![Page 1: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/1.jpg)
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
![Page 2: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/2.jpg)
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
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 26 37 68 29 1
Sum
![Page 3: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/3.jpg)
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•
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 2 106 3 187 6 428 2 169 1 9
Sum 14 95
786.614
95
n
xfx
![Page 4: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/4.jpg)
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•
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 2 10 -1.7866 3 18 -0.78577 6 42 0.21438 2 16 1.21439 1 9 2.2143
Sum 14 95
786.614
95
n
xfx
![Page 5: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/5.jpg)
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•
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 2 10 -1.786 3.18886 3 18 -0.7857 0.617357 6 42 0.2143 0.045928 2 16 1.2143 1.47459 1 9 2.2143 4.9031
Sum 14 95
786.614
95
n
xfx
![Page 6: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/6.jpg)
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•
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 2 10 -1.786 3.1888 6.3786 3 18 -0.7857 0.61735 1.8527 6 42 0.2143 0.04592 0.2768 2 16 1.2143 1.4745 2.9499 1 9 2.2143 4.9031 4.903
Sum 14 95 16.357
786.614
95
n
xfx
![Page 7: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/7.jpg)
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•
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 2 10 -1.786 3.1888 6.3786 3 18 -0.7857 0.61735 1.8527 6 42 0.2143 0.04592 0.2768 2 16 1.2143 1.4745 2.9499 1 9 2.2143 4.9031 4.903
Sum 14 95 16.357
786.614
95
n
xfx
![Page 8: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/8.jpg)
Standard Deviation of Grouped Data
122.1
13
357.16
1
2
2
n
fxxss
•The calculator also gives 1.122
x f xf x - xbar (x – xbar)^2 (x – xbar) ^2 * f
5 2 10 -1.786 3.1888 6.378
6 3 18 -0.7857 0.61735 1.852
7 6 42 0.2143 0.04592 0.276
8 2 16 1.2143 1.4745 2.949
9 1 9 2.2143 4.9031 4.903
Sum 14 95 16.357
![Page 9: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/9.jpg)
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.
![Page 10: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/10.jpg)
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
![Page 11: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/11.jpg)
Standard Deviation of Grouped Data
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1
1 2 3 4 50
1
2
3
4
5
6
Frequency versus Midpoints
![Page 12: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/12.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 22 33 54 45 1
Sum
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1
![Page 13: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/13.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 22 3 63 5 154 4 165 1 5
Sum 15 44
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
933.215
44
n
xfx
![Page 14: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/14.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 2 -1.9332 3 6 -0.9333 5 15 0.0674 4 16 1.0675 1 5 2.067
Sum 15 44
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
933.215
44
n
xfx What does this
add to?
![Page 15: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/15.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 2 -1.9332 3 6 -0.9333 5 15 0.0674 4 16 1.0675 1 5 2.067
Sum 15 44 0
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
933.215
44
n
xfx What does this
add to?
![Page 16: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/16.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 2 -1.933 -3.8672 3 6 -0.933 -2.8003 5 15 0.067 0.33334 4 16 1.067 4.26675 1 5 2.067 2.067
Sum 15 44 0
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
933.215
44
n
xfx What does this
add to?
![Page 17: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/17.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 2 -1.933 -3.8672 3 6 -0.933 -2.8003 5 15 0.067 0.33334 4 16 1.067 4.26675 1 5 2.067 2.067
Sum 15 44 0 0
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
933.215
44
n
xfx
![Page 18: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/18.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 2 -1.933 -3.867 3.738 7.4762 3 6 -0.933 -2.800 0.871 2.6133 5 15 0.067 0.3333 0.004 0.0224 4 16 1.067 4.2667 1.137 4.5515 1 5 2.067 2.067 4.271 4.271
Sum 15 44 0 0 18.933
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
•
933.215
44
n
xfx
![Page 19: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/19.jpg)
Standard Deviation of Grouped Data
x f xf x - xbar (x – xbar) * f (x – xbar)^2 (x – xbar) ^2 * f
1 2 2 -1.933 -3.867 3.738 7.4762 3 6 -0.933 -2.800 0.871 2.6133 5 15 0.067 0.3333 0.004 0.0224 4 16 1.067 4.2667 1.137 4.5515 1 5 2.067 2.067 4.271 4.271
Sum 15 44 0 0 18.933
• The cell midpoints are 1, 2, 3, 4, and 5• The frequencies are 2, 3, 5, 4, and 1•
•
933.215
44
n
xfx
163.1
14
933.18
1
2
2
n
fxxss
![Page 20: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/20.jpg)
• How can we do this in our calculator?• Put the “x” values in L1• Put the frequency in L2• Stat• Calc• 1-Var Stats• 2nd L1, 2nd L2, Enter
Standard Deviation of Grouped Data
![Page 21: 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](https://reader036.vdocuments.net/reader036/viewer/2022062315/5697c02d1a28abf838cd9c46/html5/thumbnails/21.jpg)
Homework
• Pg 81 & 82, # 29 – 32 all (4)