Basic Statistical Concepts
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Spreadsheets are very useful for handling basic statistics like
the mean, median, mode, frequency, and
range. These concepts become increasingly important as
students learn to collect and analyze large sets of data. These
basics statistics also enable us to make intelligent predictions and
discover trends. The other key advantage of using a spreadsheet with
basic statistics is that we can chart the results.
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Math Objective
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The purpose of this lesson is to:
- introduce students to basic statistical concepts
- enable them to manipulate data on the
spreadsheet
- graph data
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Skills/Outcomes
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- Collect, organize, graph, and interpret data from
real-life situations and apply results in solving
- problems
- Summarize data using mean, median, mode,
frequency, and range
- Make data tables
Spreadsheet Skills
- make a data table
- sort data
- make a frequency table
- use built-in statistical function (mode, median,
range) or enter formulas
- make charts from data tables
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Classroom
Discussion and Activities
Computer Lab Activities
Added Exercises
Classroom
Discussion and Activities (Whole Group)
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Teacher Note: In this activity, you will be able
to collect simple data from the students as a basis for
exploring statistical concepts. You will use the length of
student names as a basis for data analysis. In the interest
of time, you may want to enter actual student grades into a
spreadsheet file in one column (or several columns of grades
if you want to extend the exercise). A sample file of
students names is included in grades.xls.
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- Discuss the problem of making sense out of school grades
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- When teachers grade student tests they also want to get a
general idea of how everyone did. Looking at scores one-by-one
doesn't help. There are some basic statistical ideas that can
help anyone understand and organize the data.
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- If you are not using actual grades from a class, pass out
grades.doc to each of the students.
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- As a class activity, students will transform the individual
scores in the column into a frequency table, which is at the
bottom of the page. Students put X's in the columns for each
score (e.g., Holly Ehm's score of 87 goes in the 87 column as
an X just above the number 87).
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- Discuss and analyze the data
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- The distribution of X's in columns gives us a
frequency. That is, it tells us how many students got
each score. But it doesn't tell us other important information
such as, "What was the class average?" and "What was the most
common score?"
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- At this point you can introduce or review the concepts
of mean, median, mode, and range. Use the
frequency table that the students have created to discuss each
concept.
Computer
Lab Activities (Individual or Paired Work)
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Teacher Note: Use the file grades.xls for
the first activity. This is the same list of students that
was used in the preceding exercise. This time students will
use functions and charts to complete the activity. You will
need to know the function names for the basic statistics
(mean, median, and mode) as well as how to
create bar charts in order to do this part of the
lesson.
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- Begin by having the students put labels to the right of the
column of scores. They should put labels for mean, median,
mode, and range
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- Sort the Data
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- This will require that the students start with the column
of numbers, drag down the entire column and then drag over the
column of names. All of the numbers and names should be
highlighted. Next use the SORT menu command to sort the numbers
from low to high (high numbers are on the bottom).
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- Find the Basic Statistics
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- Teach the students how to use the functions by typing in
the function name. For example, to find the average of the
numbers in B1-B15, the function would be =average (B1:B15).
Function names are =average (for the mean), =median (for
median), and =mode (for mode). Students can look
at the top and bottom numbers in the sorted column of data to
find the range.
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- Create a Chart
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- You can use your frequency table from grades.doc as
a basis for creating a bar chart. Students can scroll to a
different part of grades.xls or create a new
spreadsheet. Enter the numbers along the bottom of the
frequency table in one column and the number of students who
had that score in the column next to it. Have the student use
the chart option to create a bar chart of the data. You can
compare the chart on the spreadsheet to the one on paper to see
how similar they are. If time permits, students can change from
a bar chart to a line chart or create 3-D charts.
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Added
Exercises
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Teacher Note: This last exercise allows students
to use all of the basic statistics as well as create line
charts that ask them to identify trends in the data. Again,
you will need to know how to use functions and create charts
to do this added exercise. Once you finish this exercise,
you are in a position to have students collect their own
data on problems that you help them identify.
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- Analyzing Soda Consumption
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- The file sodacon.xls contains data on how much soda
the students have purchased from the school's vending machines
for the last five years. The data show the number of cans of
Coke, Pepsi, Dr. Pepper, Mountain Dew, and 7-Up sold during
each of the five years.
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- Have the students find the average number of cans for each
type of soda for the five years. For example, what was the
average number of Pepsi's sold from 1992-1997? Without sorting
the data, have them identify the range.
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- Finally, have them create a line chart that has all of the
soda data in it. This line chart will show changes in
consumption of the different sodas over the five years. Have
the students talk about the trends in the data. Which sodas are
becoming more popular? Which ones are staying the same?
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- As a dynamic way to show how spreadsheets can redraw
information, tell them that one year's data were wrong. Supply
them with new data for that year and have them pay attention to
how changes in the data for one year change the averages and
the lines on the chart. If time permits, you could also have
students experiment with 3-D charts.