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  • Level: GCSE
  • Subject: Maths
  • Word count: 4098

Maths data handling project on basketball

Extracts from this document...

Introduction

Statistics Coursework

Topic – Basketball

Hypothesis

  • The position of a basketball player will affect how many points per game they get
  • The height of a basketball player will effect the position they play
  • In general the height of a basketball player effects how many points they get per game

Guards

Forwards

Centres

PPG

Height (cm)

PPG

Height (cm)

PPG

Height (cm)

6.1

188

5.9

196

5.6

213

1.8

196

3.2

206

5.1

213

7.1

191

7.3

205

4.5

208

3.7

201

5.6

211

11.4

206

15.1

191

7.2

208

7.8

208

19.3

201

1.8

213

1.8

211

17

201

6.2

201

1.3

213

5.4

196

18.2

213

4.2

213

7.9

196

5.7

203

9.5

213

6.5

206

1.9

203

2.2

208

7.8

183

6.5

203

3.7

208

5.7

188

4.6

201

4.1

216

3.8

185

17.9

201

2.3

218

11.4

201

2.9

213

10.1

203

12.8

208

15.9

198

10.7

206

8.4

196

3.5

213

6.3

188

20

206

3.3

191

6

206

Guards

Points Per Game (PPG)

Frequency

0 up to but not including 4

4

4 up to but not including 8

8

8 up to but not including 12

3

12 up to but not including 16

2

16 up to but not including 20

2

20 up to but not including 24

0

Height (cm)

Frequency

180 up to but not including 190

5

190 up to but not including 200

8

200 up to but not including 210

6

210 up to but not including 220

0

Forwards

Points Per Game (PPG)

Frequency

0 up to but not including 4

5

4 up to but not including 8

8

8 up to but not including 12

2

12 up to but not including 16

1

16 up to but not including 20

2

20 up to but not including 24

1

Height (cm)

Frequency

180 up to but not including 190

0

190 up to but not including 200

1

200 up to but not including 210

13

210 up to but not including 220

5

Centres

Points Per Game (PPG)

Frequency

0 up to but not including 4

5

4 up to but not including 8

6

8 up to but not including 12

2

12 up to but not including 16

0

16 up to but not including 20

0

20 up to but not including 24

0

Height (cm)

Frequency

180 up to but not including 190

0

190 up to but not including 200

0

200 up to but not including 210

5

210 up to but not including 220

8

Guards Mean For PPG

Points Per Game (PPG)

Middle Value x

Frequency f

fxx

0 up to but not including 4

0 + 4 = 4 ÷ 2 = 2

4

2 x 4 = 8

4 up to but not including 8

4 + 8 = 12 ÷ 2 = 6  

8

9 x 6 = 54

8 up to but not including 12

8 + 12 = 20 ÷ 2 = 10

3

3 x 10 = 30

12 up to but not including 16

12 + 16 = 28 ÷ 2 = 14

2

2 x 14 = 28

16 up to but not including 20

16 + 20 = 36 ÷ 2 = 18

2

2 x 18 = 36

20 up to but not including 24

20 + 24 = 44 ÷ 2 = 22

0

0 x 22 = 0

Totals:

19

156

Estimate of mean = sum of (middle values x frequencies) ÷ sum of frequencies =

fx ÷ f = 156 ÷ 19 = 8.21 (2 d.p)

Forwards Mean For PPG

Points Per Game (PPG)

Middle Value x

Frequency f

fxx

0 up to but not including 4

0 + 4 = 4 ÷ 2 = 2

5

5 x 2 = 10

4 up to but not including 8

4 + 8 = 12 ÷ 2 = 6  

8

8 x 6 = 48

8 up to but not including 12

8 + 12 = 20 ÷ 2 = 10

2

2 x 10 = 20

12 up to but not including 16

12 + 16 = 28 ÷ 2 = 14

1

1 x 14 = 14

16 up to but not including 20

16 + 20 = 36 ÷ 2 = 18

2

2 x 18 = 36

20 up to but not including 24

20 + 24 = 44 ÷ 2 = 22

1

1 x 22 = 22

Totals:

19

150

Estimate of mean = sum of (middle values x frequencies) ÷ sum of frequencies =

fx ÷ f = 150 ÷ 19 = 7.89 (2 d.p)

Centres Mean For PPG

Points Per Game (PPG)

