Mathematics — Data Analysis
Grade 4
Data Collection, Benchmark C
02. Represent and interpret data using
tables, bar graphs, line plots and line graphs.
Data Collection, Benchmark C
04. Compare different representations
of the same data to evaluate how well each representation shows
important aspects of the data,
and identify appropriate ways to display the data.
Statistical Methods,
Benchmark E
07. Identify the median of a set
of data and describe what it indicates about the data.
Grade 6
Statistical Methods, Benchmark G
06. Make logical inferences from
statistical data.
Grade 8
Statistical Methods, Benchmark D
08. Describe how the relative size
of a sample compared to the target population affects the validity
of predictions.
Statistical Methods,
Benchmark F
09. Construct convincing arguments
based on analysis of data and interpretation of graphs.
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As a class, introduce this scenario
and ask the students to tell why it was or was not an appropriate
statistical study:
The school’s athletic booster club offered
$1,000 to the team that was most popular in the school.
The students decided
to do a
survey to find the most popular team. Students conducted
their survey in the hall after wrestling practice. It turned
out
that wresting
was the most popular sport in the school.
-
Pass out face-down the
100 Random Rectangles handout or show it on the overhead or
on the computer.
-
Have each student number a separate paper from
one to three and label number one as Guess, number two as Judgment
Sample
and number
three
as Random Sample.
-
Review the concept of area as the number of
squares it takes to cover an object. Give an example on the
board or overhead.
-
Tell the students that they are going to try
to find out what the mean or average area is for the rectangles
using three
different methods:
Guess: Have the students turn over the
100 Random Rectangles page and have the students study
it for 30 seconds. On
the guess line,
they need to write what they think the average
or mean number of squares on the page is.
Judgment Sample: Now
the students need to study the 100 Random Rectangles page
and write the numbers
of five
rectangles that they think are
representative of the rectangles on the page.
They then write
the area of each of the rectangles they found
and find the mean of
those five rectangles.
Random Sample: Using a
random number generator (either a graphing calculator or
the handout),
students should
get
five random
numbers between 1 and 100. They will then write
the area of the five
rectangles that were randomly generated and
find the mean.
-
Students
should make three number lines in a row, as indicated below,
making sure that all have the same intervals and
are the same size.
-
Have students make a line plot for
each set of data. They should round their means to the nearest
whole number.
Record
their
means on the board under the appropriate titles of
Guess, Judgment and Random.
-
Instruct students to write a few
sentences that explain what their graph is showing them. They
should find
that the mean
of the random
number area is the closest to the actual mean which
is 7.29.
-
Ask students whether the results would be
different if your sample was smaller or larger than five. Answer: If
the sample is random,
the greater the sample, the closer to the actual
number it will be.
- Help the class understand why
it is important when conducting a survey to have a random sample.
This activity was printed with permission from Dick Scheaffer
who authored it. It was also published in Activity-Based
Statistics,
Key College Publishing.
