Assignment PH STAT

NATIONAL UNIVERSITY OF SCIENCES & TECHNOLOGY (NUST)

GROUP ASSIGNMENTPROBABILITY & STATISTICS

SUBMITTED BY: GROUP Ba) Adnan Yousafb)Asad Javedc) Ans Farukhd)Haroon Rafiquee) Amjadf) Murtaza

PROGRAMME: MS TRANSPORTATION ENGINEERING

SUBMITTED TO: DR. MUHAMMAD IRFAN

NATIONAL INSTITUTE OF TRANSPORTATION (NIT)SCHOOL OF CIVIL & ENVIRONMENTAL ENGINEERING (SCEE) NUST ISLAMABAD

Question no 1: Using PH Stat and PASW software draw the box and whisker plot, Dot plot, stem and leaf plot and histograms for the following data set.

Y=GPA X= ACT Score

Y= GPA X= ACT Score

Y= GPA X= ACT Score

Y= GPA X= ACT Score

3.897 21 3.927 25 2.922 25 3.886 243.885 14 2.375 16 2.716 23 2.183 273.778 28 2.929 28 3.37 25 3.429 25

2.54 22 3.375 26 3.606 23 3.024 183.028 21 2.857 22 2.642 30 3.75 293.865 31 3.072 24 2.452 21 3.833 242.962 32 3.381 21 2.655 24 3.113 273.961 27 3.29 30 3.714 32 2.875 21

0.5 29 3.549 27 1.806 18 2.747 193.178 26 3.646 26 3.516 23 2.311 18

3.31 24 2.978 26 3.039 20 1.841 253.538 30 2.654 30 2.966 23 1.583 183.083 24 2.54 24 2.482 18 2.879 203.013 24 2.25 26 2.7 18 3.591 323.245 33 2.069 29 3.92 29 2.914 242.963 27 2.617 24 2.834 20 3.716 353.522 25 2.183 31 3.222 23 2.8 253.013 31 2 15 3.084 26 3.621 282.947 25 2.952 19 4 28 3.792 282.118 20 3.806 18 3.511 34 2.867 252.563 24 2.871 27 3.323 20 3.419 223.357 21 3.352 16 3.072 20 3.6 303.731 28 3.305 27 2.079 26 2.394 203.925 27 2.952 26 3.875 32 2.286 203.556 28 3.547 24 3.208 25 1.486 313.101 26 3.691 30 2.92 27 3.885 20

2.42 28 3.16 21 3.345 27 3.8 292.579 22 2.194 20 3.956 29 3.914 283.871 26 3.323 30 3.808 19 1.86 16

3.06 21 3.936 29 2.506 21 2.948 28

Solution A:

The results obtained using PH STAT Software are given below.

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THE BOX & WHISKER PLOT

GPA & ACT Box and Whisker Plot

Five-number Summary Y= GPA X1=ACTMinimum 0.5 14First Quartile 2.655 21Median 3.0775 25Third Quartile

3.6 28

Maximum 4 35

0 5 10 15 20 25 30 35

2.5

2

2.5

3

X1=ACT

1

Y= GPA

GPA & ACT Box and Whisker Plot

STEM & LEAF PLOT

Y= GPA STEM & LEAF PLOT

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Stem unit:

0.1

5 0

6

7

8

9

10

11

12

13

14 9

15 8

16

17

18 1 4 6

19

20 0 7 8

21 2 8 8 9

22 5 9

23 1 8 9

24 2 5 8

25 1 4 4 6 8

26 2 4 5 5

27 0 2 5

28 0 3 6 7 7 8 8

29 1 2 2 3 5 5 5 5 6 6 7 8

30 1 1 2 3 4 6 7 7 8 8

31 0 1 6 8

32 1 2 4 9

33 0 1 2 2 5 5 6 7 8 8

34 2 3

35 1 2 2 4 5 5 6 9

36 0 1 2 5 9

37 1 2 3 5 8 9

38 0 1 1 3 6 7 8 8 8 9

39 0 1 2 2 3 4 6 6

40 0

Statistics Y= GPA

Sample Size 120

Mean 3.07405

Median 3.0775

Std. Deviation 0.644338

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Minimum 0.5

Maximum 4

X=ACT STEM & LEAF PLOT

Stem unit:

1

14 0

15 0

16 0 0 0

17

18 0 0 0 0 0 0 0

19 0 0 0

20 0 0 0 0 0 0 0 0 0 0

21 0 0 0 0 0 0 0 0 0

22 0 0 0 0

23 0 0 0 0 0

24 0 0 0 0 0 0 0 0 0 0 0 0

25 0 0 0 0 0 0 0 0 0 0

26 0 0 0 0 0 0 0 0 0 0

27 0 0 0 0 0 0 0 0 0 0

28 0 0 0 0 0 0 0 0 0 0

29 0 0 0 0 0 0 0

30 0 0 0 0 0 0 0

31 0 0 0 0

32 0 0 0 0

33 0

34 0

35 0

Statistics X=ACT

Sample Size 120

Mean 24.725

Median 25

Std. Deviation 4.4720654

Minimum 14

Maximum 35

DOT SCALE PLOT The dot scale plot for the respective data sets are attached separately at the end.

