Statistics Coursework
Introduction
I will be examining a fictional school entitled Clementswood High School also recognised as Mayfield High School; however the information collected is real data from real students. Altogether there are 5 year groups ranging from year 7 to year 11 and 1183 students in total. This is secondary data from the Edexcel website which I will use for my investigation. Secondary data also known as desk research is when you find data through another source and do not conduct it yourself. I will be investigating the relationship between the gender of students in KS3 and KS4 and the height and weight. The data I will use is secondary which I acquired from the edexcel website.
An advantage of secondary data is that it is quick and easy to access which saves time than having to gather it yourself. On the other hand it can sometimes be unreliable and inaccurate which affects the results which are a drawback. Secondary data can also be out of date, which is a negative aspect, as it is better to have the latest data in order to carry out an accurate and successful investigation.
Primary data is information conducted by yourself, which is quite advantageous as it is more reliable than secondary research as the information is acquired by you and you get the answers to the exact questions that you carry out. However it is time consuming which is a drawback and also the more expensive to carry out which is a disadvantage.
In my investigation I will examine the relationship between height, weight, age and gender so this is my line of enquiry. I have chosen to inspect this because it is said that the heavier the weight the shorter the person and the older you are the taller you are which is why I am investigating if this is true. If there are any erroneous results or outliers, I will replace them because they will affect the final outcome and give me inaccurate results.
Plan
I will first conduct a pilot study to see if there is a purpose of doing this investigation and will create a scatter diagram and check if there is any correlation. If so, then there is a point in doing the investigation but if no correlation then the line of inquiry will have to be altered. Some advantages of the primary data collected, is that it is reliable and quite recent which will influence in the accuracy of the results.
Secondly, a hypothesis will be made which is a prediction I will make and then later seen if it is correct or incorrect.
I will then take a random sample because I cannot select hundreds of people so this sampling method will help me choose without being bias and will conduct a stratified sample so that I can have the right amount of students in proportion to the year group.
Once I have done this, I will then see if there are any erroneous results (outliers) and will replace those pupils with others by again using random sampling. Outliers are results that either fall under the minimum or over the maximum boundary.
Scatter diagrams will be made all the groups of age and gender and will be compared as well as correlation between the graphs will be compared to see who has stronger and weaker correlation.
The mode, median and range will be worked out and then will be compared and then I will also comment on how spread out the data is.
The mean of the grouped data will also be found as well as the modal class. I will construct cumulative frequency graphs and box plots. I will comment on the box plots and will talk about how strong or weak the correlation is.

Pilot Study
This is the pilot study which I have used in order to see whether there is an aim to carry the investigation any further. Here are the results which display the height and weight of the people in my class who were part of the study. My hypothesis is that the taller you are the heavier you are. Gender | Height (m) | Weight (kg) | M | 1.68 | 43 | M | 1.67 | 72 | F | 1.58 | 50 | F | 1.6 | 50 | M | 1.75 | 56 | M | 1.69 | 60 | F | 1.59 | 70 | M | 1.81 | 57 | M | 1.76 | 69 | F | 1.63 | 65 | F | 1.49 | 57 | M | 1.81 | 83 | F | 1.6 | 47 | F | 1.64 | 47 | F | 1.69 | 56 | F | 1.61 | 47 | F | 1.63 | 43 | M | 1.77 | 60 | F | 1.6 | 74 | F | 1.58 | 48 | M | 1.78 | 58 | M | 1.7 4 | 52 | F | 1.61 | 75 | M | 1.87 | 103 | F | 1.56 | 55 |

Here are the results plotted on the graph which show there is positive strong correlation so it is worth carrying on with the investigation. As you can also see the three tallest pupils are the heaviest. A disadvantage of the primary data collected is that human error could have occurred whilst measuring, especially the heights. The accuracy of the results may have suffered as a result of this.

Hypothesis
For my hypothesis I predict that the taller the person, the heavier they weigh. I also predict males will weigh more than females. However I think that females will be taller than males.
A random sample is when every person has a fair chance of being chosen so biasness is avoided. I did this by typing a formula in Edexcel and then dragged it down for the other random numbers.

Sampling methods
A census is when you survey every person in a population. This is often very costly in terms of money and is time consuming as every person in the population has to be included. To counter this problem samples are taken from populations. A sample must be large enough to give a good representation of the population and therefore accurate results but small enough to be manageable. Here are some sampling methods.

RANDOM SAMPLING
Random sampling ensures that everyone in the project has and equal chance of being selected. This prevents biasness in the survey or project. You could do this by numbering names and if a sample size included 100 people, then 100 numbers could be randomly generated by computer or the numbers could also be picked out of a hat. The numbers are then matched to the names. An advantage is that it is simple and easy to do especially when small populations are involved. This is not so good and time consuming to do for large populations.

SYSTEMATIC SAMPLING

Systematic sampling works by choosing in intervals. This technique could also be used when questioning people in a sample survey. An advantage of systematic sampling is that it is easier to select one random number and then every ‘5th’ member on the list for example, than to select as many random numbers as the sample size. Another advantage is that it gives a good spread across the population.

