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  • Level: GCSE
  • Subject: Maths
  • Document length: 2836 words

Correlation between the heights and weights of boys and girls over the years 7, 8, 9.

Extracts from this essay...

Introduction

Statistics coursework Correlation between the heights and weights of boys and girls over the years 7, 8, 9. I will need to collect data on heights and weights of from the years 7, 8, 9, in Mayfield High School, to determine a population for my investigation. The information I have taken from the spreadsheet is made up data from a real school, Mayfield School. I have chosen this source of information as it is easily available and it was the information that I needed. I will need to collect 30 pieces of data and I will ensure it is a fair sampling by using random stratified sampling. I will use the data to compare the heights of boys and girls and then compare the weight of boys and girls. Using the data I will calculate the mean, mode, median and the range. These particular calculations are useful because it gives me a single data so I can use it to compare the boys with the girls. The range will tell me how much the data is spread out, the bigger the range, the bigger the spread. I will show the information using box and whisker diagrams and stem and leaf diagrams. These particular diagrams are useful because it allows me to see how the data is distributed and it is easier to find the mean and mode. The box and whisker diagrams will help me to compare skews#, the inter-quartile range and the median. As a result of the calculations and diagrams I can compare the heights and weights of boys and girls. I am going to investigate data provided by Mayfield High School.

Middle

Most of the people in the years were between 150cm and 160cm in height. Weight Males: 35-36-42-45-48-49-51-52-53-53-54-54-59-60-60 kg 30 5, 6 40 2, 5, 8, 9 50 1, 2, 3, 3, 4, 4, 9 60 0, 0 Females: 26-28-40-41-42-42-43-46-47-48-48-48-52-53-53 Kg 20 6, 8 30 40 0, 1, 2, 2, 3, 6, 7, 8, 8, 8 50 2, 3, 3 Mixed: 26-28-35-36-40-41-42-42-42-43-45-46-47-48-48-48-48-49-51-52-52-53-53-53-53-54-54-59-60-60 Kg 20 6, 8 30 5, 6 40 0, 1, 2, 2, 2, 3, 5, 6, 7, 8, 8, 8, 8, 9 50 1, 2, 2, 3, 3, 3, 3, 4, 4, 9 60 0, 0 As you can see from the above diagram: The lightest person from all the years is 26kg and the heaviest person is 60kg. The lightest male is 35kg and the heaviest is 60kg. The lightest female is 26kg and the heaviest is 52kg Most of the people in the years were between 40kg and 50kg in weight. From my stem and leaf diagrams it is now possible to calculate the mode, median, mean and the range. Height Males: § Mode - 171cm § Mean - 158.53cm § Median - 162cm § Range - 39cm Females: § Mode - 160cm, 163cm, 180cm § Mean - 158.2cm § Median - 160cm § Range - 49cm Mixed: § Mode - 160cm, 171cm § Mean - 158.53cm § Median - 160cm § Range - 49cm Weight Males: § Mode - 53kg, 54kg, 60kg § Mean - 50kg § Median -52 kg § Range - 25kg Females: § Mode - 48kg § Mean - 43.8kg § Median - 46kg § Range - 27kg Mixed: § Mode - 48kg, 53kg § Mean - 46.9kg § Median - 48kg § Range - 34kg I have now decided to represent my data in box and whisker diagrams: These diagrams are for males.

Conclusion

6 (AT 140.5) 16 (AT 150.5) 24 (AT 160.5) 30 (AT 170.5) Weight (kg) 21-30 31-40 41-50 51-60 Frequency 2 3 13 12 Cumulative Frequency 2 (AT 20.5) 5 (AT 30.5) 18 (AT 40.5) 40 (AT 50.5) Analysis: I began this investigation with the aim to find the average heights and weights of males and females in years 7, 8 and 9. From this investigation I found out that the average height for a student in year 7, 8, and 9 was 158.53 cm and the average weight for a student in year 7, 8, and 9 was 46.9kg. I also found out that the average weight for females in years 7, 8, and 9 was 43.8kg, that the lightest female was 26kg and the heaviest was 53kg, giving a range of 27kg. In terms of height, the average height for females in year 7, 8, and, 9 was 158.2cm, the tallest female was 180cm and the shortest female was 131cm, giving a range of 49cm. For the males the average weight was 50kg, the lightest male student was 35kg and the heaviest was 60cm, giving a range of 25kg. In terms of height, the average height for a male student was 158.53cm, the shortest male student was 131cm and the tallest was 171cm tall, giving a range of 39cm. Conclusion On average the graph shows that the taller boys are heavier than the taller girls, and on average I would say my graphs show the boys to be heavier. My graphs show that the correlation is positive but they are both weak. Small boys are lighter in weight than small girls. Medium boys are heavier in weight than medium girls, with tall boys and tall girls. So my original prediction is correct, the majority of boys are heavier than girls.

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