Middle Value x

Frequency f

fxx

0 up to but not including 4

0 + 4 = 4 ÷ 2 = 2

5

5 x 2 = 10

4 up to but not including 8

4 + 8 = 12 ÷ 2 = 6  

6

6 x 6 = 36

8 up to but not including 12

8 + 12 = 20 ÷ 2 = 10

2

2 x 10 = 20

12 up to but not including 16

12 + 16 = 28 ÷ 2 = 14

0

0 x 14 = 0

16 up to but not including 20

16 + 20 = 36 ÷ 2 = 18

0

0 x 18 = 0

20 up to but not including 24

20 + 24 = 44 ÷ 2 = 22

0

0 x 22 = 0

Totals:

13

66

Estimate of mean = sum of (middle values x frequencies) ÷ sum of frequencies =

fx ÷ f = 66 ÷ 19 = 3.47 (2 d.p)

Guards Modal Class Interval for PPG

Points Per Game (PPG)

Middle Value x

Frequency f

fxx

0 up to but not including 4

0 + 4 = 4 ÷ 2 = 2

4

2 x 4 = 8

4 up to but not including 8

4 + 8 = 12 ÷ 2 = 6  

8

9 x 6 = 54

8 up to but not including 12

8 + 12 = 20 ÷ 2 = 10

3

3 x 10 = 30

12 up to but not including 16

12 + 16 = 28 ÷ 2 = 14

2

2 x 14 = 28

16 up to but not including 20

16 + 20 = 36 ÷ 2 = 18

2

2 x 18 = 36

20 up to but not including 24

20 + 24 = 44 ÷ 2 = 22

0

0 x 22 = 0

Totals:

19

156

...read more.

Middle

5

5 x 2 = 10

4 up to but not including 8

4 + 8 = 12 ÷ 2 = 6  

8

8 x 6 = 48

8 up to but not including 12

8 + 12 = 20 ÷ 2 = 10

2

2 x 10 = 20

12 up to but not including 16

12 + 16 = 28 ÷ 2 = 14

1

1 x 14 = 14

16 up to but not including 20

16 + 20 = 36 ÷ 2 = 18

2

2 x 18 = 36

20 up to but not including 24

20 + 24 = 44 ÷ 2 = 22

1

1 x 22 = 22

Totals:

19

150

Modal class intervals equals ‘4 up to but not including 8’ because it has the highest frequency

Centres Modal Class Interval for PPG

Points Per Game (PPG)

Middle Value x

Frequency f

fxx

0 up to but not including 4

0 + 4 = 4 ÷ 2 = 2

5

5 x 2 = 10

4 up to but not including 8

4 + 8 = 12 ÷ 2 = 6  

6

6 x 6 = 36

8 up to but not including 12

8 + 12 = 20 ÷ 2 = 10

2

2 x 10 = 20

12 up to but not including 16

12 + 16 = 28 ÷ 2 = 14

0

0 x 14 = 0

16 up to but not including 20

16 + 20 = 36 ÷ 2 = 18

0

0 x 18 = 0

20 up to but not including 24

20 + 24 = 44 ÷ 2 = 22

0

0 x 22 = 0

Totals:

13

66

Modal class intervals equals ‘4 up to but not including 8’ because it has the highest frequency

Guards Median for PPG

Points Per Game (PPG)

Frequency

0 up to but not including 4

4

4 up to but not including 8

8

8 up to but not including 12

3

12 up to but not including 16

2

16 up to but not including 20

2

20 up to but not including 24

0

Total

19

Median equals n + 1 ÷ 2 = 19 + 1 ÷ 2 = 10th value. Which is in the class interval ‘4 up to but bot including 8.

Forwards Median for PPG

Points Per Game (PPG)

Frequency

0 up to but not including 4

5

4 up to but not including 8

8

8 up to but not including 12

2

12 up to but not including 16

1

16 up to but not including 20

2

...read more.

Conclusion

195.53

190 up to but not including 200

190 up to but not including 200

7.50

Forwards

207.11

200 up to but not including 210

200 up to but not including 210

5.02

Centres

211.15

210 up to but not including 220

210 up to but not including 220

5.03

Centres have the highest mean followed by forwards and guards last. Which is the reverse order of the mean for PPG, which I investigated earlier. This suggests that the height and PPG of each position correlates. The modal class interval and median were equal and the same for each position. Suggesting that the most often height for each position is equal to its middle value. The modal class interval and median increases for each position. It shows that tallest players are centres, the shortest players are guards and the average height players are forwards. Guards had the highest standard deviation. Meaning that the guards data is more spread out across the mean than any other position. There was only a 0.1 difference between forwards and centres standard deviation. This shows that both there data is similarly spread across the mean.
Evidence from my data suggests 42% of guards height were between 190 and 200 cm. 68% of forwards height were between 200 and 210 cm. 62% of centres height were between 210 and 220 cm. These conclusions are based on a sample of only 50 players. I could extend the sample or repeat the whole exercise to confirm my results.

...read more.

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