Chapter 1. Mean and Median

Introduction

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.

Click the "Quiz Me" button to complete the activity.

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.

Question 1.1

Experiment with the applet to answer the following question: with two values, the mean and median are 70CLCpBLrVbDCFBRNlN3CbUQVcOA8IvWMU9RkQ== exactly the same.

2
Try again.
Incorrect. With only two values, the mean and median are always exactly the same.
Great job.

Question 1.2

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3
To answer this question make sure the lower value is set to 0, the upper value is set to 10, you have placed at least 5 points on the number line and they are all below 5, and the mean and median are equal. Please try again.
Great job. Do not clear the graph or add/move any points. Please proceed to the next question.
Sorry, that is incorrect. One possible correct answer is shown above. Do not clear the graph or add/move any points. Please proceed to the next question.
Add 5 points where the median and median are identical.

Question 1.3

Now add another point on the far right side of the graph. This has the effect of making the mean VfuRCwlTAeoKF9pu9xJtP/pVxaesXIFfyDyNuf+wz7qgt9RNZwn83w== the median.

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

Question 1.4

myVCgmxoFGhiEQsrBmeEnuiTbLZ7p0WvsTs1eMu4mdEAsrHJMeQ3K4/kjK57xxfw36Ltz7HPN0DCv6zWaSv20PHLVucm53OHDkkjNK92MloNNrU7PrNU0QGBWCYqxtzZZcnQjDQ4DBtF2xew24GXwMfSsKFxFA5ujlhDe23ODvQqaDOdCsARoI9sQRM9OEC0xFvr1bbByg9li6AbFpphlK4pFPXVm4YMnkH1y7JWbZwLxikFhwIdbqUWfOK5otqzugW7wi9WIsjrFmuBKulA2Zhgthg0gZB8Vbm6xkK2SL2LRebefFfBIRdmablzoHydgHHpWeNJ7+jYWUqXw1Cm1rhj1f/sz5p/HVwG8S3mbG9elDpf
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.