# From the data I have received I have chosen to conduct an investigation comparing height and weight because I feel there much relevance between ones and height and weight.

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Introduction

Mathematics Coursework

In this investigation, I have been given data from Mayfield School.

From the data I have received I have chosen to conduct an investigation comparing height and weight because I feel there much relevance between ones and height and weight. I have chosen to compare height and weight because I feel I will get clear results and therefore conduct a meaningful and knowledgeable investigation. I will be trying to determine whether ones height has any relevance to ones weight and then I will attempt to find out whether separating boys from girls will show different trends and in general have much difference from the group as a whole.

I will first investigate heights and weight for year 7 and for year 11 and as an extension I will make comparisons and comment for both years. For my investigation I will need to start with a random sample of 50 students (25 girls, 25 boys) from year 7. I have data from a total of around 170 students, and the amount of boys and girls are roughly even, hence meaning there are about 85 boys and 85 girls. To get a completely unbiased sample of students I will be using random selection. I have figured out that because there are around 85 boys it will be sensible to choose every third boy in the list starting with the third boy down the list. Theoretically this will mean that around 10 students will not even be considered at the bottom of the list because 3 × 25 = 75 and 85 – 75 = 10. However this method of random selection will give me a completely random and unbiased sample of student. The exact same applies for the girls. When I have done the random sample selection I will have a total of 50 students, 25 of which are boys and 25 of which are girls.

Middle

Weight, w (kg) | Height in standard class intervals | Freq. | Frequency density |

25 ≤ w < 40 | 3 | 10 | 10 ÷ 3 = 3.3 (to 1 d.p) |

40 ≤ w < 45 | 1 | 12 | 12 ÷ 1 = 12 |

45 ≤ w < 50 | 1 | 10 | 10 ÷ 1 = 10 |

50 ≤ w < 55 | 1 | 13 | 13 ÷ 1 = 13 |

55 ≤ w < 65 | 2 | 5 | 5 ÷ 2 = 2.5 |

(Please refer to the graph on page 17)

From looking at the histogram for frequency density against weight you can see that there are;

10 people who weigh between 25 – 40kg.

12 people who weigh between 40 – 45kg.

10 people who weigh between 45 – 50kg.

13 people who weigh between 50 – 55kg.

5 people who weigh between 55 – 65kg.

50 – 55kg has the largest area and so therefore is the most popular group.

I will now do cumulative frequency for my data. This will enable me to compare my different sets of data. Here is the cumulative for the height for boy, girls and mixed population.

Height, h (cm) (Up to and including) | Cumulative frequency | ||

Boys | Girls | Mixed | |

< 120 | 0 | 1 | 1 |

< 130 | 0 | 2 | 2 |

< 140 | 1 | 4 | 5 |

< 150 | 7 | 8 | 15 |

< 160 | 19 | 19 | 38 |

< 170 | 24 | 24 | 48 |

< 180 | 25 | 25 | 50 |

I will now use this data to do a cumulative frequency graph.

(Please refer to the graph on page 19)

Height, h (cm) | Median | Lower quartile | Upper Quartile | Interquartile range |

Boys | 155 | 149 | 160 | 11 |

Girls | 154 | 147 | 160 | 13 |

Mixed | 153 | 148 | 159 | 11 |

If I wanted to estimate the number of boys who had a height between 140 – 160cm. The cumulative frequency curve for boys shows me that 1 boy in the sample had a height up to 140cm and 19 boys had a height up to 160cm. This means that 19 – 1 = 18 boys had a height between 140 – 160cm. So I can estimate that 18 out of 25 or 72% of boys will be between 140 – 160cm tall. So if I were to select a boy at random from the school, my data suggests that the probability of him having a height between 140 – 160cm is 0.72.

If I wanted to estimate the number of girls who had a height between 150 – 170cm. The cumulative frequency curve for the girls shows me that 7 girls in the sample have a height up to 150cm and 24 have a height up to 170cm.

Conclusion

For the frequency density of 7 year students I found for height and weight that I had to combine the lower and higher intervals together in order to make there frequencies large enough to plot on a histogram. This indicates that before any combining of intervals was made that the most popular intervals were in the middle intervals of my data.

For the averages of the year 11 students I found that there was much more difference between boys and girls for height and weight, this indicates that for year 11 there is a much different variety of results compared to year 7 students.

Overall I feel I have conducted a very successful investigation which has answered the accuracy of most of my hypothesises, however there have been some unexpected results which I am sure are down to the chance of the random sample. So therefore with another sample I may get different 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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