# have chosen to show the relationship between height and weight. The main reason for this is because the data for height and weight is continuous, unlike eye and hair colour and KS2 results which are discrete or qualitative

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Introduction

Ben Krawiec File: Maths-PAJ/Mayfield Coursework/Mayfield High School.doc

Mayfield High School – Edexcel GCSE Coursework

Introduction:

The data we have been given is taken from a real school, while Mayfield High School is a fictitious school. The school consists of 1183 pupils, of which there is the following number of pupils:

Year Group | Number of Males | Number of Females | Total |

7 | 151 | 131 | 282 |

8 | 145 | 125 | 270 |

9 | 118 | 143 | 261 |

10 | 106 | 94 | 200 |

11 | 84 | 86 | 170 |

For each child the following data was provided: Age, Year Group, IQ, Weight, Height, Hair Colour, Eye Colour, Distance from home to school, Usual method of travel, Number of brothers/sisters, & KS2 Result in English, Mathematics and Science. This gives us a total of 31941 datum points (1183 x 27).

There is a number of different possible lines of enquiry that could be follow, some examples of these are:

- the variations in hair colour,
- the variations in eye colour,
- the relationship between the above two colours,
- the distance travelled to school,
- the relationship between height and weight,
- the relationship between KS2 results,
- the relationship between IQ and KS2 results,
- the height to weight ratio in terms of body mass index.

From the lines of enquires, I have chosen to show the relationship between height and weight. The main reason for this is because the data for height and weight is continuous, unlike eye and hair colour and KS2 results which are discrete or qualitative, continuous data I can put it into Box Plots, Histograms, Pie Charts, Scatter Graphs and Stem & Leaf diagrams.

Hypothesis:

Before analysing the data I can make hypothesises to show, how what results I am expecting to get. These hypothesise are:

- There will be a positive correlation between weight and height, as when a person gets taller, they will also become heavy, due to bone and muscle growth.

Middle

10F12

53

4.65

The equation y = 37.394x – 9.5096 can now be used to find the correct data for the anomalies above (highlighted in italics), the actual results are:

Number | Incorrect Data | Predicted Data | ||

Weight (kg) | Height (m) | Weight (kg) | Height (m) | |

8M57 | 5 | 1.58 | 50 | 1.58 |

10F12 | 53 | 4.65 | 53 | 1.67 |

I am happy to use this equation as it has been taken from a chart that uses 119 points and has an R-value of 0.4412 that shows good correlation.

Now that I had found out that my first hypothesis is correct I can check my second hypothesis, also using charts. The first chart is of the males’ weight against height:

The second chart shows the females’ weight against height:

The above charts can be used to show whether or not my second hypothesis is correct. The value I need to see if my hypothesis is correct is the R-value. The R-value for the males’ chart is 0.5118 and the females’ chart has an R-value of 0.3154. From these figures I can tell that the males have a greater correlation than the females do, so my second hypothesis is confirmed. Another way to judge the correlation is using a visual comparison, but these two graphs show little difference, making it impossible to compare them.

From this data I can also compare the R-values for the best-fit line of males and females to that of the value for the whole school. From this I can tell if the correlation from the school sample is made up of males or females. The R-value for the school is 0.4412, for the males it is 0.5118 and for the females it is 0.3154. From these figures I can say that the correlation for the whole school is made up from both sexes, but is largely made up of the male population of the school.

Weight throughout the school:

Conclusion

For the year eleven males a final histogram is needed.

This histogram shows near to normal distribution, and again Pearson’s measure of skewness will be used to confirm the skew. . Although this histogram has a slight negative skew, when looking at it, it can be seen that the skew is near to normal distribution. This means my tenth hypothesis can be rejected.

Overall, in Mayfield show varying EQI results, with year 7’s having negative skew, year 9’s have positive skew and year 11’s have normal distribution, which shows a variation between each year groups.

Overall, the investigation has shown that as height increases, so to does weight and visa versa. This information can then be used to predict other anomalous points. The investigation had also shown how weight of different sexes changes, and how it changes through the school. Hypotheses that were confirmed included one that showed that males with have a wider spread of weight data in year eleven than females do. The final part of the investigation shows the obesity levels, and how they change throughout the school, one thing that can be taken from the investigation is that obesity level are low in all year groups, although two histograms show negative, this is to a small degree and therefore would not effect the results too greatly. All the hypotheses were based on real life, and therefore I can use these to show if Mayfield is a good example of the population. The investigation showed that six of the ten hypotheses were correct, so I can therefore say that Mayfield gives a good example of the young population, although it does not necessary give an accurate one.

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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