Report on Statistical Analysis of Cricketers
Table of Contents
INTRODUCTION TO SPSS
SPSS
is among the most widely used programs for statistical analysis in
social science and it helps organizations predict future events and
proactively act upon that insight to drive better business outcomes.
We
have done the statistical analysis of the cricketers for this we have
chosen the four world class batsmen. These batsmen are
- Brian Charles Lara
- Mohammad Yousuf
- Ricky Thomas Ponting
- Sachin Ramesh Tendulkar
BOX PLOT
In
descriptive statistics, a box plot or boxplot (also known as a
box-and-whisker diagram or plot) is a convenient way of graphically
depicting groups of numerical data through their five-number
summaries: the smallest observation (sample minimum), lower quartile
(Q1), median (Q2), upper quartile (Q3), and largest observation
(sample maximum). A boxplot may also indicate which observations, if
any, might be considered outliers.
Boxplots
display differences between populations without making any
assumptions of the underlying statistical distribution.
MEAN
In
statistics, the mean is the mathematical average of a set of numbers.
The average is calculated by adding up two or more scores and
dividing the total by the number of scores
MEDIAN
In
probability theory and statistics, a median is described as the
numerical value separating the higher half of a sample, a population,
or a probability distribution, from the lower half. The median of a
finite list of numbers can be found by arranging all the observations
from lowest value to highest value and picking the middle one. If
there is an even number of observations, then there is no single
middle value; the median is then usually defined to be the mean of
the two middle values
MODE
In
statistics, the mode is the value that occurs most frequently in a
data set or a probability distribution.[1] In some fields, notably
education, sample data are often called scores, and the sample mode
is known as the modal score
STANDARD DEVIATION
Standard
deviation is a widely used measurement of variability or diversity
used in statistics and probability theory. It shows how much
variation or "dispersion" there is from the average (mean,
or expected value). A low standard deviation indicates that the data
points tend to be very close to the mean, whereas high standard
deviation indicates that the data are spread out over a large range
of values.
VARIANCE
In
probability theory and statistics, the variance is used as a measure
of how far a set of numbers are spread out from each other. It is one
of several descriptors of a probability distribution, describing how
far the numbers lie from the mean (expected value). In particular,
the variance is one of the moments of a distribution. In that
context, it forms part of a systematic approach to distinguishing
between probability distributions.
PERCENTILE
In
statistics, a percentile (or centile) is the value of a variable
below which a certain percent of observations fall. For example, the
20th percentile is the value (or score) below which 20 percent of the
observations may be found.
SKEWNESS
In
probability theory and statistics, skewness is a measure of the
asymmetry of the probability distribution of a real-valued random
variable. The skewness value can be positive or negative, or even
undefined. Qualitatively, a negative skew indicates that the tail on
the left side of the probability density function is longer than the
right side and the bulk of the values (possibly including the median)
lie to the right of the mean. A positive skew indicates that the tail
on the right side is longer than the left side and the bulk of the
values lie to the left of the mean. A zero value indicates that the
values are relatively evenly distributed on both sides of the mean,
typically but not necessarily implying a symmetric distribution.
HISTOGRAM
In
statistics, a histogram is a graphical representation, showing a
visual impression of the distribution of data. It is an estimate of
the probability distribution of a continuous variable and was first
introduced by Karl Pearson. A histogram consists of tabular
frequencies, shown as adjacent rectangles, erected over discrete
intervals (bins), with an area equal to the frequency of the
observations in the interval. The height of a rectangle is also equal
to the frequency density of the interval, i.e., the frequency divided
by the width of the interval. The total area of the histogram is
equal to the number of data. A histogram may also be normalized
displaying relative frequencies. It then shows the proportion of
cases that fall into each of several categories, with the total area
equaling 1. The categories are usually specified as consecutive,
non-overlapping intervals of a variable. The categories (intervals)
must be adjacent, and often are chosen to be of the same size.
