module 3 example 15
TRANSCRIPT
![Page 1: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/1.jpg)
Example 15: Miles RunClass Boundaries Frequency
5.5 – 10.5 110.5 – 15.5 215.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
![Page 2: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/2.jpg)
Example 15: Miles RunClass Boundaries Frequency
5.5 – 10.5 110.5 – 15.5 215.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) = =
![Page 3: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/3.jpg)
Example 15: Miles RunClass Boundaries Frequency
5.5 – 10.5 110.5 – 15.5 215.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) = =
![Page 4: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/4.jpg)
Example 15: Miles RunClass Boundaries Frequency
5.5 – 10.5 110.5 – 15.5 215.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 5: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/5.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 110.5 – 15.5 215.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 6: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/6.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 215.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 7: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/7.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 320.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 8: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/8.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 525.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 9: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/9.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 430.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 10: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/10.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 11: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/11.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 12: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/12.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) =
![Page 13: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/13.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 14: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/14.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 15: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/15.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 1315.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 16: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/16.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 1820.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 17: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/17.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 2325.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 18: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/18.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 2830.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 19: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/19.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 3335.5 – 40.5 2 (35.5+40.5)/2 = 38
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 20: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/20.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1)
![Page 21: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/21.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ( · )
![Page 22: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/22.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ( · )
![Page 23: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/23.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 24: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/24.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 810.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 25: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/25.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 2615.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 26: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/26.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 5420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 27: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/27.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 11525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 11230.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 28: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/28.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 9935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 29: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/29.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 30: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/30.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ,
![Page 31: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/31.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 32: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/32.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 33: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/33.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 16915.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 34: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/34.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 32420.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 35: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/35.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 52925.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 36: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/36.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 78430.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 37: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/37.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 108935.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 38: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/38.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 39: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/39.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444 2∙1444 = 2888
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) , ( · )
![Page 40: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/40.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444 2∙1444 = 2888
= ∑ = 20 ∑( · ) = 490
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ( · )
![Page 41: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/41.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444 2∙1444 = 2888
= ∑ = 20 ∑( · ) = 490 ∑( · 2) = 13310
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) ( · )
![Page 42: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/42.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444 2∙1444 = 2888
= ∑ = 20 ∑( · ) = 490 ∑( · 2) = 13310
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = ∑( · ) − ∑( · ) ( − 1) = 20 13310 − (490)
20(19) = 266200 − 240100380 = 26100
380 ≈ 68.7
![Page 43: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/43.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444 2∙1444 = 2888
= ∑ = 20 ∑( · ) = 490 ∑( · 2) = 13310
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = 26100380 ≈ 68.7
![Page 44: Module 3 example 15](https://reader034.vdocuments.us/reader034/viewer/2022042706/589c07741a28ab4f598b60dd/html5/thumbnails/44.jpg)
Example 15: Miles RunClass Boundaries Frequency x, Midpoint f∙x x2 f∙x2
5.5 – 10.5 1 (5.5+10.5)/2 = 8 1∙8 = 8 82 = 64 1∙64 = 6410.5 – 15.5 2 (10.5+15.5)/2 = 13 2∙13 = 26 132 = 169 2∙169 = 33815.5 – 20.5 3 (15.5+20.5)/2 = 18 3∙18 = 54 182 = 324 3∙324 = 97220.5 – 25.5 5 (20.5+25.5)/2 = 23 5∙23 = 115 232 = 529 5∙529 = 264525.5 – 30.5 4 (25.5+30.5)/2 = 28 4∙28 = 112 282 = 784 4∙784 = 313630.5 – 35.5 3 (30.5+35.5)/2 = 33 3∙33 = 99 332 = 1089 3∙1089 = 326735.5 – 40.5 2 (35.5+40.5)/2 = 38 2∙38 = 76 382 = 1444 2∙1444 = 2888
= ∑ = 20 ∑( · ) = 490 ∑( · 2) = 13310
Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the variance and standard deviation
: = 26100380 ≈ 68.7 : = = 26100
380 ≈ 8.3