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Standard Deviation of Grouped Data Standard deviation can be found by summing the square of the deviation of each value, or, If the value is present more than once, the square of the deviation can be calculated once and multiplied by the frequency of occurrences
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Standard Deviation of Grouped Data Find the sample standard deviation of the following data: 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 52 63 76 82 91 Sum
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Standard Deviation of Grouped Data Find the sample standard deviation of the following data: 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 5210 6318 7642 8216 919 Sum1495
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Standard Deviation of Grouped Data Find the sample standard deviation of the following data: 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 5210-1.786 6318-0.7857 76420.2143 82161.2143 9192.2143 Sum1495
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Standard Deviation of Grouped Data Find the sample standard deviation of the following data: 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 5210-1.7863.1888 6318-0.78570.61735 76420.21430.04592 82161.21431.4745 9192.21434.9031 Sum1495
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Standard Deviation of Grouped Data Find the sample standard deviation of the following data: 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 5210-1.7863.18886.378 6318-0.78570.617351.852 76420.21430.045920.276 82161.21431.47452.949 9192.21434.90314.903 Sum149516.357
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Standard Deviation of Grouped Data Find the sample standard deviation of the following data: 7, 6, 7, 6, 7, 8, 5, 6, 7, 5, 7, 8, 9, 7 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 5210-1.7863.18886.378 6318-0.78570.617351.852 76420.21430.045920.276 82161.21431.47452.949 9192.21434.90314.903 Sum149516.357
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Standard Deviation of Grouped Data The calculator also gives 1.122 xfxfx - xbar(x – xbar)^2(x – xbar) ^2 * f 5210-1.7863.18886.378 6318-0.78570.617351.852 76420.21430.045920.276 82161.21431.47452.949 9192.21434.90314.903 Sum149516.357
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Standard Deviation of Grouped Data We grouped the data in the above example. The same process can be used when given data in the form of a histogram or pie chart. Since the values of the specific data points has been lost,assume all the data points within a cell have the same value as the cell midpoint. The student is left to review Example 10 on page 77.
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Standard Deviation of Grouped Data Assume the histogram on the following slide represents our data. Make a table of values (x values – the midpoint of each column), including the frequency of each column. Calculate the sample standard deviation of the data represented in the histogram
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Standard Deviation of Grouped Data The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 12 23 35 44 51 Sum The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122 236 3515 4416 515 Sum1544 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122-1.933 236-0.933 35150.067 44161.067 5152.067 Sum1544 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1 What does this add to?
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122-1.933 236-0.933 35150.067 44161.067 5152.067 Sum1544 0 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1 What does this add to?
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122-1.933-3.867 236-0.933-2.800 35150.0670.3333 44161.0674.2667 5152.067 Sum1544 0 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1 What does this add to?
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122-1.933-3.867 236-0.933-2.800 35150.0670.3333 44161.0674.2667 5152.067 Sum1544 0 0 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122-1.933-3.8673.7387.476 236-0.933-2.8000.8712.613 35150.0670.33330.0040.022 44161.0674.26671.1374.551 5152.067 4.271 Sum1544 0 018.933 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1
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Standard Deviation of Grouped Data xfxfx - xbar(x – xbar) * f(x – xbar)^2(x – xbar) ^2 * f 122-1.933-3.8673.7387.476 236-0.933-2.8000.8712.613 35150.0670.33330.0040.022 44161.0674.26671.1374.551 5152.067 4.271 Sum1544 0 018.933 The cell midpoints are 1, 2, 3, 4, and 5 The frequencies are 2, 3, 5, 4, and 1
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How can we do this in our calculator? Put the “x” values in L1 Put the frequency in L2 Stat Calc 1-Var Stats 2 nd L1, 2 nd L2, Enter Standard Deviation of Grouped Data
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Homework Pg 81 & 82, # 29 – 32 all (4)
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