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GCSE: Height and Weight of Pupils and other Mayfield High School investigations
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I will be selecting my data after organising it because it makes it easier to get the sample that There was approximately 200 males and 200 females and if you divide 200 by 5 you get 80 which is how many people I want in my sample. The problems with systematic sampling are that the different ways in which the sample can get organised is not taking the different ratios of the different categories (Gender, IQ etc) into account. The benefits of using systematic sampling are that it is easy to sort out/organise, it isn't as time-consuming as stratified sampling as all you need to do is click on a button and find the command that you want to use.
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so does weight * There is a link between the height and weight of Year 11 and Year 7 Boys and Girls * Are there any other relationships between the height and weight between Year 7 and Year 11 students I believe there will be a strong link between height and weight. I believe that the higher the height, the higher the weight. This is because taller people are larger than smaller people and therefore weigh more. Plan of Action - Data Collection The data I have collected is that of Year 11 and Year 7 boys and girls.
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Hypothesis: the taller you are the heavier you are Sub hypotheses: year 11 boys are heavier than year 9 boys Year 9 girls are taller than year 7 girls Boys are heavier than girls Key stages 4 are heavier than key stage 3 I have chosen these hypotheses because I feel that heights and weights are easy to compare with each other and easy to establish relationships, and this is the stage in life which you grow so it would be easier for me to prove my hypotheses.
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Also girls may feel unacceptable to be certain weights so will be conscious on their weight more than boys. I will now show the mean and range for each year in the tables below, this will then help me find out whether or not my hypothesis was correct. My results are as follow: Year 7 Year 7 Female Male Type: Weight (kg) Weight (kg) 53 45 60 51 44 45 53 52 54 60 60 52 53 75 54 36 70 45 49 53 48 40 40 40 26 41 52 52 42 52 Mean: 50.53 49.27 Mean without outliers:
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I will then analyse this data thoroughly also to try and prove that my hypothesis is valid with 2 different samples. MALE NUMBER HEIGHT (cm) FOOT LENGTH (cm) 4 142 23 5 156 23 11 159 25 12 144 22 15 161 25 25 141 21 31 147 23 33 155 25 51 142 24 54 143 23 55 154 25 57 147 25 61 145 23 69 148 20 73 141 22 83 162 24 84 152 25 86 150 26 90 144 22 94 145 24 96 142 22 107 155 25 116 147 22 118 149 23
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1.106704 4 2.052 4.210704 4 2.052 4.210704 4 2.052 4.210704 6 4.052 16.418704 6 4.052 16.418704 8 6.052 36.626704 9 7.052 49.730704 Total of (Xi - )� = 169.5401 Xi Amount = 58 169.5401 � 58 = 2.923105172 Variance = 2.923105172 Standard Deviation = V2.923105172 Standard Deviation = 1.7097 (Rounded) Means of Travel: Tram TRAM Distance From School (km) Frequency Cumulative Frequency 1 ?d<2 0 0 2 ?d<3 7 7 3 ?d<4 5 12 4 ?d<5 4 16 5 ?d<6 15 31 6 ?d<7 7 38 7 ?d<8 4 42 8 ?d<9 2 44 Students that have to travel a distance of 1.99km or less to school do not travel to school using a tram at all.
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Once I have collected the data I am going to put it into tally charts. Using a tally chart means it is easier to work out the totals for cumulative frequency graphs and is also easier to make a histogram from. A stem and leaf diagram will also make it easier to find the median of the data. I should use the median, mode, mean and range to help me make some simple generalisations and statements about my hypothesis. I can use them to compare the boys and girls and also help me prove my hypothesis.
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I did this on a calculator by pressing rand# and rounded of the decimals as this was a fair way of gaining these numbers. I eventually did the same thing with every gender of every year although I would get different amounts of random numbers (but the same percentage of students). Here are the results I got, which I have split into genders simply because it is clearer: Year Random Numbers (Boys) Random Numbers (Girls) 7 80 218 7 20 263 7 12 239 7 128 217 7 79 224 7 3 270 7 64 168 7 119 152 7
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Using a stratified sample makes sure that there is no bias to both year groups and by using the random number button on my calculator ensures there is no bias towards any person and everyone has an equal opportunity of being chosen. By sampling, I am both saving time and making the calculations needed to be performed easier although I am losing some accuracy, the amount of accuracy lost should not damage the results too much. I want to find the mean average height and weight of years 10 and 11 together and years 10 and 11 separately.
