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

# Maths data handling project on basketball

Extracts from this document...

Introduction

Statistics Coursework

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

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

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

##### 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.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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