Actual Median: Actual Mean: Actual Median: Actual Mean
Handout#16
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Means and Medians practice
Go to this website httP://statweb.calpolv.eduichance/applets/DotPlotAppleUDotPlotApplet.html
1.
2. 3.
Click the Draw Sample button until you find a distribution that is skewed to the
right.
Click the Guess the Mean/Median box. Two lines will appear. Move these lines to where you think the mean and then the median will be positioned. Click the Show Actual box. How did you do?
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
4-
Repeat steps 1-3 for a symmetric distribution.
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
5.
Repeat steps 1-3 for a distribution skewed to the left.
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
6.
Repeat steps 1-3 for a distribution has a large outlier.
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
7.
Now click on that outlier and move it to be further and further away from the rest of the distribution.
How does the mean change?
The median?
39
t
Handout#17
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What Does a Median Mean?
Let's go back to the Post-lt@ Notes. This time, only use 9 of them.
1.
Arrange them on the plot Age Scale so that the median is 21years. What did you have to do to achieve a median of 21?
2.
Now change one of the values that is currently higher than 21years. lf you move it higher or lower than it is right now, but keep the value higher than 21 years, is the median affected? Explain.
3.
Now move all of the values that are above 21 years so that each one has a higher value than it does currently. Did this have any effect on the median? Explain.
4.
Now move all of the values that are lower than 2l years so that each one has a lower value than it does currently. Did this have any effect on the median? Explain.
5.
What would you have to do with a data value to change the median? Explain.
4t
Handout#17
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What Does a Median Mean?
Things to Consider
.
.
.
.
.
What factors affect the median for a data set? Using our set of 9 Post-lt@ Notes, under what conditions does the median change or stay the same?
What would change if we used 10 Post-lt@ Notes and tried to find the median?
What are the properties of the median? How do those differ from properties of the mean?
When does a median seem to be a better measure of what is typical about a data set?
lf we think of lhe mean as a "balance point" of the deviations, what would the median balance?
42
-
Means and Medians practice
Go to this website httP://statweb.calpolv.eduichance/applets/DotPlotAppleUDotPlotApplet.html
1.
2. 3.
Click the Draw Sample button until you find a distribution that is skewed to the
right.
Click the Guess the Mean/Median box. Two lines will appear. Move these lines to where you think the mean and then the median will be positioned. Click the Show Actual box. How did you do?
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
4-
Repeat steps 1-3 for a symmetric distribution.
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
5.
Repeat steps 1-3 for a distribution skewed to the left.
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
6.
Repeat steps 1-3 for a distribution has a large outlier.
Guessed Mean:
Actual Mean:
Guessed Median:
Actual Median:
7.
Now click on that outlier and move it to be further and further away from the rest of the distribution.
How does the mean change?
The median?
39
t
Handout#17
-
What Does a Median Mean?
Let's go back to the Post-lt@ Notes. This time, only use 9 of them.
1.
Arrange them on the plot Age Scale so that the median is 21years. What did you have to do to achieve a median of 21?
2.
Now change one of the values that is currently higher than 21years. lf you move it higher or lower than it is right now, but keep the value higher than 21 years, is the median affected? Explain.
3.
Now move all of the values that are above 21 years so that each one has a higher value than it does currently. Did this have any effect on the median? Explain.
4.
Now move all of the values that are lower than 2l years so that each one has a lower value than it does currently. Did this have any effect on the median? Explain.
5.
What would you have to do with a data value to change the median? Explain.
4t
Handout#17
-
What Does a Median Mean?
Things to Consider
.
.
.
.
.
What factors affect the median for a data set? Using our set of 9 Post-lt@ Notes, under what conditions does the median change or stay the same?
What would change if we used 10 Post-lt@ Notes and tried to find the median?
What are the properties of the median? How do those differ from properties of the mean?
When does a median seem to be a better measure of what is typical about a data set?
lf we think of lhe mean as a "balance point" of the deviations, what would the median balance?
42
