Data Handling

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Introduction:

What is my investigation about?

My second coursework for my Mathematics GCSE course is based on statistics. I have been provided with data for Mayfield High School. Mayfield is a fictitious High School but the data is based on a real school.

Mayfield has 1183 students from years 7 to 11. The data that is provided on each student includes, Name, Age, Year Group, IQ, Weight, Height, Hair Colour, Eye colour, Distance from home to school, usual method of travel to school, number of brothers and sisters, key stage 2 results in English, Mathematics and Science.

Year Group

Number of Boys

Number of Girls

Total

7

51

31

282

8

45

25

270

9

18

43

261

0

06

94

200

1

84

86

70

Total

604

579

183

This is the data given to us on the main question sheet. We had to go and retrieve the data for each pupil from the schools network in order for us to carry out the investigation.

There are a number of possible lines of enquiries that we could carry out. For example:

. the variations in hair colour

2. the variations in eye colour

3. the relationship between the hair colour and the eye colour

4. the distances travelled to school

5. the relationship between the height and the weight

6. the relationship between two sets of Key Stage 2 results

7. the relationship between IQ and Key Stage 2 results

8. the height to weight ratio in terms of body mass index

9. the relationship between the number of hours of TV watched and the IQ

0. the relationship between the gender and the IQ

After discussion with my teacher I have decided to carry out an investigation between the height and the weight of a sample of students. I was considering doing the average number of hours of TV watched per week and the IQ of each student. However, I could not continue with this as my results may have been affected as the results should also take into consideration what types of programs they watch. If someone watches a lot of television, but watches educational programs may have a higher IQ than someone who doesn't watch as much television but watches cartoons and other programs. This is why I could not continue with this enquiry. Therefore I chose the height vs. the weight.

I will look to establish a relationship between the height of the students and the weight of a randomly selected group of students. I will use various methods to present and analyse my results. I believe that the two sets of data will be directly proportional, the taller you are the more you weigh.

Height vs. Weight

Sample:

I have decided take a sample of 30 students from the school. I chose 30 as it divides exactly into 360 which are how many degrees there are in a circle therefore it will make it easier to draw a pie chart from the data I will have collected.

Now that I have decided to take 30, I will first take 30 students from the school to compare the boys against the girls. I will later in my investigation take each year in turn. I will take 30 students from the school but I will make have to make sure I minimise the possibility of having biased results and making sure that every student has equal opportunity in being selected.

Year Group

Number of Boys

Number of Girls

Total

7

51

31

282

8

45

25

270

9

18

43

261

0

06

94

200

1

84

86

70

Total

604

579

183

The total in the school is 1183 and there are 604 boys and 579 girls. To find a correct amount of boys and girls to take a sample of I have to find the ratio of how many girls to the total number of students there are and to multiply that number by 30 (sample size). In I will also do the same for the boys this will give me a fair number of how many boys and girls I will need to select which would consider the proportion of boys which is slightly higher than girls.

I will also need to consider the number of boys and girls to pick from each year. This is how I worked it out:

Year 7:

To determine how many boys and how many girls I will need to pick from year 7 I need to first find out how many boys and girls I need from year 7. To do this I will divide the total in year 7 by the total number of students.

==> 282/1183 = 0.24

==> 0.24 x 30 = 7.2 --> 7 (nearest whole number)

From the total of 30 students 7 will come from year 7. The next step is to find out how many boys and how many girls I will pick from year 7. I divided 7 by the total number of boys and girls then I multiplied that figure by the number of boys then by the number of girls.

Number of boys:

==> (7/282) x 151 = 3.748 --> 4 (nearest whole number)

This means that I will pick 4 boys from year 7. Again a slight degree of bias is introduced when I rounded up.

Number of girls:

==> (7/282) x 131 = 3.251 --> 3 (nearest whole number)

This means that I will pick 3 girls from year 7. Rounding the number has introduced bias again.

Year 8:

I will use the same method that I used for year 7 to generate the numbers of boys and girls from year 8.

==> 270/1183 = 0.23

==> 0.23 x 30 = 6.9 --> 7 (nearest whole number)

From year 8 I will also select 7 students.

