• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
• Level: GCSE
• Subject: Maths
• Word count: 2324

# Investigating the relationship between height and weight.

Extracts from this document...

Introduction

## Hypothesis

In year 7 females are generally taller than males but males are heavier in weight. By year 11 males are taller and heavier than girls.

## Introduction

I will be investigating the relationship between height and weight; I will try to prove the above hypothesis. As my hypothesis suggests I will be using year 7 male and females and year 11 males and females from Mayfield High School.

The information I already know is that females tend to grow sooner and faster than boys their growing rate slows down while males continue to grow on average to a taller height and their weight is also heavier regardless of height.

To begin with I will have to look at the data provided on the Mayfield High School database. Investigating the database I have filtered all necessary data and separated it from the initial data. The form of sampling that I will be using is stratified sampling. This is a good method to avoid bias results.

In year 7 there are a total number of:   282        students

In year 11 there are a total number of: 170        students

Total:  452        students

I will be taking a sample of 100 students for in my investigation:

 Year group Students Number of students sampling-100 7 282 282/452 x 100 = 62.38938 = 62 11 170 170/452 x 100 = 37.61062 = 38

I now know that I need 62 people from year 7 and 38 from year 11. Now I need to find out how many male and female students to make this a fair test.

 Year Group Sex Number of students sampling from each gender 7 Male 151/282 x 62 = 33.19858 = 33 7 Female 131/282 x 38 = 28.80142 = 29 11 Male 84/170 x 38 = 18.77647 = 19 11 Female 86/170 x 38 = 19.22353 = 19

Middle

35  h < 40

7

10

40  h < 45

7

17

45  h < 50

13

30

50  h < 55

0

30

55  h < 60

1

31

60  h < 65

1

32

65  h < 70

1

33

 Weight- Year 7 females Frequency Cumulative Frequency 30 ≤ h < 35 1 1 35 ≤ h < 40 2 3 40 ≤ h < 45 16 19 54 ≤ h < 50 7 26 50 ≤ h < 55 3 29 55 ≤ h < 60 1 30

Conclusion from cumulative frequency graphs (previous page):

In the cumulative frequency graphs for height I can see that the males and females graphs are quite parallel. I calculated the interquartile range from these graphs and results show that the interquartile range for year 7 males is 152.2m and females is 150.75m, the smallest range indicates that much of the data is concentrated about the median. This shows that year 7 males’ height varies a lot.

In the Cumulative Frequency graphs for weight I cans see that the females have a tighter range, most of the females are in the middle half of the graph. There is more variation on the males weight; again this shows that the female’s interquartile range is smaller.

## Box Plots

I have decided to draw box plots to show the interquartile ranges better:

Conclusion from box plots (next page):

The cumulative frequency graph representing height shows us that year 7 females have a higher median, and this tells us that on average females are taller than males.

The females also have a larger gap between that upper quartile and lower quartile ranges this shows that they have more varied height range, whilst the males have a smaller gap. The box plot for weight shows that the interquartile range is bigger for the male students. The median for both the males and females is very similar this shows that males averagely weigh the same amount as the females, although they have a bigger upper quartile so they have a more varied scale.

## Standard Deviation

Using the Excel formula =STDEV (D4:D33) which was given to us by our maths teacher, I calculated the standard deviation of my data.

For year 7 males height the standard deviation is:0.085cm to 3 decimal places.

For year 7 females height the standard deviation is:  0.106cm to 3 decimal places.

The females have a higher standard deviation shows the spread of the values from their mean, therefore the less reliable the data. The standard deviation shows that the males data was closer together and more accurate.

For year 7 boys weight the standard deviation is:   7.79kg to 3 decimal places.

For year 7 boys the standard deviation is:               5.47kg to 3 decimal places.

The males again have a lower standard deviation than the females it is fair to say that my random sampling of males was more reliable than my random sample of female.

#### Year 11

Scatter graphs

From these graphs I can see that the females have poor correlation, the males have better correlation. In both of the graphs the majority of students are in the 1.4 to 2 ranges though the males are more spread out.

The weight scatter graph shows that the females are more close together, widely held within the boundaries of 40 and 60 kg. This scatter graph is even more compact than the year 7 results. The male students are a lot more varied. As I have stated in my prediction the males are heavier by year 11.