STRATIFIED SAMPLING

In stratified sampling, the population is divided into groups and a sample is taken from within these strata. Stratified sampling is most useful when you want to observe and see relationships like in a survey. An important aspect of this sample is that it is used to choose more of one group than another. So in a small group you may take a small sample whereas in a large group you may take a bigger sample.

CLUSTER SAMPLING
Cluster sampling divides the population into clusters (groups). Some clusters are chosen randomly to represent the population. An advantage of this sampling method is that it is less time consuming and more cost efficient as there are less people involved. However a disadvantage is that the sample is more localised in few clusters sometimes not giving reliable results.

Main Study
As there are too many students for me to carry this investigation on, so I will be using the program Microsoft Excel to take a random sample of students and then be taking a stratified sample of the students in each year group, males and females. I will be using 10% of the data as it is a convenient amount of people to study and will give me reliable results.
Below I have displayed the sample taken of each male and female in each year group using stratified sampling.
No. of each group in sample =
Year 7 students: 282 x 118 ÷1183 = 28 students
No. of Year 7 boys = x 118 = 15 students
No. of Year 7 girls = x 118 = 13 students
No. of Year 8 boys = x 118 = 14 students
No. of Year 8 girls = x 118 = 12 students
No. of Year 9 boys = x 118 = 12 students
No. of Year 9 girls = x 118 = 14 students
No. of Year 10 boys = x 118 = 11 students
No. of Year 10 girls = x 118 = 9 students
No. of Year 11 boys = x 118 = 9 students
No. of Year 11 girls = x 118 = 9 students

Total Sample Size = 118 Here is the lower quartile, median, upper quartile and the interquartile range on all the gender age groups. KS4 Females Height Lower Quartile: 1.585 Median: 1.705 Upper Quartile: 1.7375 Inter-quartile range: 0.1525
1.5*IQR: 0.22875

KS4 Males Height Lower Quartile: 1.615 Median: 1.715 Upper Quartile: 1.8 Inter-quartile range: 0.185
1.5*IQR: 0.2775 KS3 Females Height Lower Quartile: 1.51 Median: 1.57 Upper Quartile: 1.63 Inter-quartile range: 0.12 1.5*IQR: 0.18 KS3 Males Height Lower Quartile: 1.52 Median: 1.57 Upper Quartile: 1.65 Inter-quartile range: 0.13
1.5*IQR: 0.195 Out of the heights the biggest median and also IQR was KS4 males height but the data was also more spread. This was followed by KS4 females height whose data was also quite spread and median was second highest, which supports the claim that the older you are the taller you are. Both KS3 males and females had the same median but KS3 females height marginally was the most consistent out of all the data. KS3 males also had very consistent data.

KS4 Females Weight Lower Quartile: 42.75 Median: 50 Upper Quartile: 51.75 Inter-quartile range: 9 1.5*IQR: 13.5 KS4 Males Weight Lower Quartile: 57.75 Median: 63 Upper Quartile: 72 Inter-quartile range: 14.25
1.5*IQR: 21.375 KS3 Females Weight Lower Quartile: 41.5 Median: 48 Upper Quartile: 52 Inter-quartile range: 10.5
1.5*IQR: 15.75 KS3 Males Weight Lower Quartile: 45 Median: 49 Upper Quartile: 54 Inter-quartile range: 9
1.5*IQR: 13.5 From the weights we can see that the highest median was KS4 males weight followed by KS4 females weight which follows the pattern of the heights as the KS4 males and females have got a bigger median than the KS3 males and females so they weigh more. However the most consistent data was KS4 females and KS3 males both with the lowest IQR. KS4 males weight was more spread. So the data backs the claim that males weigh more than females because the KS4 males and KS3 males have the highest upper quartile compared to the females.

To get the minimum number allowed you take Q1 and subtract 1.5*IQR from it. This will give you the minimum number allowed because any lower than it is classified as an outlier. In order to get the maximum number allowed you take Q3 and add it with 1.5*IQR. The number that you are left with is the maximum figure that the number could be, as any higher than it is also an outlier.

