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  • Level: GCSE
  • Subject: Maths
  • Word count: 3021

I am to find a relationship between height and weight for both male and females attending Mayfield High School in key stage three.

Extracts from this document...

Introduction

Mathematics Coursework                                          Handling data-Statistics

Mayfield High School

Aim

I am to find a relationship between height and weight for both male and females attending Mayfield High School in key stage three.

Plan

In this coursework I will be attempting to find out the average between height and weight of both genders, male and female. Out of 1200 students, I will pick 60 students at random, 30 boys and 30 girls from Mayfield High School.

I will then gather all the information required by randomly selecting 60 students out key stage three from Mayfield High School. The random selection will consist of 30 boys and 30 girls.

I will collect the random selection of students using a calculator. I will press shift and Ran _random) buttons which will give me a number between 1-0. Using this number I will multiply it by 1200 (i.e. the amount of students attending Mayfield high school). I will then round the number to nearest integer. This will then give me a random number. I will do this for both boys and girls.

After I have gathered all the information I will assemble the information into a tally and a frequency table. I will then have to find the mean, mode, median and range of height and weight of both boys and girls.

I will then put the information collected in to different graphs and tables, such as stem and leaf graphs, frequency polygons and histograms.

...read more.

Middle

50w<60

IIII I

6

60w<70

IIII

4

70w<80

0

80w<90

I

1

90w<100

0

The above is the height and weight which has been put into a frequency table for girls.

I could now make a statement to compare the weight of boys and girls.

‘The mode shows that boy’s weight in my sample was higher than girls. Therefore there will be fewer boys weighing from 20kg to 50kg’.

Graphs for Height & Weight

Since the data is grouped into class intervals, it also makes sense to record it in a stem and leaf diagram. This will make it easier to read off the median values. I will use the following information which is stem leaf diagrams and frequency density table.

Boys, Height:

Stem

Leaf

Frequency

1.20

5,6

2

1.30

0

1

1.40

8

1

1.50

0,2,2,2,3,4,5,5,5,5,5,7,7,8,9

15

1.60

1,3,4,5,6

5

1.70

0,2,5,8

4

1.80

1

1

1.90

0

1

I could analyse the data about height in exactly the same way as the weight because height and weight is continuous, so you need to record it on a histogram.

image00.png

I can compare continuous data by drawing the frequency polygons on the same graph.

image01.png

Boys, Weight:

Stem

Leaf

Frequency

20

0

30

2

1

40

0,0,1,2,2,2,3,4,5,5,7,7,8

13

50

0,0,2,2,2,3,4,5,5,6,9

11

60

1,2

2

70

2

1

80

5

1

90

0

1

I will be able to find the same information in the following histogram,

image11.png

I can compare continuous data by drawing the frequency polygons on the same graph.

image12.png

Girls, Height:

Stem

Leaf

Frequency

1.20

0

1

1.30

0

1

1.40

3

1

1.50

0,1,1,4,4,6,8,9,9

9

1.60

0,0,1,2,2,2,2,3,4,7

10

1.70

1,2,3,3,5,5,5

7

1.80

0

1

1.90

0

image13.png

I can compare continuous data by drawing the frequency polygons on the same graph.

image14.png

Girls, Weight:

Stem

Leaf

Frequency

20

0

30

6,8

2

40

0,0,0,0,2,2,2,4,4,4,5,6,7,7,8,8,9

17

50

0,0,4,4,5,8

6

60

2,4,5,5

4

70

0

80

0

1

90

0

image15.png

I can compare continuous data by drawing the frequency polygons on the same graph.

image16.png

I am now going to show the mean, mode median and range for each of the results of the boy’s and girl’s height and weight.

Height

Mean Height

I calculate the mean easily from the frequency tables.

Mean Height for boys = 161.0

Mean Height for girls = 162.3

Modal Height

I read the modes of the height for boys and girls from the frequency table.

Modal Height for boys = 1.50h<1.60

Modal Height for girls = 1.60h<1.70        

Median Height

There were 30 people in each sample, so the median will be halfway between the 15th and 16th values.

Median Height for boys = 1.615 (m)

Median Height for girls = 1.615 (m)

Range Height

The range of the height will show you how spread your data is

Range for Height for boys = 0.56(m)

Range for Height for girls = 0.60(m)        

Height

Mean

Mode

Median

Range

Boys

161

1.50h<1.60

1.615(m)

0.56(m)

Girls

162.3

1.60h<1.70

1.615(m)

0.60(m)

Weight

Mean Weight

I calculate the mean easily from the frequency tables.

Mean Weight for boys = 53.3(kg)

Mean Weight for girls = 50.3(kg)

Modal Weight

I read the modes of the height for boys and girls from the frequency table.

Modal Weight for boys = 40w<50

Modal Weight for girls = 40w<50

Median Weight

There were 30 people in each sample, so the median will be halfway between the 15th and 16th values.

Median Weight for boys = 50(kg)

Median Weight for girls = 47(kg)

Range Weight

The range of shoe sizes will show you how spread your data is

Range for Weight for boys = 52(kg)

Range for Weight for girls = 44(kg)

Weight

Mean

Mode

Median

Range

Boys

53.3 (kg)

40w<50

50kg)

52(kg)

Girls

50.3(kg)

40w<50

47(kg)

44(kg)

I now have more evidence to describe the difference in weight between boys and girls.

All three measures of average (mean, median and mode) are greater for boys than for girls. In conclusion, although there are a small number of boys who weighed light and girls who weighed heavy, the evidence suggests that in general, the weight for boys are greater than the weight for girls.

Extending the investigation

I can now extend the line of enquiry and give myself a hypothesis to test.

   In general it is that when the height increases so does the weight.

To test this hypothesis we need a new random sample of 30 students of any gender.

Second Sample

I have now collected a second sample to extend my line of investigation that there is a correlation with height and weight between boys and girls

Boys

Height

Weight

1.72

53

1.62

80

1.67

49

1.49

58

1.62

55

1.55

65

1.54

44

1.68

57

1.51

48

1.75

52

1.68

65

1.59

49

1.60

50

1.54

46

1.71

60

1.43

41

1.61

45

1.55

50

1.51

45

1.62

42

1.53

44

1.48

40

1.48

42

1.54

38

1.68

51

1.65

59

1.60

60

1.69

59

1.60

51

1.72

65

...read more.

Conclusion

The scatter graphs can be used to give reasonable estimates of weight and height. This can be done either by reading from the graph or by using equations of lines of best fit.The median weight for boys is higher than the median weight for girls.
  • I could have had a greater confidence in our results if I had taken larger samples or given some consideration to the ages of the students in the sample.
  • My predictions are based on general trends observed in the data. In both samples there were exceptional individuals whose results fell outside the general tend.

Conclusion:

Based on the evidence that I have found and my hypothesis I say that when the height increases so will the weight. And there are many restrictions that I took part in such as gender and age and both of these has helped me to conclude this project by saying the height and weight depend on gender and age, by this I am saying that the height and weight will increase depending on the gender and age.  

If I were to the investigation again I would consider the height and weight in more detail and have a greater sample of both genders.

I have proved that there is a positive correlation between the height and weight of both male and females.

Nahidur Rahman                 10o MA7

...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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