Chapter 1. Mean and Median

Statistical Applets

Click below the line to add an observation. The red arrow marks the median. The green arrow marks the mean. When the median and mean are equal a single yellow arrow is shown. You can move a point by dragging it along the line, or remove it by dragging it to the trash. At the left you can enter new values for the upper and lower limits of your distribution and click the UPDATE button to save them.

A description of a distribution almost always includes a measure of its center. The two common measures of center are the mean and the median. This applet lets you explore the relationship between the mean and median as the points in a dataset change.

1.

Experiment with the applet to answer the following question: with two values, the mean and median are exactly the same.

2
Try again.
Incorrect. See above for the correct answer.
Great job.

2.

Make sure that the lower value is set to 0 and the upper value to 10 (these are the default values), then add at least 5 points to the graph in a distribution that has the following two characteristics: a) All values are below 5 (that is, on the left side of the number line); b)The median and mean are identical

3
To answer this question you must add points to the numberline.
Great job.
Add 5 points where the median and median are identical.

3.

Now add another point on the far right side of the line. This has the effect of making the mean the median.

2
Try again.
Incorrect. See above for the correct answer.
Great job.

4.

Did adding this additional point affect the mean or median the most? (That is, which value—mean or median—changed the most when you added the new point?) Explain how this illustrates why one statistic is more resistant than the other.

The median is more resistant to outlying values than the mean. Therefore, the mean is more affected by adding the extreme point on the right side of the graph.