Statistics assignment 2.2

Business Statistics (BUS 505) Assignment II

Question: 01

13 15 8 16 84 21 11 3 15

Ascending Order for this Population Number:

3 4 8 8 11 13 15 15 16 21

Population Mid Hinge: = = =11. 125

Population Inter Quartile Range (IQR): Q3 – Q1= 15.25 – 7 = 8.27

Population Variance:

= -

= -129.96

= 29.04

Population Standard Deviation:

= = = 5.39

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Population Mean Absolute Deviation:

=

= = 4.56

Population Coefficient of Variance:

= x 100 = x100 = 47.27%

Xi Xi- µ

3 -8.4 8.44 -7.4 7.48 -3.4 3.48 -3.4 3.411 -.04 .0413 1.6 1.615 3.6 3.615 3.6 3.616 4.6 4.621 9.6 9.6Total: 0 45.64

1


Question: 02

21 22 27 36 22 2922 23 22 28 36 33


21 22 22 22 22 23 27 28 29 33 36 36

22 23 22 28 36 33Ascending Order for this Sample Number:

22 22 23 28 33 36

Population Mid Hinge: = = =27

Here, Q1 =.25 =.25 =3.25 =22+.25(22-22) =22

Q3=.75 =.75 = 9.75 = 29+.75(33-29) = 32

Sample Mid Hinge: = = =27.875

Here, Q1 =.25 =.25 =1.75 =22+.75(22-22) =22

Q3=.75 =.75 = 5.25 = 33+.25(36-33) = 33.75

Population Inter Quartile Range (IQR): Q3 – Q1= 32 – 22 = 10

Sample Inter Quartile Range (IQR):Q3 – Q1= 33.75 – 22 = 11.75


= -

= -

= - 715.56

= 29.52

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= = = 5.43Sample Variance:

=

= = =36.898

Sample Standard Deviation: = = = 6.07


=

= = 4.75

Sample Mean Absolute Deviation :

=

= = 5

Xi Xi- µ

21 -5.75 5.7522 -4.75 4.7527 .25 .2536 9.25 9.2522 -4.75 4.7529 2.25 2.2522 -4.75 4.7523 -3.75 3.7522 -4.75 4.7528 1.25 1.2536 9.25 9.2533 6.25 6.25Total: 0 57

Xi Xi-

22 -5.33 5.33

23 -4.33 4.33

22 -5.33 5.33

28 .67 .67

36 8.67 8.67

33 5.63 5.63Total: 0 30Page 23



= x 100 = x100 = 20%

Sample Coefficient of Variance:

= x 100 = x100 = 22%

Question: 03

3.6 3.1 3.9 3.7 3.53.7 3.4 3.0 3.6 3.4


3.0 3.1 3.4 3.4 3.5 3.6 3.6 3.7 3.7 3.9

3.7 3.4 3.0 3.6 3.4 Ascending Order for this Sample Number:

3.0 3.4 3.4 3.6 3.7

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Population Mid Hinge: = = =3.5125

Here, Q1 =.25 =.25 =2.75 =3.1+.75(3.4-3.1) =3.325

Q3=.75 =.75 = 8.25 = 3.7+.25(3.7-3.7) = 3.7


Here, Q1 =.25 =. 25 = 1.5 =3+.5 (3.4-3) =3.2

Q3=.75 =. 75 = 4.5 = 3.6+.50 (3.7-3.6) = 3.65

Population Inter Quartile Range (IQR): Q3 – Q1= 3.7 – 3.325 = 0.375

Sample Inter Quartile Range (IQR):Q3 – Q1= 3.65– 3.20 = 0.45


= -

= -

=12.249- 12.1801

= 0.0689Population Standard Deviation:

= = = 0.2625

Sample Variance: =

=

= =0.072


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=

= = 0.212

Sample Mean Absolute Deviation:

=

= = 0.184


= x 100 = x100 = 7.52%


= x 100 = x100 = 7.85%

Xi Xi- µ3.6 .11 .113.1 -.39 .393.9 .41 .413.7 .21 .213.5 .01 .013.7 .21 .213.4 -.09 .093.0 -.49 .493.6 .11 .113.4 -.09 .09

0 2.12

Xi Xi- 3.7 .28 .283.4 -0.2 .23.0 -.42 .423.6 .18 .183.4 -0.02 .02

Total: 0 0.92

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Question: 04

2 4 2 35 4 3 2


2 2 2 3 3 4 4 5

3 5 4 3 2 Ascending Order for this Sample Number:

2 3 3 4 5

Population Mid Hinge: = = =3

Here, Q1 =.25 =.25 =2.25 =2+.25(2-2) =2

Q3=.75 =.75 = 6.75 = 4+.75(4-4) = 4


Here, Q1 =.25 =.25 =1.5 =2+.5(3-2) =2.5

Q3=.75 =.75 = 4.5 = 4+.50(5-4) = 4.5

Population Inter Quartile Range (IQR): Q3 – Q1= 4 – 2 = 2

Sample Inter Quartile Range (IQR):Q3 – Q1= 4.5– 2.5 = 2


= -

= -

= 1.11



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=

=

= =1.3



=

= = 0.91


=

Xi Xi- µ2 -1.125 1.1254 .875 .8752 -1.125 1.1253 -.125 .1255 1.875 1.8754 .875 .8753 -.125 .1252 -1.125 1.125Total: 0 7.25

Xi Xi- 3 -.4 .45 1.6 1.64 .6 .63 -.4 .42 -1.4 1.4Total: 0 4.4Page 29


= = .88


= x 100 = x100 = 33.6%


= x 100 = x100 = 33.53%

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Question: 05

42 29 21 37 4033 38 26 39 47


21 26 29 33 37 38 39 40 42 47

33 38 26 39 47 Ascending Order for this Sample Number:

