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Exploring Histograms
The interactive data analysis tool in this investigation
allows students to create their own sets of data and examine
how various statistical functions such as mean, median,
and standard deviation depend on the choice of data.
This i-Math investigation is still in development. Stay tuned for future
additions to this investigation - additions that will include student
activities and reflective questions concerning pedagogical issues. Meanwhile,
by following the directions below, you can begin to become familiar with
the interactive tool itself.
To use this interactive tool:
- Entering and editing data: Enter data by clicking
in the "Data Input" box; type the value and
press "Enter" on the keyboard. To edit data,
select a data value by clicking on it and either delete
the value or enter a new one. You can order your data
values by checking the Order Data box. Use the slider
to change the length of the intervals used to create
the histogram.
- Looking at the histogram: When you click on a particular bar
on the histogram, the percentage of data values represented by that
bar is displayed. Place the mouse cursor along the bottom axis to reveal
the values determining the endpoints of each interval.
- Summary statistics: In the Summary Statistics box, the length
of the intervals, the number of data points, as well as the mean, median,
and the standard deviation are displayed.
Below the interactive tool are two sample activities
that students can use to learn about statistics. Both
activities in this investigation make use of the interactive
tool.
Sample Activity 1
- Clear any previous data.
- Enter the numbers 2,3, 4,4 and 5 into the bar chart.
- Note the summary statistics. What is the value of the mean? The median?
- Describe the shape of the histogram. Which of the following is easily
"seen" on the histogram: mean, median, or mode?
- Now enter 77.
- What happened to the mean? To the median? To the mode?
- How does the histogram change?
- What happens to the shape of the bar chart if you change the width of the bars?
Sample Activity 2
- Clear any previous data.
- Enter the numbers 2, 3, 4, 4 and 5 using "Data
Input."
- Note the summary statistics. What is the value of the mean? The median?
- Describe the shape of the histogram. What is the value of the mode?
- Now repeatedly enter the number 5.
- What happened to the mean? To the median? To the mode?
- How does the histogram change?
- What happens to
the shape of the histogram if you change the length of the intervals?
References and
Credits
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