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Drag a new Case Table off the shelf. (See Figure 1) Figure 1Enter data from rectangle sheet using **Number, Length**and**Width**as attributes. (See Figure 2a) -
Create a new attribute, **Area**by typing its name where you the <new> column heading. Then press enter or tab. -
To create the formula for **Area**, highlight the column and choose Edit > Edit Formula. The formula editor appears; enter**Length * Width**and then press OK to close the editor. (See Figure 2b) Figure 2a Figure 2b Drag a new graph off the shelf; drag the name of the attribute area to the horizontal axis. Change from Dot Plot to Histogram. (See Figure 3) Figure 3Choose Graph > Plot Value. The formula editor appears; enter **mean ( )**and then press OK to close the editor. Repeat for**median ( ).**(See Figure 4) Figure 4Drag a summary table off the shelf. (See Figure 5a) Figure 5aThen drag **Area**to the cell below the down arrow. A value for mean will appear automatically. Note the summary table must be selected for the summary table to appear. (See Figure 5b) Figure 5bChoose Summary > Add Formula; enter in **median ( ).**(See Figure 6) Figure 6- Select the collection
**Rectangles**(gold balls). Choose Analyze > Sample Cases. You will see the collection**Sample of Rectangles**appear. Double click on **Sample of Rectangles;**the Inspector will appear. Deselect 'Animation' and 'With Replacement;' type in**5**for Cases. Click 'Sample More Cases.' (See Figure 7) Figure 7Drag a new Case Table off the shelf for **Sample of Rectangles.**This will show a random sample of 5 cases from the**Rectangles**collection. Note that if the sample collection is not selected, this will not work. (See Figure 8) Figure 8Drag a new graph off the shelf; create a histogram of area. (See Figure 9) Figure 9- Choose Graph > Plot Value; Enter
**mean ( )**and press OK to close the formula editor. The mean appears as a vertical line in the graph. Repeat for**median ( ).**(See Figure 10) Figure 10 Double click on the Collection **Sample of Rectangles**to get the**Inspector.**Click on**Measures;**type in**MeanArea.**Click on the 'Formula' cell for the**MeanArea**and enter**mean**(area ). (See Figure 11) Figure 11Select the collection **Sample of Rectangles;**choose Analyze > Collect Measures. A new collection,**Measures from Sample of Rectangles**will appear.Drag a Case Table from the shelf for the collection **Measures from a Sample of Rectangles.**It will show**5**means, each of which is the result of selecting**5**random rectangles, which was done**5**different times. (See Figure 12a)Double click on the collection **Measures from Sample of Rectangles**to get the Inspector. Deselect 'Animation' and enter '100' for measures; click 'Collect More Measures.' Your Case Table should now have 100 entries. (See Figure 12b)Figure 12a Figure 12b Drag a new graph from the shelf; create a histogram of Mean Area. Use the Edit > Edit Formula; enter mean ( ). Repeat for median ( ). (See Figure 13) Figure 13Compare the graphs and their properties to the original data. Students should note any differences in spread, shape, mean, median, and mode. There is a tendency for people to select a sample of rectangles with large area, thus causing bias. Was there evidence of this bias in your original sample? How do you know?**Extension:**Collect more measures (1000) and plot the Normal Curve on the Histogram. To accomplish this:- With the graph selected, choose Graph > Scale > Density
- Choose Graph > Plot Function
- Enter
**normalDensity(x,mean( ),s( )).**
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With program support provided by Math for America This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. |