# Maths open box

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Introduction

By Lev Murynets

Statistics coursework

Introduction

In this assignment I will be investigating and comparing student data concerning Mayfield high school the two hypotheses below to see whether they are correct

1

I believe that in most cases the taller the student is, the more they would weigh, due to the taller person having a larger BMI, although there may be acceptions to the rule this is commonly the case.

In order to prove this hypothesis I will look for a trend between the height and weight of assorted students from Mayfield School’s 1183 pupils with the help of scatter diagrams to analyse whether there is a correlation between the height and weight across year 10 and 11, eliminating all other data that is unneeded to find this result

2

I believe that in most cases male students are taller than females in year 11, this may not be the case in lower year groups, in the later stages of puberty males tend to be taller than females, but the lower year groups will most probably have different results as puberty occurs at different times for different people

This will be tested in a number of graphs comparing the results of the height to weight ratio for year 7’s with the ratio for year 11’s

Middle

Theodopolopodus

Gustafina

1.60

55

7

Fenton

Jake

1.85

55

8

Killinghamshire

Joshua

1.83

57

9

Hardy

Laurel

1.57

45

10

Mozin

Warren

1.72

57

11

Bigglesworth

Wayne

1.77

66

12

Weed

Zac

1.80

51

This graph clearly shows a strong positive correlation, as seen by the line of best fit

For this graphs line of best fit, I found the mean of the data (1.57, 55), and drew the line from that point dividing the results so that the amounts on both sides are equal

For year ten I used a different method of sampling, using systematic sampling, meaning that for the year 10 chosen females I took every 9th female and added them to the list, doing the same for the males in the same year group, the results of which are shown in the samples below

Below are the chosen statistics of the year 9 chosen males showing height weight surname and forename

Year 10 Chosen Females | ||||

1 | Brandward | Amy | 1.65 | 53 |

2 | Taylor-Wall | Angela | 1.70 | 55 |

3 | Long | Anne | 1.74 | 47 |

4 | Slater | Becky | 1.61 | 59 |

5 | White | Helen | 1.60 | 50 |

6 | Blashaw | Holly | 1.73 | 51 |

7 | Connerly | Jenny | 1.70 | 48 |

8 | Thompson | Lishan | 1.55 | 50 |

9 | Skully | Josephine | 1.60 | 66 |

Below shown is the scatter diagram for year 10 females, showing an uneven

correlation between height and weight

For this graphs line of best fit, I found the mean of the data (1.65, 53), and drew the line from that point dividing the results so that the amounts on both sides are equal

Below are the chosen statistics of the year 9 chosen males showing height weight surname and forename

Year 10 Chosen Males | ||||

1 | McManus | Anthony | 1.73 | 50 |

2 | Dolt | Anthony | 1.60 | 47 |

3 | Powers | Austin | 1.57 | 54 |

4 | Leech | Alistair | 1.65 | 55 |

5 | Scundrick | Andrew | 1.74 | 80 |

6 | Smith | Arnold | 1.54 | 54 |

7 | Pritchard | Peter | 1.67 | 60 |

8 | Air | Jason | 1.90 | 70 |

9 | Walton | Kevin | 1.80 | 68 |

10 | Lock | Sean | 1.50 | 50 |

11 | Carr | Jimmy | 1.72 | 58 |

Below shown is a strong positive correlation between the results of the ear ten height and weight, which means they are all getting significantly taller

Below is shown the box and whisker diagram on which males tend to have a wider range than females in year 10

Standard Deviation = 0.1183

Variance = 0.01398

______________________________________________________________________

Table of Values of Raw Data:

Class Int. Mid. Int. (x) Class Width Freq. Cum. Freq.

1.3 ≤ x < 1.5 1.4 0.2 6 6

1.5 ≤ x < 1.7 1.6 0.2 20 26

1.7 ≤ x < 1.9 1.8 0.2 1 27

∑f = 27

∑fx = 42.2

∑fx² = 66.2

Mean = 1.563

Standard Deviation = 0.09486

Variance = 0.008999

______________________________________________________________________

Table of Values of Raw Data:

Class Int. Mid. Int. (x) Class Width Freq. Cum. Freq.