Outliers
The results highlighted in green represent the outlier. These are the results that have exceeded the minimum or maximum value so they are either under or over the boundary. KS3 M | KS3 M | KS3 F | KS3 F | KS4 M | KS4 M | KS4 F | KS4 F | Height (m) | Weight (kg) | Height (m) | Weight (kg) | Height (m) | Weight (kg) | Height (m) | Weight (kg) | 1.52 | 47 | 1.63 | 45 | 1.65 | 68 | 1.90 | 40 | 1.52 | 37 | 1.62 | 49 | 1.68 | 72 | 1.73 | 51 | 1.62 | 50 | 1.42 | 29 | 1.80 | 68 | 1.54 | 45 | 1.62 | 49 | 1.51 | 50 | 1.80 | 54 | 1.61 | 59 | 1.36 | 38 | 1.56 | 57 | 1.75 | 59 | 1.57 | 45 | 1.42 | 48 | 1.48 | 34 | 1.66 | 63 | 1.41 | 55 | 1.58 | 59 | 1.64 | 47 | 1.60 | 50 | 1.80 | 50 | 1.54 | 48 | 1.60 | 50 | 1.55 | 65 | 1.80 | 60 | 1.41 | 31 | 1.73 | 49 | 1.80 | 72 | 1.58 | 36 | 1.60 | 43 | 1.56 | 53 | 1.57 | 40 | 1.53 | 42 | 1.55 | 47 | 1.45 | 41 | 1.77 | 72 | 1.67 | 52 | 1.60 | 60 | 1.63 | 60 | 1.85 | 73 | 1.73 | 48 | 1.60 | 38 | 1.55 | 40 | 1.63 | 59 | 1.80 | 42 | 1.52 | 32 | 1.63 | 45 | 1.51 | 40 | 1.72 | 51 | 1.52 | 54 | 1.61 | 52 | 1.8 | 62 | 1.69 | 51 | 1.53 | 45 | 1.45 | 51 | 1.52 | 60 | 1.74 | 39 | 1.50 | 50 | 1.51 | 38 | 1.81 | 54 | 1.73 | 50 | 1.52 | 43 | 1.70 | 58 | 1.62 | 63 | 1.60 | 54 | 1.32 | 48 | 1.60 | 50 | 1.85 | 73 | | | 1.57 | 51 | 1.32 | 48 | 1.91 | 82 | | | 1.55 | 45 | 1.52 | 58 | | | | | 1.62 | 38 | 1.63 | 42 | | | | | 1.42 | 26 | 1.57 | 46 | | | | | 1.50 | 45 | 1.45 | 49 | | | | | 1.50 | 52 | 1.42 | 50 | | | | | 1.57 | 50 | 1.58 | 40 | | | | | 1.55 | 47 | 1.62 | 42 | | | | | 1.67 | 51 | 1.62 | 46 | | | | | 1.73 | 56 | 1.55 | 36 | | | | | 1.78 | 50 | 1.6 | 46 | | | | | 1.73 | 66 | 1.53 | 52 | | | | | 1.70 | 65 | 1.68 | 57 | | | | | 1.80 | 70 | 1.49 | 40 | | | | | 1.61 | 45 | 1.8 | 60 | | | | | 1.58 | 51 | 1.50 | 38 | | | | | 1.83 | 57 | 1.65 | 54 | | | | | 1.65 | 50 | 1.7 | 48 | | | | | 1.80 | 48 | 1.52 | 41 | | | | | 1.56 | 60 | 1.54 | 68 | | | | | 1.77 | 66 | | | | | | | 1.70 | 85 | | | | | | |

This table is perfect in the sense that the outliers have been replaced to give better and more accurate results. KS3 M | KS3 M | KS3 F | KS3 F | KS4 M | KS4 M | KS4 F | KS4 F | Height (m) | Weight (kg) | Height (m) | Weight (kg) | Height (m) | Weight (kg) | Height (m) | Weight (kg) | 1.52 | 47 | 1.63 | 45 | 1.65 | 68 | 1.90 | 40 | 1.52 | 37 | 1.62 | 49 | 1.68 | 72 | 1.73 | 51 | 1.62 | 50 | 1.42 | 29 | 1.80 | 68 | 1.54 | 45 | 1.62 | 49 | 1.51 | 50 | 1.80 | 54 | 1.61 | 59 | 1.36 | 38 | 1.56 | 57 | 1.75 | 59 | 1.57 | 45 | 1.42 | 48 | 1.48 | 34 | 1.66 | 63 | 1.41 | 55 | 1.58 | 59 | 1.64 | 47 | 1.60 | 50 | 1.80 | 50 | 1.54 | 48 | 1.60 | 50 | 1.55 | 65 | 1.80 | 60 | 1.45 | 40 | 1.73 | 49 | 1.80 | 72 | 1.58 | 36 | 1.60 | 43 | 1.56 | 53 | 1.57 | 40 | 1.53 | 42 | 1.55 | 47 | 1.45 | 41 | 1.77 | 72 | 1.67 | 52 | 1.60 | 60 | 1.63 | 60 | 1.85 | 73 | 1.73 | 48 | 1.60 | 38 | 1.55 | 40 | 1.63 | 59 | 1.80 | 42 | 1.52 | 32 | 1.63 | 45 | 1.51 | 40 | 1.72 | 51 | 1.52 | 54 | 1.61 | 52 | 1.8 | 62 | 1.69 | 51 | 1.53 | 45 | 1.45 | 51 | 1.52 | 60 | 1.74 | 39 | 1.50 | 50 | 1.51 | 38 | 1.81 | 54 | 1.73 | 50 | 1.52 | 43 | 1.70 | 58 | 1.62 | 63 | 1.60 | 54 | 1.32 | 48 | 1.60 | 50 | 1.85 | 73 | | | 1.57 | 51 | 1.65 | 58 | 1.91 | 82 | | | 1.55 | 45 | 1.52 | 58 | | | | | 1.62 | 38 | 1.63 | 42 | | | | | 1.65 | 45 | 1.57 | 46 | | | | | 1.50 | 45 | 1.45 | 49 | | | | | 1.50 | 52 | 1.42 | 50 | | | | | 1.57 | 50 | 1.58 | 40 | | | | | 1.55 | 47 | 1.62 | 42 | | | | | 1.67 | 51 | 1.62 | 46 | | | | | 1.73 | 56 | 1.55 | 36 | | | | | 1.78 | 50 | 1.6 | 46 | | | | | 1.73 | 66 | 1.53 | 52 | | | | | 1.70 | 65 | 1.68 | 57 | | | | | 1.75 | 63 | 1.49 | 40 | | | | | 1.61 | 45 | 1.8 | 60 | | | | | 1.58 | 51 | 1.50 | 38 | | | | | 1.83 | 57 | 1.65 | 54 | | | | | 1.65 | 50 | 1.7 | 48 | | | | | 1.80 | 48 | 1.52 | 41 | | | | | 1.56 | 60 | 1.54 | 68 | | | | | 1.77 | 66 | | | | | | | 1.62 | 40 | | | | | | |

