In this exploration you will investigate standard
deviation and deveop a better undertstanding of how it can help you
measure the spread of a data set.
This exploration will reinforce the concepts in Lesson 2.2 of Discovering
Advanced Algebra: An Investigative Approach.
This sketch shows 12 data points, with values that you
can adjust from 0 to 30 by dragging. The numerical values of the data
points and their sum are shown. You can see the mean by pressing Show
Mean. You can also press buttons to see the deviations from the
means and their sum, the squares of the deviations, and the standard
deviation. When the standard deviation is displayed, vertical lines
will enclose all points that lie within one standard deviation of the
- For the data points shown, make a guess about where
the mean is. Click to show the mean. Were you close? Now hide the mean,
change the data points, and try again.
- For the data points you have, make a guess about
which points lie from one standard deviation below the mean to one
standard deviation above the mean. Click to show the standard
deviation. Were you close? Now hide the standard deviation, change the
data points, and try again.
- Click to show the deviations. What is their sum? Will
this always be the case? Drag some points to test your conjecture. Can
you explain why your conjecture is true?
- Click to show the mean and the standard deviation.
How can you make the standard deviation large? Small?
- Drag some points so that you have outliers. What
effect do outliers have on the mean? On the standard deviation? For
which is the effect greater? Explain.
- If all of the data points were shifted 10 units to
the right, what would happen to the mean? To the standard deviation?
- Compare and contrast the information you get from the
mean with that from the standard deviation.
- If you have already studied box plots, compare and
contrast the information gained from a box-and-whiskers plot with this
graph of standard deviation.