RANDOM SAMPLE
In
statistics, a sample is a subject chosen from a population for
investigation; a random sample is one chosen by a method involving an
unpredictable component. Random sampling can also refer to taking a
number of independent observations from the same probability
distribution, without involving any real population. The sample
usually is not a representative of the population from which it was
drawn— this random variation in the results is termed as sampling
error. In the case of random samples, mathematical theory is
available to assess the sampling error. Thus, estimates obtained from
random samples can be accompanied by measures of the uncertainty
associated with the estimate. This can take the form of a standard
error, or if the sample is large enough for the central limit theorem
to take effect, confidence intervals may be calculated.
STATISTICAL ANALYSIS:
We
have done the statistical analysis of the cricketers for this we have
chosen the four world class batsmen. These batsmen are
- Brian Charles Lara
- Mohammad Yousuf
- Ricky Thomas Ponting
- Sachin Ramesh Tendulkar
We
have done the statistical analysis of their career records that
include:
- Batting averages
- Highest scores
- Strike rates
- Centuries
- Half centuries
- Total runs scored
- Total matches played
We
have taken only their test matches record. And their career records
are given below.
Sachin Ramesh Tendulkar:
Full
name: Sachin Ramesh Tendulkar
Born: April
24, 1973, Bombay (now Mumbai), Maharashtra
Current
age: 38 years 87 days
Major
teams: India, Asia XI, Mumbai, Mumbai
Indians,Yorkshire
Playing
role: Top-order batsman
Batting
style: Right-hand bat
Bowling
style: Right-arm offbreak, Legbreak googly
Height: 5
ft 5 in
Batting and fielding averages
|
|
Mat
|
Inns
|
NO
|
Runs
|
HS
|
Ave
|
BF
|
SR
|
100
|
50
|
4s
|
6s
|
Ct
|
St
|
|
Tests
|
177
|
290
|
32
|
14692
|
248*
|
56.94
|
|
|
51
|
59
|
|
64
|
106
|
0
|
|
ODIs
|
453
|
442
|
41
|
18111
|
200*
|
45.16
|
20980
|
86.32
|
48
|
95
|
1981
|
193
|
136
|
0
|
|
T20Is
|
1
|
1
|
0
|
10
|
10
|
10.00
|
12
|
83.33
|
0
|
0
|
2
|
0
|
1
|
0
|
|
First-class
|
281
|
443
|
48
|
23611
|
248*
|
59.77
|
|
|
78
|
105
|
|
|
174
|
0
|
|
List
A
|
540
|
527
|
55
|
21663
|
200*
|
45.89
|
|
|
59
|
113
|
|
|
171
|
0
|
|
Descriptive
Statistics
|
|||||||||||
|
|
N
|
Range
|
Minimum
|
Maximum
|
Mean
|
||||||
|
|
Statistic
|
Statistic
|
Statistic
|
Statistic
|
Statistic
|
Std.
Error
|
|||||
|
Sachin
|
260
|
217.00
|
.00
|
217.00
|
45.8654
|
2.99621
|
|||||
|
Valid
N (listwise)
|
260
|
|
|
|
|
|
|||||
|
Descriptive
Statistics
|
|||||||
|
|
Std.
Deviation
|
Variance
|
Skewness
|
||||
|
|
Statistic
|
Statistic
|
Statistic
|
Std.
Error
|
|||
|
Sachin
|
48.31246
|
2334.094
|
1.431
|
.151
|
|||
|
Case
Processing Summary
|
|||||||||
|
|
Cases
|
||||||||
|
|
Valid
|
Missing
|
Total
|
||||||
|
|
N
|
Percent
|
N
|
Percent
|
N
|
Percent
|
|||
|
Sachin
|
260
|
84.1%
|
49
|
15.9%
|
309
|
100.0%
|
|||
|
Descriptive
|
||||
|
|
|
|
Statistic
|
Std.
