x axis with the midpoint of each class. Scale y axis appropriately to plot the frequencies. Step 3: Using the midpoints for the x values and the frequencies for the y values, plot the points. Step 4: Connect the plotted points with line segments.

  14. The Ogive (pronounced o-jive) The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution. Ogive frequency graphs are constructed similar to a histogram, with one exception. In this case the y axis represents the cumulative frequency.

  15. Cumulative Frequency

  16. Relative frequency graphs Relative frequency graphs are constructed similar to a histogram, with one exception. In this case the y axis represents the relative frequency.

  17. Relative Frequency Histogram

  18. Cumulative Relative frequency graphs Relative cumulative frequency graphs are constructed similar to a histogram, with one exception. In this case the y axis represents the cumulative relative frequency.

  19. Cumulative Relative Frequency

  20. Graphing Calculator • Page 61 • Constructing histograms from raw data • Page 62 • Constructing a Histogram from a frequency distribution table

  21. Homework: Read pages 51-60. Applying Concepts 2-2 page 60 Make sure to answer all questions completely. Graphs must be done on graph paper; make sure to use a ruler. Homework Exercises 2-2, page 61 starting with # 1 every other odd problem.