# Mayfield High. I have decided to make my hypothesis: The distance a student lives from the school determines they method of travel they use to get to school.

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Introduction

Ahsan Malik

Maths Coursework

In this investigation I have been given data on Students from Mayfield High School, each student has a vast amount of data about them

I have decided to make my hypothesis: The distance a student lives from the school determines they method of travel they use to get to school.

I have taken out all irrelevant data from my database and left the Age, distance from school and means of travel for each student in the database.

For Key Stage 3 and Key Stage 4 I used a random method to cut down the amount of students for each means of travel this was done so it would make it easier for me to carry out the investigation.

I will be using a random sampling method to cut down the data as I will not be able to compare every student.

There are many ways that I could use to get my random data, Stratified sampling is one method, it is where a person is placed into a group, then random samples are taken from each group. Another method is systematic sampling which is where you can go and pick out every 10th or so person.

I did not use either of those above to sample my data instead

Middle

11

11

2 ≤d<3

15

26

3 ≤d<4

8

34

4 ≤d<5

6

40

5 ≤d<6

3

43

6 ≤d<7

2

45

7 ≤d<8

2

47

8 ≤d<9

2

49

9 ≤d<10

1

50

Travelling by car is used by most of the students that travel by car to school and only have to travel 4.99km, this is 40 students. Only 10 more students travel by car, when the distance is 5km and more. The lower quartile is 2.3Km, the median is 2.9Km, the upper quartile is 4.5Km and the inter-quartile range is 2.2Km.

Standard Deviation for Car Travel

(1 x 8) + (1.5) + (1.75 x 2) + ( 2 x 14) + (2.5) ( 3 x 8) + (4 x 6) + (5 x 3) +

(6 x 2) + (7 x 2) + (8) + (8.5) + (10) = 159

159 ÷ 50 = 3.18

Mean or = 3.18

Xi | Xi - | (Xi - )² |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1 | -2.18 | 4.7524 |

1.5 | -1.68 | 2.8224 |

1.75 | -1.43 | 2.0449 |

1.75 | -1.43 | 2.0449 |

2 | --1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

2 | -1.18 | 1.3924 |

Xi | Xi - | (Xi - )² |

2.5 | -0.68 | 0.4624 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

3 | -0.18 | 0.0324 |

4 | 0.82 | 0.6724 |

4 | 0.82 | 0.6724 |

4 | 0.82 | 0.6724 |

4 | 0.82 | 0.6724 |

4 | 0.82 | 0.6724 |

4 | 0.82 | 0.6724 |

5 | 1.82 | 3.3124 |

5 | 1.82 | 3.3124 |

5 | 1.82 | 3.3124 |

6 | 2.82 | 7.9524 |

6 | 2.82 | 7.9524 |

7 | 3.82 | 14.5924 |

7 | 3.82 | 14.5924 |

8 | 4.82 | 23.2324 |

8.5 | 5.32 | 28.3024 |

10 | 6.82 | 46.5124 |

Total of (Xi - )² = 222.225

n = 50

222.225 ÷ 50 = 4.4445

Variance = 4.4445

Standard Deviation = √4.4445

Standard Deviation = 2.108 (Rounded)

The standard deviation shows me …. FINISH THIS BIT OFF

Means of Travel: Walking

WALK | ||

Distance From School (Km) | Frequency | Cumulative Frequency |

0 ≤d<1 | 7 | 7 |

1 ≤d<2 | 25 | 32 |

2 ≤d<3 | 16 | 48 |

3≤d<4 | 3 | 51 |

4 ≤d<5 | 3 | 54 |

5 ≤d<6 | 0 | 54 |

6 ≤d<7 | 2 | 56 |

7 ≤d<8 | 0 | 56 |

8 ≤d<9 | 1 | 57 |

9 ≤d<10 | 1 | 58 |

48 out of the 58 Students that walk to school, have to walk 2.99km and below. From the distance of 3km the amount of students walking to school decreases, only 10 students walk to school from the distance of 3km to 9.99km. The lower quartile is 1.3km, the median is 1.9Km, the upper quartile is 2.