Error
|
|
Sachin
|
|
Mean
|
45.8654
|
2.99621
|
|
95%
Confidence Interval for Mean
|
Lower
Bound
|
39.9653
|
|
|
|
Upper
Bound
|
51.7654
|
|
||
|
|
5%
Trimmed Mean
|
40.8718
|
|
|
|
Median
|
31.0000
|
|
||
|
Variance
|
2334.094
|
|
||
|
Std.
Deviation
|
48.31246
|
|
||
|
Minimum
|
.00
|
|
||
|
Maximum
|
217.00
|
|
||
|
Range
|
217.00
|
|
||
|
Interquartile
Range
|
58.75
|
|
||
|
Skewness
|
1.431
|
.151
|
||
|
Kurtosis
|
1.558
|
.301
|
||
|
Percentiles
|
||||||||
|
|
|
Percentiles
|
||||||
|
|
|
5
|
10
|
25
|
50
|
75
|
||
|
Weighted
Average(Definition 1)
|
Sachin
|
.0000
|
2.0000
|
9.0000
|
31.0000
|
67.7500
|
||
|
Tukey's
Hinges
|
Sachin
|
|
|
9.0000
|
31.0000
|
67.5000
|
||
|
Percentiles
|
||||||
|
|
|
Percentiles
|
||||
|
|
|
90
|
95
|
|||
|
Weighted
Average(Definition 1)
|
Sachin
|
115.8000
|
154.9000
|
|||
|
Extreme
Values
|
||||||
|
|
|
|
Case
Number
|
Value
|
||
|
Sachin
|
Highest
|
1
|
116
|
217.00
|
||
|
2
|
295
|
214.00
|
||||
|
3
|
290
|
203.00
|
||||
|
4
|
167
|
193.00
|
||||
|
5
|
52
|
179.00
|
||||
|
Lowest
|
1
|
252
|
.00
|
|||
|
2
|
228
|
.00
|
||||
|
3
|
186
|
.00
|
||||
|
4
|
182
|
.00
|
||||
|
5
|
160
|
.00a
|
||||
|
a.
Only a partial list of cases with the value .00 is shown in the
table of lower extremes.
|
||||||
Ricky Thomas Ponting:
Full
name: Ricky Thomas Ponting
Born: December
19, 1974, Launceston, Tasmania
Current
age: 36 years 213 days
Major
teams: Australia, ICC World XI, Kolkata Knight
Riders,Somerset, Tasmania
Playing
role: Top-order batsman
Batting
style: Right-hand bat
Bowling
style: Right-arm medium
Height: 1.78
m
Batting and fielding averages
|
|
Mat
|
Inns
|
NO
|
Runs
|
HS
|
Ave
|
BF
|
SR
|
100
|
50
|
4s
|
6s
|
Ct
|
St
|
|
Tests
|
152
|
259
|
28
|
12363
|
257
|
53.51
|
20827
|
59.36
|
39
|
56
|
1406
|
72
|
178
|
0
|
|
ODIs
|
362
|
352
|
38
|
13406
|
164
|
42.69
|
16633
|
80.59
|
30
|
79
|
1195
|
161
|
155
|
0
|
|
T20Is
|
17
|
16
|
2
|
401
|
98*
|
28.64
|
302
|
132.78
|
0
|
2
|
41
|
11
|
8
|
0
|
|
First-class
|
255
|
436
|
55
|
21332
|
257
|
55.98
|
|
|
73
|
94
|
|
|
270
|
0
|
|
List
A
|
434
|
424
|
51
|
15762
|
164
|
42.25
|
|
|
34
|
94
|
|
|
187
|
0
|
|
Twenty20
|
22
|
21
|
2
|
460
|
98*
|
24.21
|
375
|
122.66
|
0
|
2
|
44
|
13
|
10
|
0
|
|
Descriptive
Statistics
|
|||||||||||
|
|
N
|
Range
|
Minimum
|
Maximum
|
Mean
|
||||||
|
|
Statistic
|
Statistic
|
Statistic
|
Statistic
|
Statistic
|
Std.
