A statistical inquiry on the relationship between height and weight based upon the students of Mayfield High School.
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I have decided to develop a statistical inquiry on the relationship between height and weight based upon the students of Mayfield High School. My hypothesis is that the taller the person the heavier they would be and that the male sex is heavier and taller than the female sex. I state this because I think that girls in a secondary school are more likely to be weight-conscious and boys are usually taller after going through puberty comparatively to girls. I also think that the boys will be spread apart more in terms of height and weight than girls. This is because recent studies have proven that the female sex anatomically matures more after the age of sixteen whereas a male body changes from puberty onwards. To start my investigation I need an unbiased representation of the entire Mayfield High School. I first need to stratify the data for my sample, proportionate to the size of the year and the different genders. I will take 40 pupils as my sample size as this number would provide a defined sense of accuracy for the representation of the various year groups and genders. The data for the 40 pupils would also be easier to manipulate than with a much larger sample. To obtain the proportion of my sample for each year I will divide the number of students in each year by the total number of pupils and multiply it by my total sample as in Example 1. Example 1. Total Year 7 Pupils = 282 282/1183 X 40 = 9.5 Total number of Pupils = 1183 The sample of Year 7 boys in my survey Sample size = 40 will be 10.
I have decided to sort my data through data capture sheet also known as a tally chart for both height and weight as this will allow me to construct a histogram. Since the data is not discrete the frequencies are distributed into class intervals. Height (m) Tally Frequency 1.3 ? h < 1.4 1 1.4 ? h < 1.5 0 1.5 ? h < 1.6 14 1.6 ? h < 1.7 12 1.7 ? h < 1.8 9 1.8 ? h < 1.9 2 1.9 ? h < 2.0 2 Weight (kg) Tally Frequency 30 ? w < 40 3 40 ? w < 50 16 50 ? w < 60 10 60 ? w < 70 7 70 ? w < 80 2 80 ? w < 90 2 The tally charts above show us the mode, or the most recurrent class interval. For height the most common class interval is 1.5 ? h < 1.6. For weight the mode is 40 ? w < 50. The measurements are in meters and kilograms respectively. We can also now calculate the mean and find the median amongst our tally charts. The median is the class interval in which the average of the 20th and 21st number is present. Median of Height: 1.6 ? h < 1.7 Median of Weight: 50 ? w < 60 Mean of Heights: (1.64+1.51+1.68+1.53+1.6+1.57+1.56+1.58+1.52+1.61+1.32+1.9+1.73+1.541.6+1.61+1.72+1.5+1.73+1.62+1.5+1.5+1.7+1.52+1.58+1.6+1.65+1.62+1.7+1.75+1.77+1.89+1.55+1.67+1.79+1.91+1.75+1.83+1.52+1.65) / 40 = 1.64m is the mean height for the pupils of Mayfield High School. = 1.6 ? h < 1.7 is the class interval in which the mean for height lies in. Mean of Weights: (50+45+40+48+60+45+57+43+43+52+35+60+59+52+74+48+50+45+62+40+70+39+47+52+50+48+45+45+60+57+80+64+48+48+45+82+68+60+38+52) / 40 =52.65kg / 53kg is the mean weight for the pupils of Mayfield high School.
The scatter diagrams show that as the height of a person increases their weight increases as well (and vice-versa). The scatter diagram shows a strong positive correlation. However there are a few exceptions. These exceptions could be people who are big-boned and so weigh more than their weight, or people from a different country so genetic characteristics from that particular region could have influenced their height or weight in comparison with the rest of the pupils. To show a stronger correlation I will construct separate graphs for boys and girls. The scatter diagrams again show that the distribution of the Boys is spread apart whereas the distribution of the Girls is concentrated. The two lines of best fit can be used to find a formula which can predict the weight of a pupil if given the height and vice versa. In conclusion I have shown that the heights of people increased as their weights did (and vice-versa). I had said in my hypothesis that "boys will be spread apart more in terms of height and weight than girls." I have shown this at least within my own sample that Boys are taller and weigh more than girls and are more diverse in their heights and weights than girls. There may be some inaccuracies due to incorrect measuring or a few extreme cases that influence the entire sample. This extreme cases could be due to a variety of reasons some of which have stated along this coursework. To further extend this investigation I could have analyzed the data from different year groups as well as from different genders. I could also have found out the formula that would allow us to estimate the height of a boy / girl if given the weight and vice-versa.
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