Scatter Diagrams KS3 Males Correlation coefficient, r = 0.497 r2 = 0.2475 = 25% There is a 25% chance that from any point on the line increasing the height will result in an increase in weight and there is also some positive correlation shown.

KS3 Females

Correlation coefficient, r = 0.424 r2 = 0.1801 = 18% That is an 18% chance that from any point on the line increasing the height will result in an increase in weight and there is also some positive correlation. KS3 Females

Correlation coefficient, r = 0.617 r2 = 0.3812 = 38% That is a 38% chance that from any point on the line increasing the height will result in an increase in weight and from the diagram there is some positive correlation. KS4 Females Correlation coefficient, r = 0.088 r2 = 0.0078 = 8% That is an 8% chance that from any point on the line increasing the height will result in an increase in weight and from the graph there is no correlation.

KS3+4 Males Correlation coefficient, r = 0.650 r2 = 0.4229 = 42% That is a 42% chance that from any point on the line increasing the height will result in an increase in weight and there is some positive correlation. KS3+4 Females Correlation coefficient, r = 0.230 r2 = 0.053 = 5% That is a 5% chance that from any point on the line increasing the height will result in an increase in weight and there is no correlation. KS3+4 Males + Females

Correlation coefficient, r = 0.500 r2 = 0.2497 = 25% That is a 25% chance that from any point on the line increasing the height will result in an increase in weight and there is some positive correlation. From the scatter diagrams the strongest correlation was KS3+4 males with 0.6 as compared to their KS3+4 female counterparts with 0.2 which is almost no correlation and was the weakest correlation from the graphs. There is also a 38% chance that from any point on the line increasing the height will result in an increase in weight from the diagram KS4 males heights and weights as opposed to an 8% chance from the KS4 females. Interestingly from KS 3+4 males heights and weights there was a 42% chance that from any point on the line increasing the height will result in an increase in weight but from KS 3+4 females heights and weights there was a measly 5% chance that from any point on the line increasing the height will result in an increase in weight and there is no correlation which is a huge difference comparing 42% chance from the males to 5% chance from the females. Here is the data grouped and I have then found the mean and modal class for all the ages and genders.

KS4 Female Heights Height (m) | Tally | Freq (f) | Mid-Point (x) | fx | 1.5 ≤ h < 1.6 | IIII | 4 | 1.55 | 6.2 | 1.6 ≤ h < 1.7 | IIII II | 6 | 1.65 | 9.9 | 1.7 ≤ h < 1.8 | II | 2 | 1.75 | 3.5 | 1.8 ≤ h < 1.9 | IIII II | 7 | 1.85 | 12.95 | 1.9 ≤ h < 2.0 | I | 1 | 1.95 | 1.95 | | | | | | TOTAL | | 20 | | 34.5 |

Mode: 1.8≤ h < 1.9
Mean: 34.5/20=1.725

KS4 Male Heights Height (m) | Tally | Freq (f) | Mid-Point (x) | Fx | 1.4 ≤ h < 1.5 | IIII II | 7 | 1.45 | 10.15 | 1.5 ≤ h < 1.6 | IIII IIII III | 13 | 1.55 | 20.15 | 1.6 ≤ h < 1.7 | IIII IIII IIII | 15 | 1.65 | 24.75 | 1.7 ≤ h < 1.8 | III | 3 | 1.75 | 5.25 | 1.8 ≤ h < 1.9 | I | 1 | 1.85 | 1.85 | | | | | | TOTAL | | 39 | | 62.15 |

Mode: 1.6≤ h < 1.7
Mean: 62.15/39=1.594 Height (m) | Tally | Freq (f) | Mid-Point (x) | Fx | 1.4 ≤ h < 1.5 | I | 1 | 1.45 | 1.45 | 1.5 ≤ h < 1.6 | IIII | 4 | 1.55 | 6.2 | 1.6 ≤ h < 1.7 | IIII | 4 | 1.65 | 6.6 | 1.7 ≤ h < 1.8 | IIII | 5 | 1.75 | 8.75 | 1.8 ≤ h < 1.9 | III | 3 | 1.85 | 5.55 | 1.9 ≤ h < 2.0 | I | 1 | 1.95 | 1.95 | | | | | | TOTAL | | 18 | | 30.5 |
KS3 Female Heights

