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• Level: GCSE
• Subject: Maths
• Word count: 3823

# HYPOTHESIS: Boys at Mayfield School are Taller and Weigh more average in comparison to females

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Introduction

Mayfield School Mathematics Handling Data Coursework

Introduction

I have been assigned to complete a statistical investigation around the fictitious data of Mayfield High School. I will be using various techniques that I have recently studied and learnt and captured to produce a successful & efficient coursework. Alternating Statistical Methods will be used throughout this assignment to prove if my hypothesis is either correct or incorrect.

HYPOTHESIS: Boys at Mayfield School are Taller and Weigh more average in comparison to females

Planning

I will need the data of Mayfield High School between the Years of 7 to 11 and this is due to the fact for a wider sampling range and sufficient and unbiased results and uses many sampling methods to make my assignment unique and unbiased. The total number of students in the school is 1183.  Here is a Table that I have produced which contains the number of boys and girls in each year.

Two Way Tables

The Table Below is a two way table due to the fact there are two variables shown at the same time and helps view results and data conclusively.

 Year Group Number of Boys Number of Girls Total 7 151 130 281 8 145 124 269 9 118 142 260 10 106 113 219 11 84 70 154 TOTAL 604 579 1183

The variables for the sample are gender and age so I had to do separate samples for boys and girls and vary the amount of samples taken from each year to keep the sample unbiased and insufficient. This was done as the different year groups had different numbers of pupils and it would be unfair to take the same number of samples from each year group i.e. 5 samples out of 55 is be more than 5 samples out of 200 so stratified sampling will be helpful this is due to the fact the

number of student in each year and so there is less chance of unequal representation.

Middle

Burton

Prudence

1.59

52

8

Campbell

Julia

1.41

30

8

Kudray

Rebecca

1.54

52

8

Water

Rebecca

1.55

57

8

Sarah

1.53

59

8

Lillie

Vinande

1.47

46

9

Atkins

Patience

1.57

40

9

Bagnall

Vveronica

1.49

37

9

Dixon

Mary

1.49

52

9

Kelsey

Sannita

1.62

46

9

Mosler

Samantha

1.58

36

9

Weez

1.52

45

9

Kat

Charb

1.56

53

10

Bhatti

Hannah

1.72

56

10

Durst

Freda

1.75

60

10

Hall

Jane

1.51

36

10

Bengi

Brown

1.57

39

10

Elizabeth

Jap

1.61

71

10

Louise

King

1.57

36

11

Marta

Sana

1.52

45

11

Ratty

Louise

1.65

59

11

Peckeleka

Chantel

1.56

38

11

Opel

June

1.58

47

TALLY AND FREQUENCY CHART

Now that I have my data I will put them into frequency/tally tables to make it easier to read and it is a useful way of representing and helps view trends within my sampling that I have produced:

Boys Heights

 BOYS Height (cm) Tally Frequency 130≤h<149 IIII 4 150≤h<159 IIIIIII 7 160≤h<169 IIIIIIIIIIIII 13 170≤h<179 III 3 180≤h<195 III 3

A Pattern I have spotted in this particular Frequency/Tally table is that nearly 75 percent of boys are of the height between 150 to 170 from my sample and this shows me that students in my sample are rather tall and a steady size or above for their age group

Boys Weights

 BOYS Weight (kg) Tally Frequency 30≤w<45 IIIIIIII 8 46≤w<49 IIIIIIII 8 50≤w<59 IIIIIIIIII 10 60≤w<69 IIII 4

This Tally and Frequency table shows the boy’s weight and the spread of data are large and not as compact as the height whereas the height are rather scattered and vary.  This however notifies me that some of the students in my sample and tall for their age but weight are average in relationship to their height.

Girls Heights

 GIRLS Height (cm) Tally Frequency 130≤h<139 I 1 140≤h<149 IIIIIII 7 150≤h<159 IIIIIIIIIIIIIII 15 160≤h<169 IIIII 5 170≤h<190 II 2

This table shows me nearly 50 percent of students are between the height of 150-160 and there are not many student who excel over 180 cm tall which and there are also not many if any student with a height between 130 to 140 cm which shows me that the spread of data is compact which makes it easier to view trends and also it shows that there are not many irregularities in height in the student in my sample that I have taken.

