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• Level: GCSE
• Subject: Maths
• Word count: 2729

# Relationship between height and weight

Extracts from this document...

Introduction

GCSE MATHS COURSEWORK

Aim: My aim in this coursework is to find out about the relationship                                           between the height and weight. I will also find out if the Boys weigh more and are taller than the girls and vice versa. I will also find out what is the best category for height and weight that everyone will fit in. I will also find the mean median and range for all of them.

Hypothesis: My hypothesis is that the more taller you are the more you weigh, also that the girls will probably weigh more because I don’t think they will do as much exercise as the boys do, but I also know that the girls will be taller because scientists say that girls are taller than boys when they are younger. I would like to find out if that is true.

Method: I will take a random sample of boys and girls, I will do this by using the calculator using the buttons: SHIFT + RAND# =

Data representation: I will represent my data in many forms such as: Scatter graph, Pie charts, histograms, cumulative frequency, graph bar charts, table, etc.

 No. Gender Height (m) Weight (kg) 1 M 1.63 60 2 M 1.75 45 3 F 1.83 60 4 F 1.67 52 5 M 1.8 49 6 M 1.66 70 7 M 1.9 70 8 F 1.6 54 9 F 1.52 45 10 F 1.62 56 11 F 1.55 36 12 F 1.8 60 13 F 1.67 66 14 M 1.67 66 15 M 1.7 57 16 F 1.6 56 17 M 1.71 57 18 M 1.52 60 19 M 1.66 66 20 M 1.6 59 21 F 1.63 44 22 F 1.63 44 23 F 1.4 45 24 F 1.73 51 25 M 1.8 60 26 F 1.72 51 27 M 1.72 63 28 M 1.75 56 29 M 1.91 82 30 M 1.77 57 31 F 1.68 54 32 F 1.73 64 33 F 1.73 50 34 F 1.63 47 35 F 1.72 56 36 F 1.62 48 37 F 1.56 50 38 M 1.8 60 39 M 1.55 64 40 F 1.75 57 41 M 1.63 50 42 M 1.86 56 43 F 1.73 51 44 M 1.81 72 45 M 1.75 60 46 M 1.72 58 47 F 1.62 48 48 M 1.54 57 49 M 1.54 66 50 F 1.69 51

This is showing the data set.

I will choose a random set of 10 boys and 10 girls, to do this I can do it in different ways such as in the calculator press SHIFT + RAND# =, or I can do it another way by writing every pupil number in the hat and randomly placing my hand and choosing 10 boys and 10 girls

I had chosen the calculator version.

MODE, MEAN, RANGE

I will first find the mean median and range for height and weight; I will do this because I want to see the best fit that average people should be in.

I will find the average by creating a frequency table:

 Weight Frequency 36-40 1 41-45 3 46-50 1 51-55 2 56-60 8 61-65 1 66-70 4

Now that I have done this, I will now create a pie chart to help me find the mode.

As you can see by the pie chart, the mode is 56-60 so the average people should be/are between 50-60 kg.

I will now find the mean mode and range for weight:

To do this I will create another frequency table.

 Weight Frequency Midpoint(x) FxX 36-40 1 36+40÷2=38 1×38=38 41-45 3 41+45÷2=43 3×43=129 46-50 1 46+50÷2=48 1×48=48 51-55 2 51+55÷2=53 2×53=106 56-60 8 56+60÷2=58 8×58=464 61-65 1 61+65÷2=63 1×63=63 66-70 4 66+70÷2=68 4×68=272 Total=20 Total=1,120

Middle

4

1.66-1.75

8

1.76-.185

2

1.86-1.95

1

Now I will create my pie chart. I will create a pie chart so that I can show the information that I have written in the Frequency table.

As you can see by the pie chart, the mode is 1.66-1.75 so the average people should be is between 1.66-1.75 m.

I will now find the mean mode and range for Height:

To do this I will create another frequency table.

 Height Frequency Midpoint(x) FxX 1.45-1.55 3 1.5 4.5 1.56-1.65 5 1.605 8.025 1.66-1.75 8 1.705 13.64 1.76-1.85 3 1.805 5.415 1.86-1.95 1 1.905 1.905 Total=20 Total=33.485

Mean= to find it as a formula = FXX÷F

Mean=33.485÷20

Mean=1.67425 or 1.6 as normal round up.