Mode: 1.7≤ h < 1.8
Mean: 30.5/18=1.694

KS3 Male Heights Height (m) | Tally | Freq (f) | Mid-Point (x) | Fx | 1.3 ≤ h < 1.4 | II | 2 | 1.35 | 2.7 | 1.4 ≤ h < 1.5 | II | 2 | 1.45 | 2.9 | 1.5 ≤ h < 1.6 | IIII IIII IIII III | 18 | 1.55 | 27.9 | 1.6 ≤ h < 1.7 | IIII IIII I | 11 | 1.65 | 18.15 | 1.7 ≤ h < 1.8 | IIII I | 6 | 1.75 | 10.5 | 1.8 ≤ h < 1.9 | II | 2 | 1.85 | 3.7 | | | | | | TOTAL | | 41 | | 65.85 |

Mode: 1.5≤ h < 1.6
Mean: 65.85/41=1.606
KS4 Females Weight Weight | Tally | Freq (f) | Mid-Point (x) | Fx | 40≤w<50 | II | 2 | 45 | 90 | 50≤w<60 | IIII | 5 | 55 | 275 | 60≤w<70 | IIII II | 7 | 65 | 455 | 70≤w<80 | IIII | 5 | 75 | 375 | 80≤w<90 | I | 1 | 85 | 85 | | | | | | TOTAL | | 20 | | 1280 |

Mode: 60 ≤ w < 70
Mean: 1280/20=64

KS4 Males Weight Weight | Tally | Freq (f) | Mid-Point (x) | Fx | 30≤w<40 | II | 2 | 35 | 70 | 40≤w<50 | IIII I | 6 | 45 | 270 | 50≤w<60 | IIII IIII | 9 | 55 | 495 | 60≤w<70 | I | 1 | 65 | 65 | | | | | | | | | | | TOTAL | | 18 | | 900 |

Mode: 50 ≤ w < 60
Mean: 900/18=50

Weight | Tally | Freq (f) | Mid-Point (x) | Fx | 30≤w<40 | IIII | 5 | 35 | 175 | 40≤w<50 | IIII IIII IIII II | 17 | 45 | 765 | 50≤w<60 | IIII IIII III | 13 | 55 | 715 | 60≤w<70 | IIII I | 6 | 65 | 390 | | | | | | | | | | | TOTAL | | 41 | | 2045 |
KS3 Males Weight

Mode: 40 ≤ w < 50
Mean: 2045/41=49.878

KS3 Females Weight Weight | Tally | Freq (f) | Mid-Point (x) | Fx | 20≤w<30 | I | 1 | 25 | 25 | 30≤w<40 | IIII | 4 | 35 | 140 | 40≤w<50 | IIII IIII IIII II | 17 | 45 | 765 | 50≤w<60 | IIII IIII IIII | 14 | 55 | 770 | 60≤w<70 | III | 3 | 65 | 195 | | | | | | TOTAL | | 39 | | 1895 |

Mode: 40 ≤ w < 50
Mean: 1895/39=48.59

Stem and Leaf diagrams
I have created these stem and leaf graphs

KS4 Female Heights 1.5: 0.01 0.02 0.05 0.07 Key 1.6: 0 0.02 0.03 0.05 0.06 0.08 1.5:01 = 1.501m 1.7: 0.05 0.07 0.1 0.1 0.1 0.1 1.8: 0.01 0.05 0.05 1.9: 0.01 Mean, x: 1.7065 Range, x: 0.4 Median: 1.715 Standard Deviation, x: 0.118629 KS4 Male Heights 1.4: 0.02 0.02 0.05 0.05 0.05 0.08 0.09 0.1 1.5: 0.01 0.01 0.02 0.02 0.03 0.04 0.05 0.05 0.06 0.06 0.07 0.08 1.6: 0 0 0 0.01 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.05 0.05 0.08 0.1 0.1 1.7: 0.03 0.1 Mean, x: 1.57692 Range, x: 0.38 Median: 1.58 Standard Deviation, x: 0.0862065 Looking at KS4 male heights, the data is more consistent because the standard deviation is lower compared to the females. As females have a higher standard deviation the data is more spread and inconsistent. The range is higher for females as they have 0.4 compared to 0.38 so their data is more varied. KS3 Female Heights 1.4: 0.01 1.5: 0.03 0.04 0.07 0.08 1.6: 0 0.01 0.07 0.09 1.7: 0.02 0.03 0.03 0.03 0.04 0.1 0.1 0.1 1.8: 0.1 Mean, x: 1.675 Range, x: 0.49 Median: 1.705 Standard Deviation, x: 0.118427 KS3 Males Heights 1.3: 0.02 0.06 1.4: 0.02 0.05 0.1 0.1 0.1 1.5: 0.02 0.02 0.02 0.02 0.02 0.03 0.04 0.05 0.05 0.05 0.06 0.07 0.07 0.08 0.08 1.6: 0 0 0 0.01 0.02 0.02 0.02 0.02 0.05 0.05 0.07 0.1 1.7: 0.03 0.03 0.05 0.07 0.08 0.1 1.8: 0.03 Mean, x: 1.675 Range, x: 0.49 Median: 1.705 Standard Deviation, x: 0.118427

