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  • Level: GCSE
  • Subject: Maths
  • Word count: 1469

To analyse the performances of two batsmen from the Indian cricket team and two batsmen from the Australian cricket team and to predict their probable scores in the forthcoming matches between them.

Extracts from this document...

Introduction

Mathematics Project

STATEMENT OF TASK

        This project deals mainly with the topics of Statistics and Probability. The main elements of these two topics that have been used in this project are 1.) Histograms            (Statistics) and 2.) Standard Deviation ( Statistics) and 3.) Probability density functions      (Probability). This project is aimed at two different topics. First of all it calculates the consistency of four of the best batsmen in the world. These are – Sachin Tendulkar, Rahul Dravid, Ricky Ponting and Matthew Hayden. The consistency has been calculated by using the standard deviation formula. The standard deviation formula calculates the amount, the batsman’s scores deviate from the mean. The mean is calculated using the frequencies of the player’s scoring at every ten run interval. This will give the consistency of the batsman about his mean.

        The second part of this project is aimed at predicting the average scores of these batsmen in the forthcoming tournament between Australia and India. This is extremely viable as all four of the batsmen belong to one of the two countries. The scores are predicted by using the probability density functions of the career graphs of these four batsmen.

...read more.

Middle

19

62

20

4

21

1

Legend

DNB – Did Not Bat

  • -  Not Out ( The batsman could have gone on to score more )

DATA PROCESSING AND PRESENTATION

I.)              Graphs showing the pdf curves of the batsmen

II.)       Calculation of the area under the graphs

  1. The standard deviation calculations

I)

  1. The first graph shows the statistics of Sachin Tendulkar. The graph how often Sachin has scored runs at 10 run intervals. The graph rises upto 89 initially as that is the number of times Sachin has scored between 0 – 10. In this manner histograms are drawn  for every 10 run interval upto 190. this is because sachins highest score is 186.
  1. The second graph shows the statistics of the Australian vice-captain Ricky Ponting.This graph does not reach as high as Sachin’s because ricky ponting has played far less matches than Sachin Tendulkar.
  1. The third graph shows the statistics of Matthew Hayden. This graph is even smaller than the other two because his career has been very short

II.)

These calculations show the probability density function of the three graphs. This is the area under the lines joining the top right hand corners of thehistograms.This area are converted in to centimeters.

1.) This is the probability density function of the graph of sachin tendulkar. After adding up all the rectangles and triangles the area comes out to   405.5 cm

  1. The area under the graph of Ricky Pontinbg is 159.2 cm

3.) The        area under the graph of Matthew Hayden is 2072.5 cm

The Predicted scores

Sachin Tendulkar

00-10

405.5/89

4.55

10-20

405.5/89

4.55

20-30

405.5/39

10.39

30-40

405.5/35

11.58

40-50

405.5/30

13.51

50-60

405.5/16

25.34

60-70

405.5/20

20.27

70-80

405.5/17.5

23.17

80-90

405.5/18

22.52

90-100

405.5/19

21.34

...read more.

Conclusion

On the other hand his averages in the tough conditions of Australia are not worth speaking. Therefore the probabilities are very rough estimates.

The averages have been manipulated a little as not outs have not been taken into consideration. The measurements on the graphs are also not very accurate.

Uncertainty of the scale – 0.05

CONCLUSION

Sachin Tendulkar

AVERAGE – 41.71 runs per match

DEVIATION – 35.18

Rahul Dravid

AVERAGE   -  35.29

DEVIATION – 26.9

Ricky Ponting

AVERAGE   -  37.44

DEVIATION – 32.23

Matthew Hayden

AVERAGE   -  37.36

DEVIATION – 27.8

From the analysis above we can conclude that the most consistent batsman is Rahul Dravid and the least consistent is Sachin Tendulkar. The second most consistent player is Matthew Hayden and third is Ricky Ponting. The following is in the decreasing levels of consistency

Rahul Dravid

Matthew Hayden

Ricky Ponting

Sachin Tendulkar

More consistency does not necessarily mean that the batsman is good. If Dravid is very consistent it only means that he scores very close to his average i.e his scores wont be too less or too much more that his average whereas if Sachin Tendulkar deviates a lot from his average it only means that he will either score too much more or too less than his average scores.

WORD COUNT

1438

SOURCE OF DATA

...read more.

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