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  • Level: GCSE
  • Subject: Maths
  • Word count: 1914

Standard Deviation in Mayfield

Extracts from this document...

Introduction

Standard Deviation for Walking

(0.5 x 7) + (1 x 21) + (1.5 x 4) + (2 x 15) + (2.5) + (3 x 3) + (4 x 3) + (6 x 2) + (8) + (9) = 113

113 ÷ 58 = 1.948 (Rounded)

Mean / = 1.948

Xi

Xi -

(Xi -  )²

0.5

-1.448

2.096704

0.5

-1.448

2.096704

0.5

-1.448

2.096704

0.5

-1.448

2.096704

0.5

-1.448

2.096704

0.5

-1.448

2.096704

0.5

-1.448

2.096704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1

-0.948

0.898704

1.5

-0.448

0.200704

Xi

Xi -

(Xi -  )²

1.5

-0.448

0.200704

1.5

-0.448

0.200704

1.5

-0.448

0.200704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

2

0.052

0.002704

3

1.052

1.106704

3

1.052

1.106704

3

1.052

1.106704

4

2.052

4.210704

4

2.052

4.210704

4

2.052

4.210704

6

4.052

16.418704

6

4.052

16.418704

8

6.052

36.626704

9

7.052

49.730704


                                 

Total of (Xi -  )² = 169.5401

Xi Amount = 58

169.5401 ÷ 58 = 2.923105172

Variance = 2.923105172

Standard Deviation = 2.923105172

Standard Deviation = 1.7097 (Rounded)

...read more.

Middle

7 ≤d<8

4

42

8 ≤d<9

2

44

image01.png

Students that have to travel a distance of 1.99km or less to school do not travel to school using a tram at all. From the distance of 2km the use of tram as travel is used, until 8.99km. The lower quartile is 3.8Km, the median is 5.5Km, the upper quartile is 6.2Km and the inter-quartile range is 2.4Km.

Standard Deviation for Tram Travel

(2 x 5) + (2.5 x 2) + (3 x 5) + (4 x 4) + (5 x 15) + (6 x 7) + (7 x 4) + (8 x 2) = 207

207 ÷ 44 = 4.704 (Rounded)

Mean / = 4.704

Xi

Xi -

(Xi -  )²

2

-2.704

7.311616

2

-2.704

7.311616

2

-2.704

7.311616

2

-2.704

7.311616

2

-2.704

7.311616

2.5

-2.204

4.857616

2.5

-2.204

4.857616

3

-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)

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

image02.png

Travelling by combination is used mostly between the distance of 3km – 3.

...read more.

Conclusion

Someone travelling by bike may only be able to cycle to a certain distance. This is why 15 out of 21 people travel to school by bike below the distance of 3Km.

Travelling by bus can be used by anyone that lives near or far, so travelling by bus is used for nearly all distances, with the frequency not being very high for one amount of distance compared to another. The same is for car.

Travelling by tram is used by nobody that has to travel a distance of 1 – 1.99 Km. This may be because many of people will either walk as it is a small distance to walk, and a small amount may travel by car, bus or bike.

Combination is evenly spread out, this is because people living far may use the bus, car or tram to travel to a certain distance then walk the rest of the way.

My hypothesis, The distance a student lives from the school determines they method of travel they use to get to school, is proven because students living closer to the school walk, as the distance from school increase the means of travel change.

...read more.

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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