To create a frequency table, a histogram, a line plot, and a box-and-whisker plot for a same set of data using Geogebra and Excel.
To interpret the results of the graphs including the measures of central tendency and variation.
To discuss the advantages and disadvantages of each graph
To determine which of those four graphs should be selected to represent data.
This lesson should be done at the end of the unit on data analysis so that students can show the connection between all the skills and concepts learned in that unit. In general, the book explains how to construct and read the graphs, but not how to apply the knowledge acquired on graphs.
Prerequisite Knowledge for teachers:Teacher needs to have some experience with Excel and Geogebra.
Prerequisite Knowledge for students: Students need to have already known how to perform basic commands in Excel and Geogebra such as sorting, using the graphs wizard in Excel, and inputting data in the input window of Geogebra.
List of materials: Excel files (data1lesson, data2lesson), Geogebra files (lineplot1, lineplot2, lineplot3, lineplot4, lineplot5, boxplot1, boxplot2, boxplot3, boxplot4, boxplot5), graph lesson PowerPoint, student laptop, three dice (optional), LCD projector
Connection to the Sunshine State Standards: MA.E.1.3.1, MA.E.1.3.2, MA.E.1.3.3, MA.E.3.3.1
List of Key Words: histogram, frequency table, scale, interval, mean, median, mode, range, line plot, outlier, box-and-whisker plot, variation, lower extreme, upper extreme, lower quartile, upper quartile, interquartile range
Introduction of Lesson:
This lesson being taught at the end of the unit on data analysis is supposed to help students make sense of the different types of graphs that they have learned to construct and interpret. Teacher should go over the unit vocabulary and have discussion about the purpose of each type of graph as explained below:
A frequency table tells how many times each piece of data occurs in a set of information.
A histogram is a bar graph that displays the frequency of data that has been organized into equal intervals. Because the data cover all possible values of data, there are no spaces between the bars of the graph. A histogram is used to show frequency of distribution among certain intervals. All the bars have the same width. The vertical scale is often a factor of the greatest frequency, and the vertical axis is usually a frequency count of items falling into each group. The advantages of a histogram are that it is visually strong and can compare to normal curve. The disadvantages are that you cannot read exact values because data are grouped into intervals. It is more difficult to compare two sets of data. It can only be used with continuous data.
A line plot is a vertical graph of the tally marks you create in a frequency table. There is no vertical scale. Each data is represented by an X placed above a number on a number line each time that data occurs. The advantages of a line plot are that you can do quick analysis of data. It shows the range, minimum and maximum values, gaps and clusters, and outliers easily. More importantly, the exact values are retained. The disadvantages are that a line plot is not visually appealing, it is best for data sets under 50 data values, and the data need to have a small range.
A box-and-whisker plot summarizes data using the median of the set of data, the median of the left side (lower quartile), the median of the right side (upper quartile), and the two extreme (lowest and greatest) values. The advantages of this graph are that it shows 5-point summary and outliers, can easily compare two or more sets of data, and it handles extremely large data sets. The disadvantages are that a box-and-wisher plot (box plot) is not as visually appealing as other graphs, and the exact values are not retained.
Procedures performed to reach the objectives of the lesson Teacher may go online at http://www.random.org/dice to access interactive dice that would simulate the rolling of 3 dice and do it 25 times and have the students record the twenty-five sums or http://randomizer.org/form.htm to generate 25 numbers at random. Then she can go to http://www.shodor.org/interactive/activities and input the data to show what the histogram and the box-and-whisker plot would look like. Then she should facilitate a discussion on what they can tell about the data looking at those two graphs.
The second demonstration by the teacher is to use the Excel file data1lesson provided to show the frequency table and histogram when the slider is at 1. Then she should use the same data to do the line plot and box-and-whisker plot in Geogebra.
Activities for students (See questions in Excel files data1lesson and data2lesson)
Homework assignment for students (See worksheet)
(Students are encouraged to go to http://www.shodor.org/interactive/activities to verify that their histogram and box plot are done correctly)
Assessment for students:
Have students move the slider to a number different than the one they practice on and answer the same questions given in the Excel files.
Closure of the lesson:
Have five students volunteer to present their work to the class and discuss their answers.
Extension and interdisciplinary activity
Write a persuasive essay about a teenage product you invented that you want to put on the market. Use an appropriate graph to illustrate why your product is a sound business proposal. Be specific about the message that you want your graph to convey (tell). Use the indicators of measure of central tendency in your sales pitch.
Other helpful links http://math.youngzones.org/stat_graph.html http://www.eia.doe.gov/neic/graphs/frequenc.htm