I have now worked out my mean. I worked it out by finding my midpoint; I found my midpoint by adding up the ranges and divided it by 2, I then multiplied my midpoint to my frequency. I added all the totals up and divided it by the frequency total.

I will now find my mode:

Mode= the range with the highest frequency.

Mode= 1.66-1.75

I have worked out my mode, now I will find out my range.

Range= the highest value takeaway the lowest.

Range= 1.9-1.52

Range= 0.38

I now know the mean mode and range for height.

I will now create a cumulative frequency graph for both height and weight.

Cumulative Frequency graphs

I will now create a tally for my cumulative frequency graph.

 Height Frequency C.F 1.45-1.55 3 3 1.56-1.65 5 8 1.66-1.75 8 16 1.76-.185 3 19 1.86-1.95 1 20

I find out by C.F by adding the first frequency to the next, until I reach the end this will give me my cumulative frequency.

I have now completed my tally chart for my cumulative frequency. I found out my cumulative frequency by adding up the previous frequency.

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile. The reason why I am creating a cumulative frequency graph is so that I can work out my upper quartile, median, lower quartile and inter quartile

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

Inter Quartile=

.

I will now do the same for Weight:

 Weight Frequency C.F 36-40 1 1 41-45 3 4 46-50 1 5 51-55 2 7 56-60 8 15 61-65 1 16 66-70 4 20

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile.

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

Inter Quartile=

Histogram:

I am going to create tally charts to help me find the frequency density

 Weight Frequency F.D 36-40 1 0.25 41-45 3 0.75 46-50 1 0.25 51-55 2 0.5 56-60 8 2 61-65 1 0.25 66-70 4 1

I have found the frequency densities; I will create a histogram to compare later on.

I will now do the same for height:

 Height Frequency C.F 1.45-1.55 3 30 1.56-1.65 5 55.555 1.66-1.75 8 88.888 1.76-.185 3 33.333 1.86-1.95 1 11.111

I will now create a histogram for the height. I will do a histogram so that the information shown is more clearly.

Now I will create a scatter graph for both height and weight, I want to do this because I want to see the line of best fit, this is were the students should really be at.

Scatter Graph:

To be able to create a scatter graph I will need to make frequency table:

 Height (m) Weight (kg) 1.63 60 m 1.75 45 m 1.83 60 f 1.67 52 f 1.8 49 m 1.66 70 m 1.9 70 m 1.6 54 f 1.52 45 f 1.62 56 f 1.55 36 f 1.8 60 f 1.67 61 f 1.67 66 m 1.7 57 m 1.6 56 f 1.71 57 m 1.52 60 m 1.66 66 m 1.63 44 f

I have now created the table, now I will plot this to a scatter graph:

As you can see there is a high collerence, most people go above the line of best fit.

Difference between boys and girls:

In this section I will try to find the difference between boys and girls.

Who weighs more?

I will now try and find out who weighs more by creating a pie charts, histogram and line graph.

To do this I will need to create a frequency table if I want create line graph.

 Weight Boys frequency Girls frequency 36-40 0 1 41-45 1 2 46-50 1 0 51-55 0 2 56-60 4 4 61-65 0 1 66-70 4 0

Conclusion

1

2

1.86-1.95

1

0

Now that I have done this, I will plot these in a histogram:

Now I will make a Cumulative frequency graph for boys and girls Height:

Boys, first I will create the boys one and to do this I need to create a cumulative frequency table:

 Height Boys frequency C.F 1.45-1.55 1 1 1.56-1.65 1 2 1.66-1.75 6 8 1.76-.185 1 9 1.86-1.95 1 10

Now I will plot this to a cumulative frequency graph:

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile.

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

Now I will create one for girls, to-do this I will need to create another frequency table:

 Height Girls frequency C.F 1.45-1.55 2 2 1.56-1.65 4 6 1.66-1.75 2 8 1.76-.185 2 10 1.86-1.95 0 10

.

I will now create my cumulative frequency graph, I will use the graph to find out the median, upper quartile, lower quartile and inter quartile

I have worked out the following:

UQ=

Median=

LQ=

I will now find out the Inter Quartile:

Inter Quartile= Difference between Upper Quartile and Lower Quartile

Inter Quartile=

My final conclusion for the difference between girls and boys Height is that:

My hypothesis is wrong and that I never expected the boys to actually be taller.

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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