KS4 Females Weight 0: Key 10: 50:4= 54kg 20: 30: 40: 0 0 50: 0 4 4 9 9 60: 0 2 3 3 5 8 8 70: 2 2 2 3 3 80: 2 90: Mean, x: 62.45 Range, x: 42 Median: 63 Standard Deviation, x: 10.684

KS4 Males Weight 0: 10: 20: 30: 6 9 40: 0 2 2 5 5 8 50: 0 0 1 1 1 2 4 5 9 60: 0 70: 80: 90: Mean, x: 48.3333 Range, x: 24 Median: 50 Standard Deviation, x: 6.57436

KS3 Males Weight 0: 10: 20: 30: 2 7 8 8 8 40: 0 0 3 3 5 5 5 5 5 7 7 7 8 8 8 8 9 50: 0 0 0 0 0 1 1 1 2 4 6 7 9 60: 0 0 3 5 6 6 70: 80: 90:

Mean, x: 49.1951 Range, x: 34 Median: 48 Standard Deviation, x: 8.05536

KS3 Females Weight 0: 10: 20: 9 30: 4 6 8 8 40: 0 0 0 1 1 2 2 5 5 6 6 6 7 8 9 9 9 50: 0 0 0 0 1 2 2 3 4 7 7 8 8 8 60: 0 0 8 70: 80: 90: Mean, x: 47.9231 Range, x: 39 Median: 49 Standard Deviation, x: 8.10946

Cumulative Frequency graphs
Cumulative frequency graphs are always plotted using the highest value in each group of data, and the cumulative frequency is plotted up a graph, not across. They can also help us to work out the median, lower quartile, upper quartile and inter-quartile range. Below I have included cumulative frequency diagrams for KS3 and KS4 heights and weights. From these I have created box plots and have commented on them. These are cumulative frequency graphs produced from the results that include the genders and ages. I have used these graphs to create box plots which I will be commenting on.

KS3 Heights

KS4 Heights

KS3 Weights

KS4 Weights

Box plots for KS3 and KS4 Heights
The box plot for KS4 females height is negatively skewed. Also KS4 males height is negatively skewed. This is also the case for KS3 females height as it is also negatively skewed. However KS3 males height is symmetrically skewed. On average males are more consistent than females because looking at the graph KS3 and KS4 males height is more consistent than KS3 and KS4 females height.
The most consistent data from the box plots is KS4 males height because the IQR is smaller than the rest of the other box plots and therefore more consistent. This is in contrast to KS4 females height as the data is very inconsistent. However KS3 males height is more spread out than the other data like KS4 males height which is more consistent.
The tallest pupils were females because KS3+4 females heights have the maximum height bigger than the males as the graph shows. The lowest minimum height belonged to KS3 males height which supports the theory that from the box plots females were taller than their male counterparts but males had more consistent data.

Box plots for KS3 and KS4 Weights

The box plot for KS4 females weight is symmetrically skewed. The KS4 males box plot is negatively skewed and this also goes for KS3 females which is also negatively skewed. However KS3 males box plot is positively skewed. The heaviest people belonged in the KS4 females group followed by the KS3 females so the from the box plots the females turned out to be heavier than the males.
However KS4 females and KS3 females had the more spread data. The most consistent data was KS3 males as well as having the lowest median. KS4 males came second with the most consistent data and had maximum weight was the lowest out of the other maximum weights from the box plots. So females ended up having the heaviest people in there groups but there data was more spread than the males. The males had the lowest maximum weights compared to the females but they had the more consistent data.

Spearmans Rank

Spearman’s rank correlation coefficient gives us a value which can determine the strength of the relationship between two sets of data. I have calculated this for all the gender and age groups and will then comment on the relationship.

KS4 Males Height | Weight | Height Rank | Weight Rank | D | d^2 | 1.51 | 40 | 1 | 1.5 | -0.5 | 0.25 | 1.57 | 40 | 4 | 1.5 | 2.5 | 6.25 | 1.60 | 50 | 5 | 3 | 2 | 4 | 1.80 | 54 | 14 | 4.5 | 9.5 | 90.25 | 1.81 | 54 | 17 | 4.5 | 12.5 | 156.25 | 1.63 | 59 | 7 | 6.5 | 0.5 | 0.25 | 1.75 | 59 | 11 | 6.5 | 4.5 | 20.25 | 1.52 | 60 | 2 | 8 | -6 | 36 | 1.8 | 62 | 16 | 9 | 7 | 49 | 1.62 | 63 | 6 | 10.5 | -4.5 | 20.25 | 1.66 | 63 | 9 | 10.5 | -1.5 | 2.25 | 1.55 | 65 | 3 | 12 | -9 | 81 | 1.65 | 68 | 8 | 13.5 | -5.5 | 30.25 | 1.80 | 68 | 14 | 13.5 | 0.5 | 0.25 | 1.68 | 72 | 10 | 16 | -6 | 36 | 1.77 | 72 | 12 | 16 | -4 | 16 | 1.80 | 72 | 14 | 16 | -2 | 4 | 1.85 | 73 | 18.5 | 18.5 | 0 | 0 | 1.85 | 73 | 18.5 | 18.5 | 0 | 0 | 1.91 | 82 | 20 | 20 | 0 | 0 | | | | | | 552.5 |