Number of Boys:

==> (7/270) x 145 = 3.759 --> 4 (nearest whole number)

Number of girls:

==> (7/270) x 125 = 3.241 --> 3 (nearest whole number)

Year 9:

Total number of boys and girls from year 9:

==> 261/1183 = 0.22

==> 0.22 x 30 = 6.6 --> 7 (nearest whole number)

Number of Boys:

==> (7/261) x 118 = 3.165 --> 3 (nearest whole number)

Number of Girls:

==> (7/261) x 143 = 3.835 --> 4 (nearest whole number)

Year 10:

Total number of boys and girls from year 10:

==> 200/1183 = 0.17

==> 0.17 x 30 = 5.1 --> 5 (nearest whole number)

Number of Boys:

==> (5/200) x 106 = 2.65 --> 3 (nearest whole number)

Number of Girls:

==> (5/200) x 94 = 2.35 --> 2 (nearest whole number)

Year 11:

Total number of boys and girls from year 11:

==> 170/1183 = 0.14

==> 0.14 x 30 = 4.2 --> 4 (nearest whole number)

Number of Boys:

==> (4/170) x 84 = 1.976 --> 2 (nearest whole number)

Number of Girls:

==> (4/170) x 86 = 2.024 --> 2 (nearest whole number)

Now that I know how many boys and how many girls I need from each year, I need to sort the data out so that I can easily source it all out. I firstly sorted the data into each year group. I then sorted out the genders. I took each set of data, e.g. boys in year 7, into a separate sheet and assign each a new number. I then needed to generate a random number to pick the specific students I was going to use in my sample. I did this for each year group.

There are two ways of selecting random students according to their special digit assigned to them. I could put all the boys (604) names into a hat and pick out 15 at random and record the names. However, in this case this is not appropriate as there is far too many people and the hat would have to be pretty big. Instead I will use my calculator using the random number button on the calculator.

How to use the random number button:

Press [shift] [ran#] on the calculator and it will display a random number between 0 and 1. You then multiply this number by the number of possibilities there are i.e. in my investigation the random number generated would be multiplied by the number of boys (604) and that will give me a number which is the number of the boy to be picked. In almost 99% of the cases the number will have to be rounded which will introduce bias into this investigation. I will do this fifteen times each time recording the number generated and if by any chance the calculator produces the same number I will simply have to ignore it and record another one.

E.g. In a lottery draw, the total number is 49.

Generate a number between 0 and 1 --> 0.496

Multiply the number by 49 --> 24.304

Gives 24.304 round the number --> 24

24 is the number generated

These four simple steps are a much better and much more efficient way rather than choosing numbers / people from a hat. That is why I will use the random button on my calculator for this investigation quite often.

Picking the sample:

To pick the random students that I will use in my investigation I have decided to use the random number button on my calculator. First I will pick the required number of students from year 7.

Year 7:

From year 7 I will need to pick four boys and three girls. First the girls, I arranged them separately in a separate excel spread sheet.

Girls:

Each girl from year 7 was assigned a special ID number, in this case ranging from 1 to 131. I used the random button to generate thirty numbers.

==> I used the following formula to generate the numbers (Ran#) x 131

Number of tries

Random Number

Number (nearest whole number)

54.234

54

2

69.037

69

3

7.816

8

There was some rounding involved which would have introduced some bias into my results also some numbers were repeated which meant that I had to ignore it and redo it.

ID

Year Group

Surname

Forename 1

Forename 2

Gender

Height (m)

Weight (kg)

8

7

Carney

Esther

Female

.50

44

54

7

Higgins

Joanne

Alicia

Female

.50

45

69

7

Kelly

Jenifer

Fay

Female

.30

45

I took those three numbers I generated and I looked through my year 7 girls' sheet and I located the three and copied only the necessary information.

Boys:

I did the same for the boys as I had done to the girls. I first sorted the boys in year 7 in a separate spread sheet and assigned each boy with a special ID ranging from 1 to 151. I then used the random number button generate four ID's and those will be the boys I select in my sample.

==> This is the formula I used to generate the numbers below (Ran#) x 151

Number of Tries

Random Number

Number (nearest whole number)

18.988

19

2

20.385

20

3

7.214

7

4

97.093

97

There was some rounding involved which would have introduced some bias into my results also some numbers were repeated which meant that I had to ignore it and redo it.

I then took these numbers and sourced out the students from my data.

ID

Year Group

Surname

Forename 1

Forename 2

Gender

Height (m)

Weight (kg)

7

7

Bingh

Daniel

Male

.56

35

20

7

Bond

James

Sean

Male

.47

50

97

7

McKracken

Phil

Peter

Male

.58

48

19

7

Sharpe

Billy

Richard

Male

.43

41

I used the same method for each year right the way through from the remaining, Year 8 to Year 11 for both the girls and the boys.

Year 8:

From year 8 I need four boys and three girls.

Girls:

==> (Ran#) x 125

Number of Tries

Random Number

Number (nearest whole number)

00.625

01

2

66.875

67

3

39.75
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40

There was some rounding involved which would have introduced some bias into my results also some numbers were repeated which meant that I had to ignore it and redo it.

ID

Year Group

Surname

Forename 1

Forename 2

Gender

Height (m)

Weight (kg)

40

8

Dom

Kate

Female

.59

50

67

8

Indera

Emily

Sophia

Female

.52

45

01

8

Neelam

Kate

Female

.45

81

...

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