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Math Coursework-Mayfield High Data Handling

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Introduction

Isaac Wong 10H Math                                                                                   5/9/2007

Math Coursework-Mayfield High Data Handling

Introduction

In this investigation, I will be using the information provided in the Mayfield High database to carry out statistical analysis to prove my hypothesis. There are a total of 1183 students in the Mayfield High database, which is a secondary data source for my investigation. I will use some statistics skills such as standard deviation, scatter graphs, box and whisker diagrams, etc. I will carry out 3 investigations which will hopefully contribute to proving my main hypothesis. I will use 2 different year groups in this investigation, Year 8 and Year 10. I have chosen year 8 and year 10 because they represent the middle section of the school community and this is good because it will be very rare for the students to cease their body growth at that age.

Hypothesis:

The year group an individual belongs has the strongeffect on their weight (The higher the year group the student belongs in, the heavier he/she is).

Sub-hypothesizes:

  1. The weights of students in year 8 are relatively lighter than the ones in year 10 (main hypothesis)
  2. The weights of the genders are similarly distributed
  3. The taller the individual, the heavier s/he would be

The first sub-hypo is the one which will give me the main information for my main hypo. I think the first sub-hypo is correct because as a person gets older, their body will physically change and growth will continue to start, therefore their weight will continue to increase. Since the year group I am obtaining from are teenagers, it is their time for growth so growth should not have ceased.

The second sub-hypo may be

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Middle

Largest/Smallest Values- The largest and smallest values of the sample

Outlier seeker: There is a formula which will be very useful for me because I have box and whisker diagrams:

        ±1.5 x IQR (inter quartile range)

        Then the number I get, I will use that positive side of it to add on to the upper quartile, then any data above that sum will be considered as an outlier. I will use the negative side of the number to add on to the lower quartile, then any data below that sum will be considered as an outlier.

Sub-Hypothesis 2

Normal distribution:

I will present the data by drawing a frequency polygon. I used frequency polygon because it would be easy for me to analyze and see whether it is normally distributed (bell shaped curve). Normal distribution is determined by many different factors such as the mode, median and mean being equal as the distribution is symmetrical, however, there will definitely be some anomalies because there are growth spurts during teenage years. I will draw 2 graphs, one will be including anomalies and one will be without any obvious anomalies. I might also use skew to analyze the data.

Skew:

A normal distribution is a bell-shaped distribution of data where the mean, median and mode all coincide (if on a frequency polygon)

If there are extreme values towards the positive end of a distribution, the distribution is said to be positively skewed. In a positively skewed distribution, the mean is greater than the mode.

A negatively skewed distribution, on the other hand, has a mean which is less than the mode because of the presence of extreme values at the negative end of the distribution.

You can calculate skew by:        

Upper Quartile – Median = x

Median – Lower quartile = y

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Conclusion

Extensions could be made to my handling project. Although I have already included a lot of information that is sufficient to support my main hypothesis, it might not be a very reliable way. If I could extend, I would increase the range of year groups I use (as stated above), I will use the whole school. This might give another effect on my hypothesis. Since the range is so small, my hypothesis is correct but if I took a larger range of data, my hypothesis might be incorrect.

Some other hypothesizes that I might investigate on:

  • Relationship between what transport they ride and weight (to see whether most of the people with light weight do more exercise – walking/bike) However this might be limited to people who are near the school because what if students live very far away, it is not possible for them to actually walk to school or ride a bike. (if I wanted to investigate on weight again)
  • Relationship between height and their favourite sport (to see if there are certain sports that can boost their height because some sports like cross-country wouldn’t)
  • Relationship between year group and their IQ (since I already found a relationship between weight and year group, I will use this chance to find more relationship that might exists between year group and other things)
  • Relationship between weight and average number of hours watching TV (to see whether relatively heavier student spend more time watching TV, which might cause lack of exercise)

These questions will let me gain more understanding on relationship between our body and how what we do in our lives.

...read more.

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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