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Solution B:

The results obtained by PASW are given below.

FREQUENCIES

Statistics

Y= GPA X1=AC

T

N Valid 120 120

Missing 0 0

Mean 3.074050 24.73

Std. Error of Mean .0588198 .408

Median 3.077500 25.00

Mode 2.1830a 24

Std. Deviation .6443383 4.472

Variance .415 19.999

Skewness -.833 -.136

Std. Error of Skewness .221 .221

Kurtosis 1.124 -.560

Std. Error of Kurtosis .438 .438

Range 3.5000 21

Minimum .5000 14

Maximum 4.0000 35

Sum 368.8860 2967

a. Multiple modes exist. The smallest value is shown

FREQUENCY TABLE

X1=ACT

Frequency Percent Valid

Percent

Cumulative

Percent

Vali 14 1 .8 .8 .8

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d 15 1 .8 .8 1.7

16 3 2.5 2.5 4.2

18 7 5.8 5.8 10.0

19 3 2.5 2.5 12.5

20 10 8.3 8.3 20.8

21 9 7.5 7.5 28.3

22 4 3.3 3.3 31.7

23 5 4.2 4.2 35.8

24 12 10.0 10.0 45.8

25 10 8.3 8.3 54.2

26 10 8.3 8.3 62.5

27 10 8.3 8.3 70.8

28 10 8.3 8.3 79.2

29 7 5.8 5.8 85.0

30 7 5.8 5.8 90.8

31 4 3.3 3.3 94.2

32 4 3.3 3.3 97.5

33 1 .8 .8 98.3

34 1 .8 .8 99.2

35 1 .8 .8 100.0

Total 120 100.0 100.0

PIE CHART

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HISTOGRAM FOR Y= GPA

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HISTOGRAM FOR X= ACT

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DESCRIPTIVES

Statistic Std. Error

Y= GPA Mean 3.074050 .0588198

95% Confidence Interval for

Mean

Lower Bound 2.957581

Upper Bound 3.190519

5% Trimmed Mean 3.112083

Median 3.077500

Variance .415

Std. Deviation .6443383

Minimum .5000

Maximum 4.0000

Range 3.5000

Interquartile Range .9315

Skewness -.833 .221

Kurtosis 1.124 .438

X1=ACT Mean 24.73 .408

95% Confidence Interval for

Mean

Lower Bound 23.92

Upper Bound 25.53

5% Trimmed Mean 24.76

Median 25.00

Variance 19.999

Std. Deviation 4.472

Minimum 14

Maximum 35

Range 21

Interquartile Range 7

Skewness -.136 .221

Kurtosis -.560 .438

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HISTOGRAM Y= GPA

HISTOGRAM X=ACT

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STEM & LEAF Y=GPA

Y= GPA Stem-and-Leaf Plot

Frequency Stem & Leaf

1.00 Extremes (=<.5) 2.00 1 . 45 .00 1 . 3.00 1 . 888 7.00 2 . 0001111 5.00 2 . 22333 8.00 2 . 44455555 7.00 2 . 6666777 19.00 2 . 8888888999999999999 14.00 3 . 00000000001111 14.00 3 . 22223333333333 10.00 3 . 4455555555 11.00 3 . 66666777777 18.00 3 . 888888888889999999 1.00 4 . 0

Stem width: 1.0000 Each leaf: 1 case(s)

STEM & LEAF X = ACT

X1=ACT Stem-and-Leaf Plot

Frequency Stem & Leaf

.00 1 .2.00 1 . 453.00 1 . 66610.00 1 . 888888899919.00 2 . 00000000001111111119.00 2 . 22223333322.00 2 . 444444444444555555555520.00 2 . 6666666666777777777717.00 2 . 8888888888999999911.00 3 . 000000011115.00 3 . 222232.00 3 . 45

Stem width: 10Each leaf: 1 case(s)

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BOX PLOT FOR Y=GPA

BOX PLOT FOR X=ACT

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Solution C:

SCATTOR PLOT

0 2 4 6 8 10 120

2

4

6

8

10

12

Y= GPA

Y= GPA

0 2 4 6 8 10 120

2

4

6

8

10

12

X1=ACT

X1=ACT

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