Exploring Online Data Analysis Tools - EdTech Leaders Online



SREB Readiness Indicators Addressed: Gather, organize, display, and interpret data (SREB Indicator #8).

Activity Rationale: People are continuously faced with data in the form of graphs, charts, survey results, and statistical information in magazines, newspapers, television, and other electronic media. To make sense of the various representations of data, middle grades students should have experiences collecting, representing, and analyzing many different types and forms of data, using logical reasoning to analyze statistical claims. Additionally, students need opportunities to develop questions to investigate and determine the best graphical representations to answer these questions.

Using technology such as graphing software and calculators can help students display data, interpret data, and work fluently with range, limit, scale, and measures of center.

In this activity, you will investigate three different data tools. You will explore the same set of data in each of the tools to see how this one set of data can be organized and represented in different graphs. You will also investigate how these different representations lend themselves to asking or answering different questions about the data set. According to NCTM, “different graphs are used in different situations; each has both advantages and disadvantages. For example, some graphs are useful for small datasets, whereas others are useful for large data sets. Some graphs display each data value individually, but others “hide” individual values in bars or other visual elements” (NCTM p. 12).

In the Histogram and Boxplot, the data is supplied within the tool, in the Stem and Leaf Plot, you will be asked to cut and paste the data into the tool.

Experience It!

1. Click the Statistics and Probability and Concepts link at the Project Interactivate website () to see the full list of probability tools.

2. Experiment with each of the tools listed below. Note the type and format of data that can be entered, which (if any) of the measures of center are given, and any other features or limitations of the tool.

• Histogram ()

A histogram is used when data elements could assume any value in a range---heights or widths of objects, for example. The data are organized in equal intervals and the data values are marked on the horizontal axis. Bars of equal width are drawn for each interval, with the height of each bar representing either the number of elements or the percent of elements in that interval; the number or percent is marked on the vertical axis. The bars are drawn without any spaces between them (NCTM p. 12).

The histogram is often confused with a traditional bar graph. Unlike the data in a bar graph, the histogram displays contiguous, rather than discrete, values within a bar. That is, each bar in a histogram represents an interval of related data.

From the pull-down menu within the Histogram tool, choose the Gas Mileage data set and experiment with the slider below the graph to see how the size of the intervals influences the display of data.

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• Boxplot 2 ()

A box plot is a special kind of graph that displays five pieces of information from left to right: the minimum value of the data set, the median value of the lower half of the data set (also called the lower quartile), the median value of the entire data set, the median value of the upper half of the data set (also called the upper quartile), and the maximum value of the entire data set.

The data elements are not displayed individually, which makes it impossible to determine if there are gaps or clusters in the data sets, especially when the data sets are very large or when they have different numbers of data elements ((NCTM p. 14).

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a. Click the What button at the top of the web page to find out more information about box plots.

b. From the pull-down menu, choose the Gas Mileage dataset and experiment with both the full set of data and the set graphed by category.

• Stem and Leaf Plotter ()

A stem-and-leaf plot is much like a histogram in what it reveals, displaying the number of times that an event within a particular range occurs. Yet, unlike a histogram, the stem-and-leaf plot can show the exact data points. It is constructed by separating the tens digits of each data point on the left side of a line, and the remaining digits on the right side of a line. The tens digits are called the stems and the ones digits are called the leaves.

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This display works best when the data set contains more than 25 elements and when the data values span several decades of values (NTCM p. 13).

The data set that you will be using within this tool is the same gas mileage data that you used with the previous tool. The data is listed in the table on the following page.

To create a stem-and-leaf plot for the data,

a. Within the PDF or html version of this activity, select the numeric data in the Gas Mileage column of the table on the following page. (Do not select the table headings or the vehicle type data.)

b. Use the Copy command to copy the data.

c. Activate the Stem-and-Leaf plotter applet and place the cursor in the data window.

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d. Use the Paste command (Ctrl-V or Apple-V) to paste the data into the data window. (If you cannot access the electronic version of the data, you can type it in. Make sure to separate each entry with a carriage return or comma.)

e. Click Update Plot.

|Gas Mileage |Type Vehicle |

|49 |COMPACT |

|49 |COMPACT |

|45 |COMPACT |

|45 |COMPACT |

|41 |COMPACT |

|38 |COMPACT |

|38 |COMPACT |

|38 |COMPACT |

|40 |COMPACT |

|37 |COMPACT |

|37 |COMPACT |

|34 |COMPACT |

|35 |COMPACT |

|36 |COMPACT |

|35 |COMPACT |

|38 |COMPACT |

|38 |COMPACT |

|32 |COMPACT |

|32 |COMPACT |

|32 |COMPACT |

|37 |MIDSIZED |

|31 |MIDSIZED |

|32 |MIDSIZED |

|31 |MIDSIZED |

|32 |MIDSIZED |

|30 |MIDSIZED |

|30 |MIDSIZED |

|32 |MIDSIZED |

|30 |MIDSIZED |

|30 |MIDSIZED |

|29 |MIDSIZED |

|28 |MIDSIZED |

|29 |MIDSIZED |

|29 |MIDSIZED |

|29 |MIDSIZED |

|30 |MIDSIZED |

|28 |MIDSIZED |

|27 |MIDSIZED |

|29 |MIDSIZED |

|30 |MIDSIZED |

|28 |SUV |

|27 |SUV |

|28 |SUV |

|27 |SUV |

|27 |SUV |

|29 |SUV |

|29 |SUV |

|29 |SUV |

|26 |SUV |

|27 |SUV |

|25 |SUV |

|25 |SUV |

|25 |SUV |

|25 |SUV |

|25 |SUV |

|25 |SUV |

|25 |SUV |

|26 |SUV |

|26 |SUV |

|27 |SUV |

For more information about the features of this applet and other mathematical explorations, click the applet’s How, What, or Why button.

3. For each of the three data tools above, create a question that the tool would help answer about this data set. Which is the best tool to look at individual data? Which is the best for comparing the gas mileage of the three types of vehicles?

Reference

Bright, George W., Brewer, Wallece, McClain, Kay. Navigating through Data Analysis in Grades 6-8. Reston, VA: National Council of Teachers of Teachers of Mathematics, 2003. 12-14.

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