1-(6∑d^) n(n^-1)

1-(6*552.5) 20(20^-1)

1-(6*552.5) 20(20^-1)

1- 3315 7980

1-0.415413533

=0.584586467

This is some positive correlation

KS4 Females

Height | Weight | Height Rank | Weight Rank | d | d^2 | 1.58 | 36 | 5 | 1 | 4 | 16 | 1.74 | 39 | 14 | 2 | 12 | 144 | 1.90 | 40 | 18 | 3 | 15 | 225 | 1.53 | 42 | 2 | 4.5 | -2.5 | 6.25 | 1.80 | 42 | 16 | 4.5 | 11.5 | 132.25 | 1.54 | 45 | 3 | 6.5 | -3.5 | 12.25 | 1.57 | 45 | 4 | 6.5 | -2.5 | 6.25 | 1.73 | 48 | 12 | 8 | 4 | 16 | 1.73 | 50 | 12 | 9.5 | 2.5 | 6.25 | 1.80 | 50 | 16 | 9.5 | 6.5 | 42.25 | 1.69 | 51 | 9 | 12 | -3 | 9 | 1.72 | 51 | 10 | 12 | -2 | 4 | 1.73 | 51 | 12 | 12 | 0 | 0 | 1.67 | 52 | 8 | 14 | -6 | 36 | 1.60 | 54 | 6 | 15 | -9 | 81 | 1.41 | 55 | 1 | 16 | -15 | 225 | 1.61 | 59 | 7 | 17 | -10 | 100 | 1.80 | 60 | 16 | 18 | -2 | 4 | | | | | | 1065.5 |

1-(6∑d^) n(n^-1)

1- 6*1065.5 18(18^-1)

1- 6393 5831

1-1.09638141

=0.09638141

KS3 Males Height | Weight | Height Rank | Weight Rank | d | d^2 | 1.52 | 32 | 10 | 10 | 0 | 0 | 1.52 | 37 | 10 | 9 | 1 | 1 | 1.36 | 38 | 5 | 4 | 1 | 1 | 1.60 | 38 | 24 | 4 | 20 | 400 | 1.62 | 38 | 28.5 | 4 | 24.5 | 600.25 | 1.45 | 40 | 9 | 6.5 | 2.5 | 6.25 | 1.62 | 40 | 28.5 | 6.5 | 22 | 484 | 1.52 | 43 | 10 | 8.5 | 1.5 | 2.25 | 1.60 | 43 | 24 | 8.5 | 15.5 | 240.25 | 1.50 | 45 | 6 | 12 | -6 | 36 | 1.53 | 45 | 16 | 12 | 4 | 16 | 1.55 | 45 | 16 | 12 | 4 | 16 | 1.61 | 45 | 34 | 12 | 22 | 484 | 1.65 | 45 | 31.5 | 12 | 19.5 | 380.25 | 1.52 | 47 | 10 | 16 | -6 | 36 | 1.55 | 47 | 16 | 16 | 0 | 0 | 1.55 | 47 | 16 | 16 | 0 | 0 | 1.32 | 48 | 19 | 19.5 | -0.5 | 0.25 | 1.42 | 48 | 6 | 19.5 | -13.5 | 182.25 | 1.54 | 48 | 8 | 19.5 | -11.5 | 132.25 | 1.80 | 48 | 38 | 19.5 | 18.5 | 342.25 | 1.62 | 49 | 28.5 | 28 | 0.5 | 0.25 | 1.50 | 50 | 6 | 25 | -19 | 361 | 1.57 | 50 | 19.5 | 25 | -5.5 | 30.25 | 1.62 | 50 | 28.5 | 25 | 3.5 | 12.25 | 1.65 | 50 | 31.5 | 25 | 6.5 | 42.25 | 1.78 | 50 | 30 | 25 | 5 | 25 | 1.57 | 51 | 19.5 | 29 | -9.5 | 90.25 | 1.58 | 51 | 21.5 | 29 | -7.5 | 56.25 | 1.67 | 51 | 28 | 29 | -1 | 1 | 1.50 | 52 | 6 | 7 | -1 | 1 | 1.52 | 54 | 10 | 11 | -1 | 1 | 1.73 | 56 | 35.5 | 35 | 0.5 | 0.25 | 1.83 | 57 | 36 | 41 | -5 | 25 | 1.58 | 59 | 21.5 | 21 | 0.5 | 0.25 | 1.56 | 60 | 39 | 36.5 | 2.5 | 6.25 | 1.60 | 60 | 24 | 36.5 | -12.5 | 156.25 | 1.75 | 63 | 33 | 37 | -4 | 16 | 1.70 | 65 | 32 | 34 | -2 | 4 | 1.73 | 66 | 35.5 | 40.5 | -5 | 25 | 1.77 | 66 | 40 | 40.5 | -0.5 | 0.25 | | | | | | 4214 |

