Question

Question 4 Using the dataset below, estimate whether there is a difference among the graduation rates - identified as percentages - of five high schools over a 10-year period. Explain your results. Yr HS 1 HS 2 HS 3 HS 4 HS 5 2003 67 82 94 65 88 2004 68 87 78 65 87 2005 65 83 81 45 86 2006 68 73 76 57 88 2007 67 77 75 68 89 2008 71 74 81 76 87 2009 78 76 79 77 81 2010 76 78 89 72 78 2011 72 76 76 69 89 2012 77 86 77 58 87

Answer 1

We have the given data as

Year. HS1. HS2 . HS3 . HS4 . HS5

2003 . 67 . 82 . 94 . 65. 68

2004 . 68 . 87. 78 . 65. 87

2005 . 65 . 83 . 81 . 45. 86

2006 . 68 . 73. 76. 57. 88

2007 . 67 . 77 . 75 . 68 . 89

2008 . 71 . 74 . 81. 76 . 87

2009 . 78 . 76 . 79 . 77. 81

2010 . 76. 78 . 89. 72. 78

2011 . 72 . 76 . 76 . 69 . 89

2012 . 77. 86 . 77. 58 . 87   

Total. 709 . 792 806 . 652 . 840

Mean . 70.9 79.2 80.6 65.2 84

(X_=Total/number)   

Standard deviation =summation of(X-X_)2÷(total number) table of| X-X_ |

2003 3.9 2.8 . 13.4. 0.2 . 16

2004 . 2.9. 7.8. 2.6. 0.2 . 3

2005 . 5.9. 3.8 . 0.4 . 20.2 . 2

2006 . 2.9 . 6.2 . 4.6 . 8.2 . 4   

2007 . 3.9 . 2.2 . 5.6 . 2.8 . 5

2008 . 0.1 . 5.2. 0.4 . 10.8 . 3

2009 . 7.1 . 3.2 . 1.6 . 11.8 . 3

2010. 5.1 . 1.2 . 8.4 . 6.8 . 6

2011 . 1.9 . 3.2. 4.6 . 3.8 . 5

2012 6.1 6.8 3.6 7.2 . 3

Table of |X-X_|square

15.21 . 7.84 . 179.56 . 0.04 . 256

8.41. 60.84 . 6.76 . 0.04. 9

34.81 . 14.44 0.16 . 408.04 . 4

8.41 38.44. 21.16 . 67.24 . 16

5.21. 4.84 31.36 . 7.84 . 25

0.01 27.04 0.16 . 116.04 9

50.41 10.24. 2.56 . 139.24 9

26.01 1.44 . 70.56 . 46.24 36

3.61 10.24 . 21.16. 14.44. 25

37.21 46..24 . 12.96 . 51.84 9

Total= 189.3 221.6 346.4 851.6 398

Standard deviation

= 18.93 22.16 34.64 85.16 39.8

There is graduation rate difference the graduation happens in high school 4 has a very high standard deviation hence we can say that HS4 shows high deviation in graduation rate but HS1 shows less deviation indicate approximately constant behaviour in the graduation rate.Hence we can see the difference in the graduation rates about the given data.