By Ryan Beil and Chris Carlson Histograms RYAN 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. 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 1-1.99 1.2 2-2.99 2.3 2.5 3-3.99 3.1 3.5 3.6 3.7 4-4.99 4.3 4.5 5-5.99 5.6 6-6.99 6.7 Read definition. Go through data and representation in the graphics. RYAN

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 1-1.99 1.2 2-2.99 2.3 2.5 3-3.99 3.1 3.5 3.6 3.7 4-4.99 4.3 4.5 5-5.99 5.6 6-6.99 6.7 Go through graphics again, explain how it works into the graph. CHRIS

Definition and Explanation Continued Proportional to Frequencies Rectangles/Widths 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. Read definition again. Explain each bold faced word and click for a label on the graph. RYAN Frequency Distribution Class Intervals

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 interval or a group of intervals. Read through and explain slowly. Give examples. CHRIS

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 FAKE DATA. Explain what is needed to make a graph and how it relates to data. Explain graph. CHRIS Interval Frequency

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 REAL DATA. Explain data and compare it to the graph. RYAN

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? Click once for part A. Second click for Part B. A: Median and Mode is 31-60 Minutes. B: Median is changed to 61-90 Minutes. CHRIS for A. RYAN for B.

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) Explain each, especially bell curves. RYAN

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. Explain all, including the graphic. CHRIS

Bibliography Images: (In Order of Appearance) Information: 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 CHRIS

Histograms Definition and Explanation Definition and Explanation Continued Definition and Explanation Continued Uses of Histograms What is Needed to Make a Histogram? How Long Does it Take Mrs. Ellwood’s 4th Period Class to do Homework? Histogram Question Advantages Disadvantages Bibliography Ask for questions. RYAN Histograms