1-7 Data and Spread Big Idea Two measures of the spread of a data set are range and mean absolute deviation. Range, the difference between the maximum.

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Presentation transcript:

1-7 Data and Spread Big Idea Two measures of the spread of a data set are range and mean absolute deviation. Range, the difference between the maximum and minimum values (M – m) of a data set is often used in statistical reports to explain the spread of a set of data. Another calculated number used to explain the spread of a data set is mean standard deviation. 1) find the mean of the data set; 2) subtract the mean from each value; 3) find the absolute value of the differences; and finally 4) find the mean of the absolute values.

To find the mean absolute deviation with a graph- ing calculator. 5,11,3,6,9,4,0,15,6,8,11,7,2,1,3,4,10,9,4,6,8,0 Go to List, type in the data set in L1. To find the mean of a data set, find the sum of the data items then divide by the total # of items by: 1.Leave List (2 nd, quit). 2.Then click 2 nd key, catalog (above prgm), scroll down to mean(, enter. 4. Click 2 nd, List select L1, enter, enter.

To subtract the mean from each data set value: 1.Go to List, arrow up to L2 at the very top 2.Click 2 nd List, select L1, enter 3.Type – mean #, enter To find the absolute value of each #: 1.Go to List, arrow up to L3 2. Then click 2nd key, catalog (above prgm), scroll down to abs(, enter 3. Click 2nd List, select L2, enter, enter Find the mean the same as before, this time for L3 You have just found the mean absolute deviation.

Instead of using the letter m to represent the mean, you will often see the symbol μ (mew) because M represents maximum value and m, minimum. Types of displays for data used often are frequency tables, bar graphs and dot plots. You need to be familiar with each type. See page 47 in your book. The outlining shape of the plotted data can add meaning to the data set. Here are some examples with their names. symmetric skewed right skewed left uniform

Using excel spreadsheet to find M.A.D. Data: 5,11,3,6,9,4,0,15,6,8,11,7,2,1,3,4,10,9,4,6,8,0 1.Type headings for columns in rows 1 and 2. 2.Type in your data values in column A. 3. Cell 26 type =, then go to box above column A, select average. A dialog box will show you what you are averaging, so click ok and 6 will appear in cell A26 4. Select cell B3, type =A3-6, enter, -1 will appear in cell B3. To do the other cells in B, click on B3 again and copy it. Then highlight the cells B4-B24 (click and drag mouse), then enter. Column B should now be filled with values. 5.Select cell C3, type =, go to the box next to average click to pull down the menu. Select abs (absolute value), in the dialog box type B3 then click ok. 1 will appear in cell C3. To complete the column, select C3, copy, highlight cells C4-C24, enter. 6.Finally go to C26 to calculate the final average. Type =, go to box to pull down the menu of options, select average, click ok in the dialog box. Your average should be 3.09 repeating. ▼ ▼