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Histograms

Histograms. By Ryan Beil and Chris Carlson. Definition and Explanation. A Histogram is a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.

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Histograms

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  1. Histograms By Ryan Beil and Chris Carlson

  2. Definition and Explanation • A Histogram is a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies. • Take the numbers: 1.2, 2.3, 2.5, 3.1, 3.5, 3.6, 3.7, 4.3, 4.5, 5.6, 6.7

  3. Definition and Explanation Continued • Take the numbers: • 1.2, 2.3, 2.5, 3.1, 3.5, 3.6, 3.7, 4.3, 4.5, 5.6, 6.7

  4. Definition and Explanation Continued Proportional to Frequencies A Histogram is a representation of a frequency distribution by means of rectangles whose widths represent classintervals and whose areas are proportional to the corresponding frequencies. Rectangles/Widths Class Intervals Frequency Distribution

  5. Uses of Histograms • Histograms are used in many different ways and forms. • United States Census • Graphing Demographics • Used when wanting to show a frequency of data for a specific intervalor a group of intervals.

  6. What is Needed to Make a Histogram? • Intervals. (X Axis) • Frequencies for the intervals or interval groups. (Y Axis) • Example: Living With Parents (100 People Surveyed Per Age Group) • 16-25: 60 People • 26-35: 40 People • 36-45: 20 People • 46-55: 15 People • 56-65: 5 People Frequency Interval

  7. How Long Does it Take Mrs. Ellwood’s 4th Period Class to do Homework? • Data: • 0-30 Minutes • 4 People • 31-60 Minutes • 8 People • 61-90 Minutes • 3 People • 91-120 Minutes • 2 People • 121-150 Minutes • 0 People • 151-180 Minutes • 3 People

  8. Histogram Question • Using the graph on the left, find the median and the mode of the data. Provide your answer in interval form. • Five new students join Mrs. Ellwood’s class in the middle of the school year. Three chose the interval 121-150 and two chose the interval 61-90 for the amount of time spent on homework. Would this cause the median to change? If yes, then to what value?

  9. Advantages • It displays a large range of data in a compact area. • Easy to compare data from different categories and intervals. • Histograms can show bell curves. (Example Below)

  10. Disadvantages • It can be more difficult to determine the exact values for data and intervals. • There is a restriction on the type of intervals and categories that can be used and compared. • Can be difficult to read with a large number of intervals.

  11. Bibliography • Images: (In Order of Appearance) • http://phys.columbia.edu/~tutorial/estimation/gauss.png • http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.html • http://area.autodesk.com/userdata/fckdata/286966/image/nicolas/histogram_large.jpg • Information: • http://quarknet.fnal.gov/toolkits/ati/histograms.html • http://www.merriam-webster.com/dictionary/histogram • http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/histogram2.html

  12. HistogramsDefinition and ExplanationDefinition and Explanation ContinuedDefinition and Explanation ContinuedUses of HistogramsWhat is Needed to Make a Histogram?How Long Does it Take Mrs. Ellwood’s 4th Period Class to do Homework?Histogram QuestionAdvantagesDisadvantagesBibliography Histograms

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