Error
|
|||||
|
Ponting
|
152
|
298.00
|
.00
|
298.00
|
81.3355
|
5.47769
|
|||||
|
Valid
N (list wise)
|
152
|
|
|
|
|
|
|||||
|
Descriptive
Statistics
|
|||||||
|
|
Std.
Deviation
|
Variance
|
Skewness
|
||||
|
|
Statistic
|
Statistic
|
Statistic
|
Std.
Error
|
|||
|
Ponting
|
67.53345
|
4560.767
|
1.141
|
.197
|
|||
|
Case
Processing Summary
|
|||||||||
|
|
Cases
|
||||||||
|
|
Valid
|
Missing
|
Total
|
||||||
|
|
N
|
Percent
|
N
|
Percent
|
N
|
Percent
|
|||
|
Ponting
|
152
|
49.2%
|
157
|
50.8%
|
309
|
100.0%
|
|||
|
Descriptives
|
||||
|
|
|
|
Statistic
|
Std.
Error
|
|
Ponting
|
|
Mean
|
81.3355
|
5.47769
|
|
95%
Confidence Interval for Mean
|
Lower
Bound
|
70.5127
|
|
|
|
Upper
Bound
|
92.1583
|
|
||
|
|
5%
Trimmed Mean
|
75.7208
|
|
|
|
Median
|
61.5000
|
|
||
|
Variance
|
4560.767
|
|
||
|
Std.
Deviation
|
67.53345
|
|
||
|
Minimum
|
.00
|
|
||
|
Maximum
|
298.00
|
|
||
|
Range
|
298.00
|
|
||
|
Interquartile
Range
|
94.50
|
|
||
|
Skewness
|
1.141
|
.197
|
||
|
Kurtosis
|
.847
|
.391
|
||
|
Percentiles
|
|||||||
|
|
|
Percentiles
|
|||||
|
|
|
5
|
10
|
25
|
50
|
75
|
|
|
Weighted
Average(Definition 1)
|
Ponting
|
6.6500
|
11.0000
|
28.5000
|
61.5000
|
123.0000
|
|
|
Tukey's
Hinges
|
Ponting
|
|
|
29.0000
|
61.5000
|
123.0000
|
|
|
Extreme
Values
|
||||
|
|
|
|
Case
Number
|
Value
|
|
Ponting
|
Highest
|
1
|
142
|
298.00
|
|
2
|
74
|
288.00
|
||
|
3
|
100
|
263.00
|
||
|
4
|
106
|
256.00
|
||
|
5
|
95
|
253.00
|
||
|
Lowest
|
1
|
40
|
.00
|
|
|
2
|
30
|
.00
|
||
|
3
|
29
|
.00
|
||
|
4
|
26
|
1.00
|
||
|
5
|
12
|
4.00
|
||
Mohammad Yousuf:
Full
name: Mohammad Yousuf
Born: August
27, 1974, Lahore, Punjab
Current
age: 36 years 327 days
Major
teams: Pakistan, Asia XI, Bahawalpur, Lahore,Lahore
Badshahs, Lancashire, Pakistan International
Airlines,Warwickshire, Water and Power Development
Authority,Zarai Taraqiati Bank Limited
Batting
style: Right-hand bat
Bowling
style: Right-arm offbreak
Batting and fielding averages
|
|
Mat
|
Inns
|
NO
|
Runs
|
HS
|
Ave
|
BF
|
SR
|
100
|
50
|
4s
|
6s
|
Ct
|
St
|
|
Tests
|
90
|
156
|
12
|
7530
|
223
|
52.29
|
14372
|
52.39
|
24
|
33
|
957
|
51
|
65
|
0
|
|
ODIs
|
288
|
273
|
40
|
9720
|
141*
|
41.71
|
12942
|
75.10
|
15
|
64
|
785
|
90
|
58
|
0
|
|
T20Is
|
3
|
3
|
0
|
50
|
26
|
16.66
|
43
|
116.27
|
0
|
0
|
5
|
1
|
1
|
0
|
|
First-class
|
141
|
239
|
20
|
10505
|
223
|
47.96
|
|
|
30
|
51
|
|
|
84
|
0
|
|
List
A
|
338
|
322
|
47
|
11026
|
141*
|
40.09
|
|
|
15
|
75
|
|
|
70
|
0
|
|
Twenty20
|
23
|
20
|
2
|
357
|
57*
|
19.83
|
322
|
110.86
|
0
|
1
|
37
|
8
|
9
|
0
|
|
Descriptive
Statistics
|
|||||||||||
|
|
N
|
Range
|
Minimum
|
Maximum
|
Mean
|
||||||
|
|
Statistic
|
Statistic
|
Statistic
|
Statistic
|
Statistic
|
Std.