1-(6∑d^) n(n^-1)

1- 6* 4214 41(41^-1)

1- 25284 68880

1-0.36707317

=0.63292683

KS3 Females Height | Weight | Height Rank | Weight Rank | d | d^2 | 1.42 | 29 | 1.5 | 1 | 0.5 | 0.25 | 1.48 | 34 | 6 | 6 | 0 | 0 | 1.55 | 36 | 15.5 | 16 | -0.5 | 0.25 | 1.50 | 38 | 8 | 4.5 | 3.5 | 12.25 | 1.51 | 38 | 9.5 | 4.5 | 5 | 25 | 1.49 | 40 | 7 | 7 | 0 | 0 | 1.55 | 40 | 15.5 | 7 | 8.5 | 72.25 | 1.58 | 40 | 20 | 7 | 13 | 169 | 1.45 | 41 | 4 | 9.5 | -5.5 | 30.25 | 1.52 | 41 | 11.5 | 9.5 | 2 | 4 | 1.62 | 42 | 26 | 11.5 | 14.5 | 210.25 | 1.63 | 42 | 29.5 | 11.5 | 18 | 324 | 1.63 | 45 | 29.5 | 13.5 | 16 | 256 | 1.63 | 45 | 29.5 | 13.5 | 16 | 256 | 1.57 | 46 | 19 | 16 | 3 | 9 | 1.6 | 46 | 22 | 16 | 6 | 36 | 1.62 | 46 | 26 | 16 | 10 | 100 | 1.64 | 47 | 32 | 32 | 0 | 0 | 1.7 | 48 | 36.5 | 36.5 | 0 | 0 | 1.45 | 49 | 4 | 21 | -17 | 289 | 1.62 | 49 | 26 | 21 | 5 | 25 | 1.73 | 49 | 38 | 21 | 17 | 289 | 1.42 | 50 | 1.5 | 24.5 | -23 | 529 | 1.51 | 50 | 9.5 | 24.5 | -15 | 225 | 1.60 | 50 | 22 | 24.5 | -2.5 | 6.25 | 1.60 | 50 | 22 | 24.5 | -2.5 | 6.25 | 1.45 | 51 | 4 | 4 | 0 | 0 | 1.53 | 52 | 13 | 28.5 | -15.5 | 240.25 | 1.61 | 52 | 24 | 28.5 | -4.5 | 20.25 | 1.56 | 53 | 17.5 | 18 | -0.5 | 0.25 | 1.65 | 54 | 33.5 | 33.5 | 0 | 0 | 1.56 | 57 | 17.5 | 32.5 | -15 | 225 | 1.68 | 57 | 35 | 32.5 | 2.5 | 6.25 | 1.52 | 58 | 11.5 | 11 | 0.5 | 0.25 | 1.65 | 58 | 33.5 | 35.5 | -2 | 4 | 1.70 | 58 | 36.5 | 35.5 | 1 | 1 | 1.63 | 60 | 29.5 | 37.5 | -8 | 64 | 1.8 | 60 | 39 | 37.5 | 1.5 | 2.25 | 1.54 | 68 | 14 | 14 | 0 | 0 | | | | | | 3437.5 |

1-(6∑d^) n(n^-1)

1- 6* 3437.4 39(39^-1)
1- 20625 59280

1 - 0.347925101

=0.652074899

Evaluation
I could have made my investigation more precise and accurate by investigating each year than just KS3 and KS4 so I can compare the data better. What would also improve the investigation is by taking a larger sample size as more people would have been investigated. Also taking the primary data myself, it would have been better as the data would have been more reliable.

Conclusion My first hypothesis which I set out to investigate was: that the taller you are the more you weigh. This was supported by my scatter graphs which showed that in general the tallest people tended to weigh more. Also from the scatter diagrams KS3+4 males the strongest correlation with 0.6 and KS3+4 female had the least with 0.2 which was the weakest correlation. My second hypothesis which was that males weigh more than females was backed from the scatter diagrams. This is because there was a 38% chance that from any point on the line increasing the height will result in an increase in weight from the diagram KS4 males heights and weights as opposed to an 8% chance from the KS4 females.
Using the results given from the box plots the tallest pupils were females because KS3+4 females heights had the maximum height bigger than the males as the graph shows. The lowest minimum height belonged to KS3 males height which supports my third hypothesis that going by what the box plots show, females were taller than the males although the males had more consistent data.
Also from the box plots the heaviest people were in the KS4 females group and then followed by KS3 females so the females turned out to be heavier than the males which goes against my third hypothesis which was that males will weigh more than females.
However KS4 females and KS3 females had the more spread data. The most consistent data was KS3 males as well as having the lowest median. KS4 males came second with the most consistent data and had maximum weight was the lowest out of the other maximum weights from the box plots. So females ended up having the heaviest people in there groups but there data was more spread than the males. The males had the lowest maximum weights compared to the females but they had the more consistent data.