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• Level: GCSE
• Subject: Maths
• Word count: 3829

# An investigation into the heights and weights of students attending Mayfield High School.

Extracts from this document...

Introduction

An investigation into the heights and weights of students attending Mayfield High School. I have chosen Mayfield High School database to test the statement; "The taller you are, the heavier you are." I feel it will be better for me to use this database, provided by the exam board Edexcel, as it would take a large amount of time to design and produce my own questionnaires and gathering the information. There is a lot of information on the database that I will not need, such as, eye and hair colour, favourite T.V. show and so on, as I will not be needing this I will delete all information other than first, second and surnames, year group, gender and also height and weight. Once I have only the information needed I will arrange each pupil into their year group and gender groups, once I have completed this I will again arrange them into alphabetical order by the pupils surnames. When each pupil is in order I will number every one of them, students in KS3, year groups 7 - 9, will be numbered 1 - 813, inclusive, and pupils in KS4, year groups 10 and 11, will be numbered 1 - 370, inclusive. When reading through the height and weight columns on the database I realised some entries were wrong, or at least unconvincing, for example, a female pupil in year group 10 is being shown at 4.65m tall. As I think of height as feet and inches I will convert this below: * 1 inch = 2.5cm * 1 foot = 30cm Therefore: 4.65m = 465cm 465/30 = 15.5 feet or 15 foot, 6 inches 15 foot 6 inches is far too tall for a girl of this age, or any other age, so I believe this data is wrong. Now I have noticed different pieces of incorrect data, these could have been from typing errors or maybe someone just not paying attention whilst inputting the data. ...read more.

Middle

This will mean I can see all of the heights and compare the distributions. I hope it will show that the range of the boys' heights goes to taller values than that of the girls', though they will start at about the same height. I will also work out the quartiles and medians to show in the diagram. I shall use the formula Lower quartile = height once all of the heights have been put into ascending numerical order. "n" stands for the amount of data which is 75 for both boys and girls. Hence the lower quartile is = 19th height. The median will be the 19�2 = 38th height and the upper quartile the 19�3 = 57th height. On my stem and leaf diagram I shall format two columns at each end to show the frequency (f) and the cumulative frequency (C.F.). The cumulative frequency will give me a useful check to see that I have included all the data as the final entry should be 75. It will also be helpful when locating the quartiles and median; I will put numbers at the bottom of the diagram to help me with this as well. Later I will use the information from the stem and leaf diagram to draw whisker and box plots as these will make any differences between the boys' and girls' heights clearer, I will now put the stem and leaf diagram below. I can see that the distributions of both the boys' and the girls' heights are similar. Both have five heights between 1.40m and 1.49m but the boys have more heights above 1.80m than the girls' do. Indeed the boys' heights almost reach 1.90m whereas the girls' only just reach 1.80m. I think this is good support for my statement. Now I will look at the box plots. Once I had drawn my box plot I used the rule "whisker length < 1.5x the inter-quartile range, to check that I had no outliers in my data. ...read more.

Conclusion

However I do think I am very safe in concluding that at this stage the boys are taller than the girls. In year 11 something weird seems to have happened as although all of the boys' key values are more than the girls' with the exception of the shortest heights which are the same. The key values are all less than they are in year 10. The plots still indicate that the boys are taller than the girls but it is very strange that the students appear to have shrunk from year 10 to year 11. I am wondering if when the data was put in to the database the person doing it confused the two year groups. If this is the case then this person must be incompetent considering all the other errors in the data. Maybe there was more than one person inputting the data but the other idea I have is that Edexcel deliberately swapped the year groups data to confuse the user. However I think there is clear evidence that the boys do grow taller than the girls but the evidence that girls are taller in year 7 is inconclusive. The plots clearly show that both genders grow taller as they get older. The median height, which is unaffected by extreme values, is always greater for the boys than the girls indicating that the boys are taller in general. Also in years 10 and 11 the boys' medians are at the same height, weird. I think I have shown that my statement is at least half true though I believe that it would have been better if I had been able to follow the same group of boys and girls through all the 5 years of secondary education. Perhaps Edexcel could consider providing this data as they have had at least five years to collect the data given that the current data is based on an actual school in the North of England. ?? ?? ?? ?? Grace Ball. Page 1 of 12 ...read more.

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1.545 3.09 2 1.545 3.09 1.6 - 1.69 3 1.645 4.935 5 1.645 8.225 1.7 - 1.79 2 1.745 3.49 2 1.745 3.49 1.8 - 1.89 1 1.845 1.845 1 1.845 1.845 1.9 - 1.99 1 1.945 1.945 ?f = 9 ?fx = 15.305 ?f = 10 ?fx = 16.65

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