Basic Statistics theorems as follows , Bar Chart, Pie Chart, Histogram, Frequency Polygon, Frequency Distribution(For Qualitative Data), Frequency Distribution (For Quantitative Data), Frequency distribution(For Grouped Data), Measure of central tendency(Mean, Mode, Median(Percentile,Quartiles,Deciles)), Box Plot, Variance, Standard Deviation, Steam Leaf, Box Plot, Correlation, Regression and Basic Probability have been used on Real life Cricket Players internal data from cricbuzz and espncricinfo.

1. APPLICATION OF STATISTICS
AND BASIC PROBABILITY ON
SAMPLE OF CRICKET PLAYERS
Md. Washif Iqbal Fayek (2018-3-22-043)
Md. Naymul Alam(2018-3-22-032)
Azadur Rahim Chowdhury Bilash (2018-3-22-036)
Md. Shahadat Hossain Rahat(2018-3-22-006)
1

2. Player’s Name Average Run Ratings Batting Position Country
Steven Smith 64.01 937 Middle Order Australia
Virat Kohli 54.98 912 Top Order India
Kane Williamson 52.22 878 Top Order New Zeland
Cheteshwar Pujara 49.48 790 Top Order
India
Ajinkya Rahane 43.74 759 Top Order India
Henry Nicholls 44.16 749 Top Order New Zeland
Joe Root 47.04 731 Top Order England
Tom Latham 43.57 724 Wicket Keeper Batsman
New Zeland
Dimuth Kuranaratne 36.93 723 Opening Batsman
Sri Lanka
Rohit Sharma 46.54 701 Opening Batsman India
Mayank Agarwal 67.08 691 Opening Batsman India
Ben Stokes 36.04 685 Middle Order England
Marnus Labuschagne 46.75 684 Middle Order
Australia
Ross Taylor 45.77 669 Middle Order New Zeland
Quinton De Kock 38.12 668 Wicket Keeper Batsman
South Africa
Babar Azam 36.22 658 Top Order Pakistan
Dean Elgar 38.77 656 Opening Batsman South Africa
Faf Du Plessis 41.67 654 Middle Order South Africa
Aiden Markram 40.06 651 Opening Batsman South Africa
Kusal Mendis 36.24 645 Wicket Keeper Batsman
Sri Lanka
Asad Shafiq 38.93 643 Middle Order Pakistan
Angelo Mathews 44.42 643 Middle Order Sri Lanka
Azhar Ali 42.95 639 Top Order Pakistan
David Warner 46.24 623 Opening Batsman Australia
BJ Watling 40.51 620 Wicket Keeper Batsman
New Zeland
Tamim Iqbal 38.98 619 Opening Batsman Bangladesh
Usman Khawaja 40.66 615 Top Order Australia
Rishabh Pant 44.35 608 Wicket Keeper Batsman
India
Jos Buttler 33.53 608 Wicket Keeper Batsman
England
Brendan Taylor 35.38 607 Wicket Keeper Batsman
New Zeland
Mushfiqur Rahim 34.79 600 Wicket Keeper Batsman
Bangladesh
Dinesh Chandimal 41.87 591 Wicket Keeper Batsman
Sri Lanka
2

3. FREQUENCY DISTRIBUTION (For Qualitative Data)
Category Tally Frequency Relative
Frequency
Percentage Angle
Opening
Batsman
|| 7 0.22 22 84
Top Order |||| 9 0.28 28 108
Middle Order || 7 0.22 22 72
Wicket Keeper
Batsman
|||| 9 0.28 28 96
Total 32 1 100 360
3

4. BAR CHART
0%
5%
10%
15%
20%
25%
30%
Opening Batsman Top Order Middle Order Wicket Keeper Batsman
Frequency
Batting Order
4

5. PIE CHART
22%
28%
22%
28%
Pie Chart
Opening Batsman Top Order Middle Order Wicket Keeper Batsman
5

6. FREQUENCY DISTRIBUTION(CONT.)
• 2k > n
Number of sample size, n=32
• 26=64>32
Here,
Number of class, k=6
Number of sample size, n=32
6

