Assignment PH STAT
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Transcript of 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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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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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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