Conclusion

-1.704

2.903616

3

-1.704

2.903616

3

-1.704

2.903616

3

-1.704

2.903616

3

-1.704

2.903616

4

-0.704

0.495616

4

-0.704

0.495616

4

-0.704

0.495616

4

-0.704

0.495616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

Xi

Xi -

(Xi - )²

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

5

0.296

0.087616

6

1.296

1.679616

6

1.296

1.679616

6

1.296

1.679616

6

1.296

1.679616

6

1.296

1.679616

6

1.296

1.679616

6

1.296

1.679616

7

2.296

5.271616

7

2.296

5.271616

7

2.296

5.271616

7

2.296

5.271616

8

3.296

10.863616

8

3.296

10.863616

Total of (Xi - )² = 118.6591

Xi Amount = 44

118.6591 ÷ 44 = 2.696797727

Variance = 2.696797727

Standard Deviation = √2.696797727

Standard Deviation = 1.642 (Rounded) 2.108 1.7097 1.642

Means of Travel: Combination

Combination | ||

Distance From School (km) | Frequency | Cumulative Frequency |

1 ≤d<2 | 5 | 5 |

2 ≤d<3 | 4 | 9 |

3 ≤d<4 | 12 | 21 |

4 ≤d<5 | 3 | 24 |

5 ≤d<6 | 6 | 30 |

6 ≤d<7 | 2 | 32 |

7 ≤d<8 | 1 | 33 |

8 ≤d<9 | 1 | 34 |

Travelling by combination is used mostly between the distance of 3km – 3.99km, but travelling by a combination is used through out all the distances. The lower quartile is 3Km, the median is 3.7Km , the upper quartile is 5.5Km and the inter-quartile range is 2.5Km.

Standard Deviation for Combination Travel

(1x5) + (2 x 3) + (2.5) + (3 x 12) + (4) + (4.5 x 2) + (5 x 6) + (6 x 2) +

(7) + (8.5) = 120

120 ÷ 34 = 3.529 (Rounded)

Mean / = 3.529

Xi | Xi - | (Xi - )² |

1 | -2.529 | 6.395841 |

1 | -2.529 | 6.395841 |

1 | -2.529 | 6.395841 |

1 | -2.529 | 6.395841 |

1 | -2.529 | 6.395841 |

2 | -1.529 | 2.337841 |

2 | -1.529 | 2.337841 |

2 | -1.529 | 2.337841 |

2.5 | -1.029 | 1.058841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

Xi | Xi - | (Xi - )² |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

3 | -0.529 | 0.279841 |

4 | 0.471 | 0.221841 |

4.5 | 0.971 | 0.942841 |

4.5 | 0.971 | 0.942841 |

5 | 1.471 | 2.163841 |

5 | 1.471 | 2.163841 |

5 | 1.471 | 2.163841 |

5 | 1.471 | 2.163841 |

5 | 1.471 | 2.163841 |

5 | 1.471 | 2.163841 |

6 | 2.471 | 6.105841 |

6 | 2.471 | 6.105841 |

7 | 3.471 | 12.047841 |

8.5 | 4.971 | 24.710841 |

Total of (Xi - )² = 107.4706

Xi Amount = 44

107.4706 ÷ 44 = 2.442513636

Standard Deviation = √2.442513636

Variance = 2.442513636

Standard Deviation = 1.563 (Rounded)

Standard Deviation Conclusion

Standard Deviation for:

Bike = 2.005

Bus = 1.948

Car = 2.108

Walking = 1.7097

Tram = 1.642

Combination = 1.563

The results from the standard deviation show me that travelling by car has the greatest variation in it, and using combinations to travel has the least variation in it.

This means the data for travelling by car is more spread than any other form of travel and the opposite for travelling to school using a combination. Travelling by bike is also high it is about 0.1 below the result for car.

As the standard deviation is the lowest for travelling by using combination it tells me that the data is less spread than any other form of travelling.

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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