I have again produced frequency tables so that I could draw my cumulative frequency graphs to show the following data:

## Frequency graphs

 Height- Year 11 males Frequency Cumulative Frequency 150 ≤ h < 155 2 2 155 ≤ h < 160 1 3 160 ≤ h < 165 1 4 165 ≤ h < 170 2 6 170  ≤ h < 175 1 7 175  ≤ h < 180 5 12 180  ≤ h < 185 4 16 185  ≤ h < 190 0 16 190  ≤ h < 195 0 16 195  ≤ h < 200 3 19

Conclusion

Another reason for their height is that boys grow faster than girls at their peak rate. They grow faster because they have higher levels of testosterone in their bloodstream than girls. The testicles release more and more testosterone into the blood stream as they mature. During puberty an average boy's production of testosterone will increase tenfold.’

My hypothesis proved this fact, and I have found that there is a relationship between age, height and weight. This connection can be seen through my graphs. I noticed in my graphs that the females always had a tighter distribution then the males; this shows that males aged between 11-16 vary a lot in terms of height and weight.

Criticisms

In the process of proving my hypothesis I used standard deviation to find out how far my data was from the mean, showing the more accurate data. I could have improved this point by having more people in my sample and this should bring the standard deviation down because there would be more samples which should in theory follow the mean.                                                                                        My scatter graphs could be improved because the points were not very clear and they were too small to interpret. Another improvement that I could have done was to produce all my graphs on the computer so that I have accurate results, but I could not do this, as I did not know how to draw more complex graphs on the computer.

Evaluation

Overall my investigation went quite well because I proved my hypothesis, showing my mathematical skills on; stratified and random sampling, producing graphs and using Excel for my scatter graphs and standard deviation.

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.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

1. ## Mayfield. HYPOTHESIS 1: Boys at Mayfield School are Taller and Weigh more on ...

Tally Frequency (f) Mid-point(x) fx 30?w<40 IIIII 5 35 140 40?w<50 IIIIIIII 8 45 360 50?w<60 IIIIII 6 55 330 60?w<70 I 1 65 65 70?w<80 0 75 0 TOTAL 20 895 Mean = 895 divided by 20 = 44.75 rounded off to 45 kg for GIRLS Mean of Boys and Girls Height BOYS Height (cm)

2. ## Conduct an investigation comparing height and weight from pupils in Mayfield School.

0,2,4,5,8 0 180 0 190 0 Total 25 Boys Girls Stem Leaf Freq. 130 0 140 0 150 0,2,5,7,8 5 160 2,2,3,5,5,7,8,8,8,9 10 170 2,3,7,9 4 180 1,2,4 3 190 2,4,6 3 Total 25 Heights (cm) Mean Modal Class Interval Median Range Boys 170 160 - 170 168 46 Girls

1. ## Maths Statistics Coursework - relationship between the weight and height

Female 15 1.58 45 10 Female 15 1.65 45 10 Female 15 1.52 47 11 Female 16 1.65 54 11 Female 16 1.69 42 11 Female 16 1.70 54 11 Female 15 1.67 48 Year Group Gender Age (years) Height (m)

2. ## Determine the relationship between the range of the jump achieved by the ski jumper ...

At this stage I started thinking why didn't it cross at the origin? This question was clarified, and found that some factors might have affected the range while doing the experiment.

1. ## COMPARE THE WAY IN WHICH MEN AND WOMEN PRODUCE AND RELEASE GAMETES

The other cells, the smaller polar bodies, do not develop, and disintegrate or divide again. The polar bodies serve to discard unnecessary chromosomes while retaining most of the cytoplasm in the egg.

2. ## I will be testing the following hypothesis in my pilot study: ...

girls, compared to boys, but because the boys will have started to go through puberty, the spread of the boys' data will increase. * I believe that in year 9 the height and weight will start be about the same.

1. ## Guesstiamte - investigating whether men or women between the ages of 15-25 are better ...

22.2% of men overestimated, almost a quarter. 38.9% of men guessed correctly. 38.9% of men underestimated. 33.3% of women underestimated. 66.7% of women guessed correctly. The frequency polygon for the angle estimates show that two women underestimated and two men underestimated. Two women guessed correctly and two men guessed correctly.

2. ## maths coursework-Height and Weight of Pupils and other Mayfield High School investigations

Median height for girls = 160+161 = 160.5 = 161 cm 2 Range of height This shows me how spread my data for height is for girls and boys. Range of height for boys = 192-136 = 56 cm Range of height for girls = 200-140 = 60 cm I will now summarise my results into a clear table.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work