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There are quite a few categories that I do not need. So I will eliminate these columns. These are: * The pupil's SURNAME: This has no effect on the pupil's IQ. * The pupil's MONTHS: This will have no effect on the correlation. * The pupil's MONTH OF BIRTH: This will have very little effect on the pupil's IQ. It will also have very little change to the correlation. * The pupil's HAIR COLOUR: This again will have no effect on the pupil's IQ.
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The samples will be selected through the process of random sampling to ensure there is no bias. I will be using the programme Microsoft Excel to collect my samples. I intend to sample the school population of Mayfield High School, taking a percentage of the 1183 students, mine being 80. I am taking a percentage of 80 as my samples, to keep the data to a convenient amount it also allows me to acquire enough data without it being too little or too much.
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From the selection of data provided, I will investigate the relationship between height and weight of people.
Introduction I will investigate three hypotheses, these are: 1) The taller you are, the heavier you are 2) How height changes with age - there will not be much of an increase 3) Height and weight according to gender - Males are normally taller and heavier Data Collection I have been given is data on Mayfield High School. It consists of 1183 students. In the columns of data are; unique reference numbers, year group, gender, height (m) and weight (kg). From this, I want to look in more detail at 100 students and I will take a random stratified sample.
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Mayfield High. From my scientific knowledge I know that at KS3 girls grow faster than boys. I will check this by drawing a frequency table.
Class Width Freq. Cum. Freq. 1.4 = x < 1.45 1.425 0.05 5 5 1.45 = x < 1.5 1.475 0.05 4 9 1.5 = x < 1.55 1.525 0.05 4 13 1.55 = x < 1.6 1.575 0.05 4 17 1.6 = x < 1.65 1.625 0.05 9 26 1.65 = x < 1.7 1.675 0.05 2 28 1.7 = x < 1.75 1.725 0.05 1 29 1.75 = x < 1.8 1.775 0.05 1 30 ?f = 30 ?fx = 46.9 ?fx� = 73.58 Mean = 1.563 Standard Deviation = 0.0937 Variance = 0.008781 Key Stage 3 Boy's Height Table of Values of Histogram [Key Stage 3 Boy's Height]: Class Int.
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If I find outliers in my sample, I will still use them in my investigation. I will calculate the following for the data: mean, median, mode, range and IQR. Range Mean Median Mode Height 0.63 1.58 1.60 1.62 Weight 45 48.80392157 48 48 Conclusions The weight and height graph supports my original hypothesis as it shows positive correlation. I used a scatter graph to display this information because the data was very spread out and most suitable for a scatter graph. Also, I have found that this coursework has assisted me in many ways. As well as allowing me to have and develop a further insight into statistics, I also understand how it would affect people in their everyday lived.
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I could use this method, however we would need to make sure that the data we have, has already been randomized and is any particular order. Random Sampling "To carry out this type of sampling, you will need to use a table of random numbers. Random numbers can also be generated using calculator or computer,. These can then be listed." For this type of sampling we need to number all of our datum points and then select correctly numbered points, that coincide with the calculators random button.
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Mayfield High. I am going to investigate the relationship between the height and weight of the pupils. I will be investigating how height and weight affect each other. For example, if an increased height means an increased weight.
A stratified random sample helps to avoid bias. I repeated this process for every year group and gender, until I had 40% of each one. After this, I made a graph using all of the data (shown below in the blue square). I started off with deleting certain records that had outlying data and values that didn't follow the range of height (1m - 3m) that most of the other's did. Some were above or below the range, and to avoid skewed results I deleted those records. This graph compares all heights and weights of the pupils in the school.