Girls Weight

 GIRLS Weight (kg) Tally Frequency 30≤w<39 IIIIIIII 8 40≤w<49 IIIIIIIIIIII 12 50≤w<80 IIIIIIIIII 10

From this I have found that many girls weigh 40-49 kg and also the girl’s weigh in this particular region or slightly above on most occasions and this shows me that some girls may stop putting weight rapidly after a particular age.

COMPARISONS OF TALLY & FREQUENCY TABLE

I will now compare each of the tables of girls & boys height and then weight and view the differences in trends and if there are and mistakes or bias.

Height Comparison: From the Sample I have taken I have come to find that boys grow rapidly at a later age where as girls grow faster from an earlier age and stop at a particular age also. This is shown since I have found that 2 students are of a height between 130- 139 cm, which shows that my data may be misleading or there is a lapse in growth. Both Girls and Boys have average heights and are fairly balanced and of equal size. Although my Sample shows that boys on some occasion grow to above average height such as over 180 cm whereas in Girls this is rare and unique.

Weight Comparison: Most Boys and Girls weigh in the region of 40- 60 from my sample and I have found that not many girls are over the weight of 60 whereas in Males usually are borderline 60 or above when they come to the age of 16.

This Pie Chart shows the percentage of each year in the School and these help me form my sample and this form of representing data is efficient accurate and eye catching and help form divisions in my data.

Calculations:

Year 7:  281 Divided by 1183 Multiplied by 360

= 86 Degrees

Year 8:  269 Divided by 1183 Multiplied by 360

= 82 Degrees

Year 9:  260 Divided by 1183 Multiplied by 360

= 79 Degrees

Year 10:  219 Divided by 1183 Multiplied by 360

= 67 Degrees

Year 11:  154 Divided by 1183 Multiplied by 360

= 46 Degrees

Total 360 Degrees

MEAN AND MODE OF FREQUENCY DATA

I will now find the Mean, Median and Mode of the Frequency that I have found and this will be quick efficient and reliable and will help me gain evidence on whether boys are taller and weigh more in comparison to girls.

Mean of Girls and Boys Weight

 BOYS Weight (kg) Tally Frequency (f) Mid-point (x) fx 30≤w<39 IIIIIIII 8 37.5 300 40≤w<49 IIIIIIII 8 48 385 50≤w<59 IIIIIIIIIII 10 55 544.5 60≤w<70 IIII 4 65 257.8 TOTAL 30 1487.3

Conclusion

30

Cumulative Frequency & Box-and-Whisker Diagram

[Girls cumulative frequency & box-and-whisker of weight diagram]

From this I have found the spread on data efficient and on the following page I will compare my results from the cumulative frequency against both boys and girls height and weight and make a suitable conclusion from this representation.

Evaluation of Hypothesis

In my opinion I feel that I successfully completed and analyzed my hypothesis and I have gained a sufficient evidence to back up my theories. I would like to remind you that my main objective for this hypothesis was to find out whether I was correct or incorrect in my thinking that Boys at Mayfield School are taller and weigh more on average than the Girls at the same school. Within this aim I was also aiming to find whether there is a certain trend or relationship between the height and weight of the students that I have chosen to analyse and as I explained earlier due to the large number of students I was not possible to analyse all students so I gained a sufficient sample which I made as unbiased as possible.

Conclusion of Hypothesis

• The Histograms, frequency polygons proved that the results were more accurate and made more sense than that from the random sampling.
• There is a positive correlation between height and weight. In general tall people will weigh more than smaller people.
• In general boys tend to weigh more and be taller then girls.
• By doing stratified sampling, there were a fewer exceptional values caused by different year groups and therefore ages. I was bound to find irregularities within my data.
• The cumulative frequency curves confirm that boys have a more spread out range in weight, with more girls having smaller weights. In height, boys tend to be taller.
• In general the taller a person is, the more they will weigh.
• If I had taken larger samples my hypothesis may become more accurate.

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