There will be a positive correlation between height and weight.The spread of boys' height will be larger than the spread of girls' height

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Mohamed Hassan                student number: 20042512

GCSE

Mathematics Data Handling Coursework

Introduction

For my investigation I am using data from a simulated school called Mayfield High School. This is a mixed secondary school with 1183 people, split into 604 boys and 579 girls. There are five-year groups, from 7 to 11. This contains many different records, including, first name, surname, height, weight, age (decimal, years and months), month of birth, sex, hand, favourite sport subject and TV program, hours of TV, IQ, distance between home and school, means of travel to school, and Ks2 and Ks3 results. I have chosen to investigate the relationship between height and weight, because it is quite probable that they influence each other. Here are my hypotheses, which are all related to height, weight or both. : -

  1. There will be a positive correlation between height and weight.
  2. The spread of boys’ height will be larger than the spread of girls’ height.
  3. The average boys’ weight will be larger than the average girls’ weight.
  4. The older someone is the better the correlation is between height and weight.

I will collect data on the height and weight of 60 pupils. I will also collect the data on their age and gender. To make sure my data sample is fair and unbiased. I will do a random stratified sample, which means I will have an amount of records from each gender year group, in correlation to their percentage of the school size.

I will investigate these hypotheses by drawing an assortment of graphs and diagrams, and making several calculations.

Any data, which seems implausible, such as a height less than 1m, or larger than 2.2m, or a weight less than 20kg, or more than 90kg, I will discount, and randomly choose another pupil of the same year and gender. I will now explain my hypotheses in more detail.

1. There will be a positive correlation between height and weight.

I will investigate this statement, by collecting data on the height and weight of 30 boys and 30 girls, and then by plotting a graph, with height on the x-axis and weight on the y-axis. I will plot all of my data points on a graph, then draw a line of best fit, and calculate an equation for the line, by reading off the y intercept, and calculating the gradient, so I have an equation in the form of y=mχ+c. I will then be able to estimate the height for people who I only have the weight for, and the weight of people whom I know their height.

2. The spread of boys’ height is larger than the spread of girls’ height.

I will investigate this hypothesis by putting the height data into a frequency table, one for girls and one for boys. I will calculate the cumulative frequency, and plot a cumulative frequency graph. This will tell me the range and the inter quartile range, which are both measures of spread. I will then use the standard deviation equation, to work out the standard deviation of the girls’ heights and the boys’ height. Standard deviation is the square root of the mean of the squares of the deviation from the mean. This will show how widely spread the heights are from the mean.

3.The average boys weight will be larger than the average girls weight

I will use three measures of central tendencies to find the averages. I will investigate this hypothesis by calculating the mode, median, and mean of the weight data of the 60 pupils in my sample population, both grouped and ungrouped. If the averages, of the boys’, are higher than the averages of the girls’ data, then my hypothesis will be proved correct. I will also draw a weight histogram, as another way of looking at the central tendency.

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4.The older someone is the better the correlation is between height and weight.

I will investigate this hypothesis by drawing a scatter graph for each year group, (7,8,9,10,11), and measuring the deviation, of the points from the line of best fit. The graph, with the least deviation will have the best correlation between height and weight.

Stratified Sample

I will need to do a stratified sample, because there are different number of pupils in each year group, so if I took the same number of pupils from each year group, my results would be biased. I ...

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