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This Exploration uses a java applet (by Keith Dear at Surfstat, with slight modification by me.) to demonstrate how changing scores in a data set effect the mean and median as referenced on page 2-14 of your text.
Instructions
The line in the box below, represents a possible range of scores in a data set.
Add scores - To add scores to the data set, use the mouse to click below the line.
Move scores - You can move individual data points by clicking on the point with the mouse and dragging to a new position.
Remove scores - You can remove individual scores by clicking the mouse on the score and dragging it to the bottom of the box.
Reset - You can reset the line to its initial state by clicking the "Reset" button.
Two diamonds, one red and the other in green , appear above the line. One of the diamonds represents the mean and the other the median. Use this applet to complete the tasks below.
- Task 1 - Put several data points below the line and watch how the diamonds change. (If the diamonds are on top of each other they will appear orange). Can you identify which diamond is the mean and which is the median? Click here for the answer.
- Task 2 - Place three data points below the line in the following order - far left, far right, centre.
(a) Write a sentence describing and explaining the changes in the mean and median.
(b) Slowly slide the central point to the left so that it eventually joins the far left point. Next slide the central point to the right so that it eventually joins the far right point. Write a sentence describing and explaining the changes in the mean and median.
- Task 3 - Place five data points as close to the far left of the line as possible. Now slowly add data points to the far right of the line, while watching the changes in the mean and median.
(a) Write a sentence describing and explaining the changes in the mean and median.
(b) Which measure of central tendency is the most resistant up to the fourth score?
(c) Explain what happens to the mean and median when the fifth score is added to the right?
(d) Which measure of central tendency is the most resistant from the fourth to the sixth score? Explain your answer.
- Task 4 - Place five data points as close to the centre of the line as possible. Now slowly add data points to the far right of the line, while watching the changes in the mean and median.
(a) Write a sentence describing and explaining the changes in the mean and median.
(b) Which measure of central tendency is the most resistant up to the fourth score?
(c) Explain what happens to the mean and median when the fifth score is added to the right?
(d) Which measure of central tendency is the most resistant from the fourth to the sixth score? Explain your answer.
- Task 5 - Investigate for a collection of random points, which is more resistant if you move a middle point, the mean or the median. Do the same for end points. In a real dataset, which (middle or end) is more likely to be a data error?
- Task 6 - Read about Measures of centre at this site. Click "Summarising and Presenting data" and then "Measures of central tendency".
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