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• Level: GCSE
• Subject: Maths
• Word count: 1184

# mayfield high school

Extracts from this document...

Introduction

Statistics coursework

The term "secondary data" means that the data was previously collected for others to study whereas primary or original data is data that has been gathered by the individual.

Some people tend to believe that using secondary data can be less expensive than gathering the data all over again. However, secondary data may not be suited for your particular purpose.

Here are some advantages and disadvantages of using primary and secondary data:

 disadvantages Advantages 1. The volume of primary data could be large. 2. Primary data is usually expensive. 3. If the data is not collected properly, then the individual might create false results. 1. Essential data2. Unbiased figures 3.Rrecords straight from the population Primary data 1. The research matter may not be the focus of the secondary data.2. There could a bias in  secondary data 1. Secondary data is usually accurate and well organised. 2. Saves time and money. Secondary data

Based on the secondary data collection that I was provided with, Mayfield high school is a mixed school with pupils in years 7, 8, 9, 10 and 11.

Middle

106+84=190

Total

Example

The stratified sample of year 11 boys would be 84/190 * 52: The number of boys in year 11 divided by the total number of boys in the whole of KS4 multiplied by the size of the sample that I want which is 52.

Now, I'm going to choose the students that I'm going to include in my sample.

Boys

Firstly, I have to find a random sample of 29 boys in year 10. To ensure my data is fair (unbiased) and representative of all boys in year 10 I'll give each boy in year 10 a number starting at 001 and finishing at 106 in year 10.

For year 10 I'm going to use a scientific calculator which is programmed to give me 3 digit numbers up to 106. I will use all the numbers to the left of the decimal place to select students (I will discard all the numbers after the decimal points and use only the ones before it).  Then I stop when 29 have been chosen. For the boys in year 11, the calculator will be programmed so that the numbers are from 001-084, I will then choose the first 23 students that come up, and this ensures the selection is random.

I repeated this process for the girls in year 10 and 11, but each time I changed the number my scientific calculator could go up to, e.g. for girls in year 11 my maximum number would become 86, because there is only 86 girls in year 11.

Once I had my Stratified random sample of 52 boys and 52 girls in KS4. I needed to find the heaviest boys and girls in my samples. So, I decided to plot my weights into a cumulative frequency in order to determine the median! Here are my cumulative frequency tables:

Boys

 Cumulative frequency Frequency Heights (m) 03926415152 0361715101 0 < x ≤3030 < x ≤ 4040 < x ≤ 50 50 < x ≤ 60 60 < x ≤ 7070 < x ≤ 8080 < x ≤ 90

Conclusion

< x  60. So, we wouldn't know their exact weight. In order for a more precise and accurate estimation of the median I will do a stem and leaf diagram and box plots for both of the 52 random samples. A stem and leaf diagram would be more accurate because unlike the cumulative frequency graph we don't group
 5     7 3 0     2     5     5     7     9 4 0     0     0     0     0     4     4     6     6     6     7     7     7     9 5 0     0     0     0     0    0     0     2     3     3     3     3     3     4     4    4     6     6     8 6 1     2     3     5     6     8 7 0     0     0     0     2 8

everything so no information is lost. Here are the 2 stem and leaf diagram (in order)

Boys in KS4

Lowest value= 35

Lower quartile= 50

Median= 60

Upper quartile= 66

Girls in KS4

 8 3 0     2     2     2     2     4     4     5     5     5     5     7     8     8     8     8     8 4 0     0     0     0     0     0     0     1     1     2     2     2     3     4     4     4     5     5     5     6 6     6     7     8     9     9     9 5 0     0     0     0     5     6     6 6

Lowest value= 38

Lower quartile= 47

Median= 51

Upper quartile= 56

Conclusion

My findings have proven that my hypothesis was actually correct which was “boys are heavier than girls". I compared both median for  girls and for boys, I found out that the median for girls is actually 10 kg less than the boy’s median which was 60 kg and for the girls: 60-10= 50 kg.

My box plots have also shown that, the weights of the boys are more spread than girls. So, this also proves that boys are heavier than girls

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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