How the mass and height of the pupils differ from each other in different year groups. Hypotheses:

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Maths Coursework

PLANNING

Introduction:

This piece of coursework that is going to be studied is about Data Handling. The data I will be looking at will be from Mayfield High. There is a whole database of information available and I will be looking at two specific pieces of data. When examining this set of data I will then be able to make various hypotheses to investigate my project with. I will then draw conclusions on the data from my results. I will also draw graphs that are relevant to prove my point. The two pieces of data that I will be investigating are:

> How the mass and height of the pupils differ from each other in different year groups.

Hypotheses:

There will be a main theme for my main hypotheses, which will be split up into three hypotheses. The main theme however will be height and mass.

) Boys are taller than girls in Year 7 and 8.

Aim: I will show this data by, firstly, plotting all the heights of boys and girls on separate so I can compare the heights of all the pupils and can easily see the spread of data. Then I will calculate the average height of the boys and girls to clearly see the taller gender. Furthermore, to prove my hypothesis I will plot a cumulative frequency graph with a box and whisker diagram with boys and girls on the same graph. This will show the quartiles of the data, the spread of the data and the median. I will also use standard deviation, which will show how much the data deviates from the mean. This will again show the spread of data.

2) Boys are heavier than girls in KS4

Aim: To show this data I will just use a histogram on which I will plot both the weights of the females and males. This will show me the spread of data and in which weight interval most the girls and boys will fall into. Therefore I can easily tell which gender is the heavier. I will also use standard deviation for the same reason as in hypothesis 1.

3) Height and weight are positively correlated in Year 7.

Aim: I will show this data by using a scatter diagram with a line of best fit. This will represent this data best because it will show the correlation clearly. This is the only hypothesis where a scatter graph can be used and I will use 30 points on the graph, which will ensure maximum reliability. Also, to explain the correlation given by the graph I will include Spearman's Rank.

Method:

I will start with a huge database of information on Mayfield High. The first step I will take is to sort the data. This will involve choosing the variables I want to investigate. The two I am going to choose is weight and height. All the other data apart from the names, years and gender will be hidden so I will be left with a clear table of height, weight, gender, year and name. Once the data is sorted I will then take my sample. But before I sample the data I will go through the data and highlight any anomalies in each year group as they will affect my results. However I won't omit them I will just highlight so I am aware of them because omitting them will ruin my sample numbers. As I am selectively sampling my data I may come across an anomaly and have to include it in my data. I will sample my data using two methods of sampling; the first will stratified sampling. This is when a certain percentage of a group is chosen in relation to its size. It also involves putting the data into groups called strata. I will need 10% of whole data and I will put it into year groups which will be my strata. I will then take an even number of samples from each year group in relation to its size. However I will then selectively sample the strata groups. This is when every nth term is chosen. The reason I will choose this as my method is because I will get a relatively even number of males and females. This is essential as it is key to my hypothesis as I am studying the differences between boys and girls.

Description of data:

There are many different types of data; each one is a different way of collecting information we have. The data that will be collected in this investigation will be quantitative data. This is data that consists of numbers. Weights are an example of quantitative data. However quantitative data can either be continuous or discrete. Discrete data can only take particular values. For example, you can buy shoes in exact sizes (6, 6 1/2, 7, 7 1/2 etc.). These values are discrete and there are no values in between them, so discrete data has an exact value.

Continuous data, on the other hand, can take any value. For example, your foot could be 18cm or 20cm or even anywhere in between these two values. Continuous data cannot be measured exactly. The accuracy of a measurement depends upon the device you measure with.

Therefore weight and height can take any value and are therefore examples of quantitative continuous data.

However the data collected from the Mayfield High database is secondary data. This is because we didn't actually collect the data ourselves. But I am going collect my primary data by using the RGS database.

Actual Data representation:

Total number of people in data = 1,182.

Therefore the number I need to obtain in my sample is 10% of this, which are 118 people.

Below is a table to represent the different strata and the number of pupils I need to take from each:

Year Group

Number of students

Size of sample 10%

Rounded number of pupils

7

281

28.1

28

8

269

26.9

27

9

260

26.0

26

0

99

9.9

20

1

69

6.9

7

Now I have my strata I have taken a 10% sample of each and ended up with the number to take from each group and a total of 118 pupils. Now I have to selectively sample each stratum. I selectively sampled each year group by choosing every 10th person.

Evaluation of data, its accuracy and potential problems:

There are not many problems with the method used to collect the data. The only real problem I can foresee is the anomalies providing inaccuracies in my graphs.

Also the data collected is secondary data and therefore there is no real way of knowing if it is reliable or not as I did not collect it myself.

There are no signs of any obvious bias either within the data I collected however it is hard to tell as the only way to really find out is to determine who produced the data. However we do know that the data was collected using the whole of Mayfield High School and therefore there shouldn't be any bias in the data.

However the data does show many signs of inaccuracy. Whilst sorting the data there are many pupils in each year that just do not fit the pattern. For example there are some people who in Year 7 have a height of 2.00 metres and some people who weigh 110 kg. These are ridiculously out of the pattern and are therefore anomalies. I overcame this by sifting through the data and highlighting the anomalies to make sure I was aware of them. Apart from these few inaccuracies the data on the whole is very accurate and a good source to sample from. The few limitations are of the method is that a 10% sample size may provide us with only a small number of pupils in each year. This will reduce the overall reliability of our results.

Patterns within the data:

it is clear to see from looking at the pupil samples taken that the higher the age group the heavier and taller the pupils are. However my hypotheses relate to the gender and the basic trend that appears is the height and weight seem to increase in the same year from girls to boys, i.e. boys are taller and heavier than girls in each year. This is the basic trend that can be seen. For example in Year 7, the shortest girl is 1.3m and the shortest boy is 1.41m. Also in Year 8 the tallest girl is 1.71m whereas the tallest boy is 2.00m. Therefore by just looking quickly at the data and picking out tallest and shortest, this is already proof that my hypotheses are half true.

For weight, the heaviest female in Year 10 is 60kg whereas the heaviest male is 68kg. This again is further proof that my hypotheses are becoming correct.

So the general trends and patterns that can be picked up simply by looking at the tables are that; boys are generally taller and heavier than girls in the same age group.

ANALYSIS

Graphs, observations and calculations:

All the graphs that will be drawn will be relevant to the data. They will show how the height and weight of girls and boys vary in each year. All the results that are coloured in red will be omitted from the calculations but included in the graphs. The reason for omitting them from the calculations is because they will provide us with inaccurate results. The anomalies were dealt with by being left out of the mean calculations but were included in the graphs.
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Hypothesis 1 - Boys are taller than girls in KS3:

Calculations:

Mean Height (m)

Modal Height (m)

Range

Year 7 Girls

.51

.48, 1.52 and 1.6

.8 - 1.3 = 0.5

Year 7 Boys

.54

.5, 1.51 and 1.65

.65 - 1.41 = 0.24

Year 8 Girls

.59

.42, 1.59, 1.62 and1.7

.71 - 1.42 = 0.29

Year 8 Boys

.62

.5, 1.55, 1.68 and 1.72

2.0 - 1.3 = 0.7

Year 9 Girls

.61

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