26 33 38 39 47


Here, Q1 =.25 =.25 =2.75 =26+.75(29-26) =28.25

Q3=.75 =.75 = 8.25 = 40+.25(42-40) = 40.50


Here, Q1 =.25 =.25 =1.5 =26+.5(33-26) =29.5

Q3=.75 =.75 = 4.5 = 39+.50(47-39) = 43


Sample Inter Quartile Range (IQR):Q3 – Q1= 43– 29.5 = 13.5


= -

= -

= - 1239.04 = 56.36



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=

=

= =60.3



=

= = 6.36


=

= = 5.68


= x 100 = x100 = 21.33%


= x 100 = x100 = 21.22%

Xi Xi- µ42 6.8 6.829 -6.2 6.221 -14.2 14.237 1.8 1.840 4.8 4.833 -2.2 2.238 2.8 2.826 -9.2 9.239 3.8 3.847 11.8 11.8Total: 0 63.6

Xi Xi- 33 -3.6 3.638 1.4 1.426 -10.6 10.639 2.4 2.447 10.4 10.4Total: 0 28.4

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Question: 06

10.2 3.1 5.9 7.0 3.72.9 6.8 7.3 8.2 4.3


2.9 3.1 3.7 4.3 5.9 6.8 7.0 7.3 8.2 10.2

2.9 6.8 7.3 8.2 4.3Ascending Order for this Sample Number:

2.9 4.3 6.8 7.3 8.2


Here, Q1 =.25 =.25 =2.75 =3.1+.75(3.7-3.1) =3.55

Q3=.75 =.75 = 8.25 = 7.3+.25(8.2-7.3) = 7.53


Here, Q1 =.25 =.25 =1.5 =2.9+.5(4.3-2.9) =3.6

Q3=.75 =.75 = 4.5 = 7.3+.50(8.2-7.3) = 7.75


Sample Inter Quartile Range (IQR):Q3 – Q1= 7.75– 3.6 = 4.15


= -

= -

= - 35.2836 = 5.1984


= = = 2.28

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Sample Variance: =

=

= =4.905



=

= = 1.96


=

= = 1.84


= x 100 = x100 = 38.38%


= x 100 = x100 = 37.54%

Xi Xi- µ10.2 4.26 4.263.1 -2.84 2.845.9 -0.04 0.047.0 1.06 1.063.7 -2.24 2.242.9 -3.04 3.046.8 0.86 0.867.3 1.36 1.368.2 2.26 2.264.3 -1.64 1.64Total: 0 19.6

Xi Xi- 2.9 -3 36.8 .9 .97.3 1.4 1.48.2 2.3 2.34.3 -1.6 1.6Total: 0 9.2

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Question: 07

15.8 7.3 28.4 18.2 15.0 24.713.1 10.2 29.3 34.7 16.9 25.3


7.3 10.2 13.1 15.0 15.8 16.9 18.2 24.7 25.3 28.4 29.3

15.8 7.3 28.4 18.2 15.0 24.7Ascending Order for this Sample Number:

7.3 15.0 15.8 18.2 24.7 28.4


Here, Q1 =.25 =.25 =3.25 =13.1+.25(15-13.1) =13.575

Q3=.75 =.75 = 9.75 = 25.3+.75(28.4-25.3) = 27.625

Sample Mid Hinge:= = =19.36

Here, Q1 =.25 =.25 =1.75 =7.3+.75(15-7.3) =13.08

Q3=.75 =.75 = 5.25 = 24.7+.25(28.4-24.7) = 25.63


Sample Inter Quartile Range (IQR):Q3 – Q1= 25.63 – 13.08 = 12.55


= -

= -

= - 396.41 = 65.24


= = = 8.08

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Sample Variance:

=

=

= =56.36



= = = 7.14


=

= = 5.54


= x 100 = x100 = 40.58%


= x 100 = x100 = 41.20%

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Question: 16

12 7 4 16 21 59 3 11 14 10 6


3 4 5 6 7 9 10 11 12 14 16 21

9 3 11 14 10 6

Ascending Order for this Sample Number:

3 6 9 10 11 14

Population Mid Hinge:

= = =9.375

Here, Q1 =.25 =.25 =3.25 =5+.25(6-5) =5.25

Q3=.75 =.75 = 9.75 = 12+.75(14-12) = 13.5

Sample Mid Hinge:

= = =8.5

Here, Q1 =.25 =.25 =1.75 =3+.75(6-3) =5.25

Q3=.75 =.75 = 5.25 = 11+.25(14-11) = 11.75

Population Range: R=XL – XS = (21 – 3) =18

Sample Range: R= XL – XS = (14 – 3) =11


Sample Inter Quartile Range (IQR):Q3 – Q1= 11.75 – 5.25 = 6.5


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= -

= -

= - 96.63

= 26.20



=

=

= =15.038



=

= = 4.17

Xi Xi- µ12 2.17 2.1707 -2.83 2.8304 -5.83 5.8316 6.17 6.1721 11.17 11.1705 -4.83 4.8309 -0.83 0.833 -6.83 6.8311 1.17 1.1714 4.17 4.1710 0.17 0.1706 -3.83 3.83Total: 0 50Page 41



=

= = 2.89


= x 100 = x100 = 52.08%


= x 100 = x100 = 43.94%

Xi Xi-

09 0.17 0.17

3 -5.83 5.83

11 2.17 2.17

14 5.17 5.17

10 1.17 1.17

06 -2.83 2.83

Total: 0 17.34

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Statistics assignment 2.2

Education

Transcript of Statistics assignment 2.2