Error
|
|||||
|
Yousuf
|
89
|
250.00
|
.00
|
250.00
|
84.6067
|
6.56364
|
|||||
|
Valid
N (listwise)
|
89
|
|
|
|
|
|
|||||
|
Descriptive
Statistics
|
|||||||
|
|
Std.
Deviation
|
Variance
|
Skewness
|
||||
|
|
Statistic
|
Statistic
|
Statistic
|
Std.
Error
|
|||
|
Yousuf
|
61.92125
|
3834.241
|
.862
|
.255
|
|||
|
Case
Processing Summary
|
|||||||||
|
|
Cases
|
||||||||
|
|
Valid
|
Missing
|
Total
|
||||||
|
|
N
|
Percent
|
N
|
Percent
|
N
|
Percent
|
|||
|
Yousuf
|
89
|
28.8%
|
220
|
71.2%
|
309
|
100.0%
|
|||
|
Descriptive
|
||||
|
|
|
|
Statistic
|
Std.
Error
|
|
Yousuf
|
|
Mean
|
84.6067
|
6.56364
|
|
95%
Confidence Interval for Mean
|
Lower
Bound
|
71.5629
|
|
|
|
Upper
Bound
|
97.6506
|
|
||
|
|
5%
Trimmed Mean
|
80.7828
|
|
|
|
Median
|
72.0000
|
|
||
|
Variance
|
3834.241
|
|
||
|
Std.
Deviation
|
61.92125
|
|
||
|
Minimum
|
.00
|
|
||
|
Maximum
|
250.00
|
|
||
|
Range
|
250.00
|
|
||
|
Interquartile
Range
|
91.00
|
|
||
|
Skewness
|
.862
|
.255
|
||
|
Kurtosis
|
.047
|
.506
|
||
|
Percentiles
|
||||||||
|
|
|
Percentiles
|
||||||
|
|
|
5
|
10
|
25
|
50
|
75
|
||
|
Weighted
Average(Definition 1)
|
Yousuf
|
9.0000
|
16.0000
|
33.0000
|
72.0000
|
124.0000
|
||
|
Tukey's
Hinges
|
Yousuf
|
|
|
34.0000
|
72.0000
|
124.0000
|
||
|
Percentiles
|
|||||
|
|
|
Percentiles
|
|||
|
|
|
90
|
95
|
||
|
Weighted
Average(Definition 1)
|
Yousuf
|
191.0000
|
213.5000
|
||
|
Extreme
Values
|
||||
|
|
|
|
Case
Number
|
Value
|
|
Yousuf
|
Highest
|
1
|
67
|
250.00
|
|
2
|
72
|
247.00
|
||
|
3
|
73
|
226.00
|
||
|
4
|
62
|
223.00
|
||
|
5
|
35
|
204.00
|
||
|
Lowest
|
1
|
19
|
.00
|
|
|
2
|
9
|
3.00
|
||
|
3
|
1
|
6.00
|
||
|
4
|
46
|
8.00
|
||
|
5
|
90
|
10.00
|
||
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