7. FREQUENCY DISTRIBUTION(CONT.)
• Now,
i≥
937−591
6
i≥57.6≃60
• Class starts from 590
Class ends at 940
• Class intervals=650-590=60
• Class midpoint=
590+650
2
= 620
7

8. FREQUENCY DISTRIBUTION(FOR GROUPED DATA)
Classes Class Midpoint Frequency Cumulative Frequency Relative Frequency
590-650 620 13 13 0.41
650-710 680 10 23 0.31
710-770 740 5 28 0.16
770-830 800 1 29 0.03
830-890 860 1 30 0.03
890-950 920 2 32 0.06
Total 32 1
8

9. FREQUENCY POLYGON
0
13
10
5
1 1
2
590-650 650-710 710-770 770-830 830-890 890-950
Frequency
Midpoints
FREQUENCY POLYGON
9

10. HISTOGRAM
10

11. MEASURE OF CENTRAL TENDENCY
• Mean:
• Average rating of the player is 687
• Median:
50% of the player has rating under 655
50% of the player has rating above 655
Mode:
638.75 is the mode
11

12. MEASURE OF CENTRAL TENDENCY(CONT.)
• P25=620.75=Q1
• P50=655=Q2=D5
• P75=729.25=Q3
12

13. MEASURE OF CENTRAL TENDENCY(AVERAGE RUN)
• P25=38.30=Q1
• P50=42.41=Q2=D5
• P75=46.47=Q3
13

14. BOX PLOT
14

15. MEASURE OF DISPERSION
• Variance(average run)==59.38165
• Standard Deviation, SD=7.7059
15

16. STEAM LEAF
Steam Leaf (32)
59 1
60 0 7 8 8
61 5 9
62 0 3
63 9
64 3 3 5
65 1 4 6 8
66 8 9
68 4 5
69 1
70 1
72 3 4
73 1
74 9
75 9
79 0
87 8
91 2
93 7
KEY: 68|4=684
16

17. x y X2 Y2 XY
64.01 937 4097.28 877969 59977.37
54.98 912 3022.8 831744 50141.76
52.22 878 2726.928 770884 45849.16
49.48 790 2448.27 624100 39089.2
43.74 759 1913.188 576081 33198.66
44.16 749 1950.106 561001 33075.84
47.04 731 2212.762 534361 34386.24
43.57 724 1898.345 524176 31544.68
36.93 723 1363.825 522729 26700.39
46.54 701 2165.972 491401 32624.54
67.08 691 4499.726 477481 46352.28
36.04 685 1298.882 469225 24687.4
45.77 669 2094.893 447561 30620.13
38.12 668 1453.134 446224 25464.16
36.22 658 1311.888 432964 23832.76
38.77 656 1503.113 430336 25433.12
41.67 654 1736.389 427716 27252.18
40.06 651 1604.804 423801 26079.06
36.24 645 1313.338 416025 23374.8
38.93 643 1515.545 413449 25031.99
44.42 643 1973.136 413449 28562.06
42.95 639 1844.703 408321 27445.05
46.24 623 2138.138 388129 28807.52
40.51 620 1641.06 384400 25116.2
38.98 619 1519.44 383161 24128.62
40.66 615 1653.236 378225 25005.9
44.35 608 1966.923 369664 26964.8
33.53 608 1124.261 369664 20386.24
35.38 607 1251.744 368449 21475.66
34.79 600 1210.344 360000 20874
46.75 684 2185.563 467856 31977
41.87 591 1753.097 349281 24745.17
∑=1392 ∑=21981 ∑=62392.83 ∑=15339827 ∑=970203.94
17

18. CORRELATION
• r = 0.6662072405
0.666 represents that the relation between average run and ratings is strongly
positive.
18

19. REGRESSION
• b=7.621801035
• a=355.357905
• y=355.357905+7.621801035x
• a=355.357905 means player’s rating is 355.357905 when average run is zero
b=7.621801035 means, if average run increases by 1, the rating will increase by
7.621801035
19