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articles I have and then times it by a hundred to find the percentage and then display my results in a bar chart. Hypothesis My hypothesis is that The Guardian will be more complex than The Daily Mail, which will be more complex than The sun. * The Sun will have the most entertainment and the Guardian will have the least amount of entertainment. * I think I will find the least amount of business in The Sun and The Guardian and the Daily Mail will have more business than The Sun.
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I will use a variety of different statistical analysis and techniques (which I will talk about later) that will help me in achieving a more accurate and unbiased piece of coursework. Tasks Stratified sampling - When you are using statistics with a large number of values, you may only want a representative sample in your survey. Using stratified sampling we could work out an unbiased amount of students. The formula used when sampling is: An example of stratified sampling is shown below; if there are 1000 students in a school and I want to take a sample of fifty representing
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Looking at this preliminary graph, I can see that the correlation is fairly strong, and is positive. This means that there is a basic relationship between my two sets of data, and so the hypothesis is worth investigating. Collecting Data: The data that I will need to collect for my main hypothesis is the IQ and the total KS2 result. I will only take this data from a sample of the students, the sample size being 120 students. I have chosen this size for my sample because it is approximately 10% of the overall number of students at the school (1183).
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To make my results more accurate I will do a stratified sample of a 150 students. I will then use those 150 pieces of data to work out correlation and trend line. The correlation will be more accurate this time because I have done stratifies sampling. A stratified sample is a way of taking data from each group proportional to the group's representation in the overall population. So if a group is small a small amount of data will be taken from it if the bigger the group is a larger amount of data will be taken from it.
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For example I get number X then as I am looking for females in year 10 I will start at the 4th female in year 10 and then write down every 4th female after the Xth female thus creating a random sample. In year 11 there are fewer pupils because of this I will throw a number on the dice and I will then after X choose every other of the selected gender. I have collected my data and have written it in the table below I will then use the data to create a cumulative frequency table, and then a graph.
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I predict that there IS a positive correlation between height and weight. I have collected 50 samples of relevant data, and I have avoided bias by choosing my samples completely at random. I have also found out the mean for height and the mean for weight; this will be useful because I will then be able to draw a line of best fit, as the line of best fit always goes through the mean. Scatter Graph Table Height (m) Weight (kg) 1.49 40 1.8 60 1.9 47 1.52 58 1.42 29 1.58 55 1.66 54 1.62 52 1.67 52 1.62 53 1.64 50 1.61 47 1.65 45 1.6 46 1.52 60 1.53
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The rule is n+1 � 3, or three times the lower quartile. 4 Interquartile range - The interquartile range is the upper quartile take away the lower quartile. Box plots/Box and whisker diagrams - A way of showing the distribution of data. It shows the median and central half of the data. It also shows the range of data. It can be used to compare two or more sets of data. Spearman's coefficient of rank correlation - Spearman's coefficient of rank correlation is a scale from minus one to positive one of which you can tell how strong the correlation of your positive or negative data is.
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For my coursework I am going to be investigating how students from key stages 3 and 4s weight affects their height and vice versa. I am going to be investigating this in Mayfield School
The variations in eye colour, (qualitative data) 3. The relationship between the above two colours, (qualitative data) 4. The distances travelled to school, (not easily interpreted onto graphs) 5. The relationship between height and weight, 6. The relationship between two sets of Key Stage 2 results, (discrete data) 7. The relationship between IQ and Key Stage 2 results (no obvious link so it would be useless) 8. The height to weight ratio in terms of the body mass index (good but not as useful and easily comparable as 5)
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mayfield high. Objective To collect analyse and compare the heights and weights of boy and girl pupils in the year 10 and 11 at mayfield high school.
3. Specific aims >To collect a resonable sample of pupil data, using a suitable sampling method. >To compare gender differences for height using histogram and frequency polygon graphs, and by finding the range and three averages for each sub-group. >To construct boy/girlheight cumulative frequency graphs for a box and whiskers group distrobution comparisons using inter quartile ranges. >To make standard deviation calculations as a measure of boy/girl height frquency distributions. >To investigate in detail boy/girl height weight correlation, finding line of best fit equations, and spearmans rank correlation coefficient. >To interpret my findings, as i go along bearing in mind my hypothesis, which i will state at the outset.
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