0 ≤ x < 0.2 0.1 0.2 0 0

0.2 ≤ x < 0.4 0.3 0.2 0 0

0.4 ≤ x < 0.6 0.5 0.2 0 0

0.6 ≤ x < 0.8 0.7 0.2 0 0

0.8 ≤ x < 1 0.9 0.2 0 0

1 ≤ x < 1.2 1.1 0.2 0 0

1.2 ≤ x < 1.4 1.3 0.2 0 0

1.4 ≤ x < 1.6 1.5 0.2 2 2

1.6 ≤ x < 1.8 1.7 0.2 7 9

1.8 ≤ x < 2 1.9 0.2 0 9

∑f = 9

∑fx = 14.9

∑fx² = 24.73

Mean = 1.656

Standard Deviation = 0.08315

Variance = 0.006914

______________________________________________________________________

Table of Values of Raw Data:

Class Int. Mid. Int. (x) Class Width Freq. Cum. Freq.

0 ≤ x < 0.2 0.1 0.2 0 0

0.2 ≤ x < 0.4 0.3 0.2 0 0

0.4 ≤ x < 0.6 0.5 0.2 0 0

0.6 ≤ x < 0.8 0.7 0.2 0 0

0.8 ≤ x < 1 0.9 0.2 0 0

1 ≤ x < 1.2 1.1 0.2 0 0

1.2 ≤ x < 1.4 1.3 0.2 0 0

1.4 ≤ x < 1.6 1.5 0.2 2 2

1.6 ≤ x < 1.8 1.7 0.2 6 8

1.8 ≤ x < 2 1.9 0.2 1 9

∑f = 9

∑fx = 15.1

∑fx² = 25.45

Mean = 1.678

Standard Deviation = 0.1133

Variance = 0.01284

These are the statistics results for the height of males in year 10 compared to females in year ten

Year 11

For year 11 I used the last of the three methods of sampling, using random sampling I chose the 10% of males and 10% of females simply by looking at typical sounding names, or names resembling a known persona this has no system and cannot be biased

Below are the chosen statistics of the year 9 chosen males showing height weight surname and forename

Year 11 Chosen Females | ||||

1 | Brown | Amy | 1.62 | 54 |

2 | McMillan | Collen | 1.58 | 48 |

3 | Warwick | Emma | 1.69 | 50 |

4 | Lewis | Claire | 1.56 | 45 |

5 | Chen | Sabrina | 1.61 | 54 |

6 | Raphiell | Sally | 1.55 | 50 |

7 | Todd | Samantha | 1.53 | 42 |

8 | Alsam | Samia | 1.55 | 36 |

9 | Compass | Sharon | 1.52 | 38 |

The results of this scatter diagram clearly show most results are near or on the line of best fit, showing a strong positive correlation

For this graphs line of best fit, I found the mean of the data (1.57, 46), and drew the line from that point dividing the results so that the amounts on both sides are equal

Below shown are the year 11 chosen males, with height weight surname and forename shown in the table below

Year 11 Chosen Males | ||||

1 | Braithwaite | Douglas | 1.8 | 72 |

2 | Ward | Alexander | 1.70 | 54 |

3 | Lee | Bruce | 1.83 | 75 |

4 | Spacey | Kevin | 1.73 | 45 |

5 | Brand | Russel | 1.78 | 67 |

6 | Mitchell | David | 1.51 | 38 |

7 | Fairfax | William | 1.71 | 57 |

8 | Major | William | 1.8 | 68 |

Conclusion

##### In conclusion I have proven that in most cases the BMI increases with height throughout Year 7-11 as shown in the diagrams above

My overall conclusion is that my two hypotheses are both correct in general. My hypothesis of there being a positive correlation between height and weight was proved correct mainly by scatter diagrams. The tables with the information on student’s heights and weights could also have been used if it was sorted correctly. But concluding my first hypothesis was proved correct by 6 out 10 scatter graphs supporting it. My second hypothesis of the year 11 boys weighing more and being taller than year 11 girls was proved correct mainly by the box and whisker diagrams showing us that the males were overall taller and the histogram frequency density showing us their weight was higher.

The graphs show the trend in male height and females. The males are shown to be taller than females. Going through the years the heights of boys tend to get higher range than the girls as before earlier the heights were almost equal. This shows that maybe puberty affects the growth of teenagers on the later years (Y10, 11) males, causing the difference in height from girls.

3rd Hypothesis

There is no correlation between BMI and hours spent watching tv

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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