20. x y Y2 𝐘 ei ei
2
64.01 937 4097.28 843.2293893 93.7706107 8792.92744
54.98 912 3022.8 774.4045259 137.595474 18932.51449
52.22 878 2726.928 753.368355 124.631645 15533.04692
49.48 790 2448.27 732.4846202 57.5153798 3308.018912
43.74 759 1913.188 688.7354823 70.2645177 4937.102452
44.16 749 1950.106 691.9366387 57.0633613 3256.227202
47.04 731 2212.762 713.8874257 17.1125743 292.8401996
43.57 724 1898.345 687.4397761 36.5602239 1336.649972
36.93 723 1363.825 636.8310172 86.1689828 7425.093593
46.54 701 2165.972 710.0765252 -9.0765252 82.38330914
67.08 691 4499.726 866.6283184 -175.62832 30845.30623
36.04 685 1298.882 630.0476143 54.9523857 3019.764694
45.77 669 2094.893 704.2077384 -35.207738 1239.584841
38.12 668 1453.134 645.9009605 22.0990395 488.3675488
36.22 658 1311.888 631.4195385 26.5804615 706.5209342
38.77 656 1503.113 650.8551311 5.14486887 26.46967572
41.67 654 1736.389 672.9583541 -18.958354 359.4191913
40.06 651 1604.804 660.6872545 -9.6872545 93.84289901
36.24 645 1313.338 631.5719745 13.4280255 180.3118686
38.93 643 1515.545 652.0746193 -9.0746193 82.3487153
44.42 643 1973.136 693.918307 -50.918307 2592.673985
42.95 639 1844.703 682.7142595 -43.714259 1910.93648
46.24 623 2138.138 707.7899849 -84.789985 7189.341532
40.51 620 1641.06 664.1170649 -44.117065 1946.315418
38.98 619 1519.44 652.4557093 -33.455709 1119.284488
40.66 615 1653.236 665.2603351 -50.260335 2526.101283
44.35 608 1966.923 693.3847809 -85.384781 7290.56081
33.53 608 1124.261 610.9168937 -2.9168937 8.508268878
35.38 607 1251.744 625.0172256 -18.017226 324.620419
34.79 600 1210.344 620.520363 -20.520363 421.085298
46.75 684 2185.563 711.6771034 -27.677103 766.0220519
41.87 591 1753.097 674.4827143 -83.482714 6969.363593
∑=1392
∑=21981 ∑=15339827 ∑=-0.0000072
∑=134003.5547
20

21. REGRESSION(CONT.)
• R2
=0.4438318463=44.38318463%
Here, r2=(0.6662072405)2=0.44383=R2
• 44.38318463% variation in Player Ratings(Y) can be explained by the variation in
Average Run(X).
21

22. y = 7.6218x + 355.36
R² = 0.4438
0
100
200
300
400
500
600
700
800
900
1000
0 10 20 30 40 50 60 70 80
PlayerRating
Average Runs
22

23. BASIC PROBABILITY
• What is Probability?
• Not mutually exclusive
Country Batting Order
23

24. BASIC PROBABILITY(CONT.)
Aus Ind Nz Eng Sri Sa Pak Ban Total
Top Order 1 3 2 1 0 0 2 0 9
Middle
Order
2 0 1 1 1 0 2 0 7
Wicket Keeper
Batsman
Opening
Batsman
0 1 3 1 2 1 0 1 9
Opening
Batsman
1 2 0 0 1 2 1 7
Total 4 6 6 3 4 3 4 2 32
24

25. BASIC PROBABILITY(FORMULAS)
• The probability of a randomly selected player is from Bangladesh
=
2
32
=0.0625
• The probability of a randomly selected player is an Opening Batsman
=
7
32
=0.21875
• The probability of a player being both Opening Batsman and plays for Bangladesh,
P(O∩B)= P(B|O)P(O)=
1
7
×
7
32
=0.03125
25

26. FORMULAS OF BASIC PROBABILITY(CONT.)
• If a person is an Opening Batsman, the probability that he is also from Bangladesh
P(B|O)=
P(O∩B)
P(O)
=
1
32
7
32
=0.1428571429
• The probability that a randomly selected player is from Bangladesh or plays as
Opening Batsman,
P(B)+P(O)-P(O∩B)=
2
32
+
7
32
-
1
32
=0.25
26