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GCSE: Height and Weight of Pupils and other Mayfield High School investigations
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- Level: GCSE
- Questions: 75
Any decimals will be rounded up or down to form an integer. Hypotheses 1. Are boys taller than girls? 2. Are boys heavier than girls? Other hypothesis ideas * Link between height and weight? * Boys are heavier than girls? * Boys are taller than girls? * Separate by gender or year group? Things to do * Draw my hypothesis * Find mean, median and mode - what do these give me? * Median = middle or halfway value * Mode = most common value * Mean = average (total of values divided by the number of values)
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Mayfield high school. We will investigate the correlation between height and weight throughout the school. These two variables are examples of quantitative data, this will allow us to use advanced statistical techniques. We will be able to extend our rese
The correlation may be weaker, the younger the person is as they may be having their growth spurts at different times and be developing at different rates. Whereas, the older the person the more even peoples heights and weights get between girls and boys. Sample I have taken a sample of 40 pupils from the school, as working with the whole population would be unmanageable. I decided to use a stratified random sample, because I want our sample to have a fair representation of each year group and gender, and I want each child to have an equal chance of being selected.
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For my Statistics coursework I have decided that I will compare weight and height. I will use the data that has been gathered from Mayfield high school and I will show various methods to prove my hypothesis correct.
This is due to the natural course that every girl will go through. Also I know that males lose weight and gain more muscle tissue quicker than girls. I am going to use the formula shown above to work out BMI. Hypothesis 3 The taller you are the more you will weigh will result in a strong positive linear correlation I have opted to use this hypothesis because I think that it will show a positive correlation. To display this I am going to use Spearman's rank correlation coefficient because this will prove whether the correlation is either weak or strong depending on if it is negative or positive.
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This data is based on Mayfield High School which is fictitious. While collecting the data, I made sure that I took a 10% sample from each sex in each year group, I also made sure that my selections were completely random, and that every student had an equal chance of being selected. The method I used to select them was - I divided each group into sections of 10, and the used the random button on my calculator to produce a random number between 0 and 1.
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I believe that if they have chosen more logical subjects than they will also watch more television having spent less time doing the creative things as a child. I hope that this will show a good connection. I plan to use to use comparative pie charts and comparative cumulative frequency polygons to evaluate the creativity levels of students' favourite subjects by gender and histograms to prove my secondary hypothesis. Selection and Collection of Data I will be using Mayfield High data provided by the exam board.
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However, this may not be the case in individual year groups, but I don't have the distribution of boys and girls for each year group, so I will have to presume that the distribution is within the year groups is the same as for the whole school. I have decided to reduce the amount of data to 120. I feel that this is a good number to work with because I will have enough data to find accurate trends but it is not too much data that I will get confused with the volume of data to analyse.
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Another one of my theories is that boys are taller than girls in each year group, I will investigate this in the same way and if the boys are taller than the girls my hypotheses will be proved correct. I also think that boys and girls in higher year groups are taller than boys and girls in lower year groups, I will investigate this and if older people are taller my hypotheses will be proved correct. Diagrams and Calculations I will use line graphs and scatter graphs to provide me with evidence that I will need to prove my hypotheses, I will use box plot graphs because it is easy to see the difference between two groups of data.
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Mayfield High. Hypothesis 1-the older the students, the taller and heavier they will be. Hypothesis 2-Girls in years 7, 8 and 9 are taller and heavier than the boys of those years but the boys in year 10 and 11 are heavier and taller than the girls.
I will first decide how to sample the given data of each year from Mayfield high school. By this I mean I will choose a sampling method from one of the following: stratified, random, convenience, systematically or quota. I first need to stratify the data for my sample, proportionate to the size of the year and the different genders. Secondly I will need to stratify the data for my sample making it proportinate to the size of the year. By doing it this way the number of pupils I pick from each year groups will in proportio to the total number in each year group.
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* I am going to produce a scatter graph showing the heights and weights of the club members. This will help me to investigate whether there is a correlation between the heights and weights of the club members - helping to prove or disprove my main hypothesis. I am not however, going to produce a scatter graph for each separate gender as I would expect very similar results to the scatter graph for the combined data. This would not significantly assist my investigation, so if I was to produce these graphs it would be called redundancy * I am then
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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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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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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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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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First I will put my data into a table so it's easier for me to find the mode, mean, median and ect. So I can interpret and understand the data more clearly, another way of to compare the data is to draw a dual bar chart and a scatter graph so I can compare and look if there is any pattern or correlation. As you can see I created a table for my data which I will use to create a dual bar chart, scatter graph and a cumulative frequencey chart.
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and GCSE maths (%) simply to show me the mode. To display my data properly I will use a frequency polygon. I then will go on to do a stem and leaf diagram comparing the Attendence (%) and GCSE maths (%) of students to find out the median. After I have done this I will plot my data Attendence (%) and GCSE maths (%) onto a scatter grapgh. Using the line of best fit I will look for a correlation to show me the relationship between the Attendence (%)
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which I have rounded up to 120. Through my chosen sample size of 10% which I carried out on each year group for both boys and girls I found that some of the numbers were not whole. In order to make these numbers whole I rounded down on all data I was presented with. As I was rounding down my sample of all student no longer was 120 but 114. I will do this by finding the number of boys or girls in a certain year group. I then divided that number by the total students at 'Mayfield High School'.
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Diagrams: I had to make sure the rule worked so I double checked by using 3-D cubes to see whether the rule was 100% correct. The sheet shows this as an example. It is a line of five cubes and it has 30 faces and 13 of the faces are hidden. I tried changing the amount of cubes, to see what results I Got. I used 7 cubes and noticed that I now had 42 faces and 19 of the faces are hidden.
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There are a number of details on the secondary data sheet for each students e.g. Name, Age, year group, height and weight. I'm going to use this secondary data to investigate the hypothesis: "Boys in KS4 are heavier than girls in KS4" There are too many pupils to employ all the results so I'll use a sample of the boys and a sample of the girls. In order to make comparison easier I will use the same number of boys as girls in my two samples.
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Once I have done this I will show my data onto a bar graph comparing the Attendence (%) and GCSE maths (%) simply to show me the mode. To display my data properly I will use a frequency polygon. I then will go on to do a stem and leaf diagram comparing the Attendence (%) and GCSE maths (%) of students to find out the median. After I have done this I will plot my data Attendence (%) and GCSE maths (%) onto a scatter grapgh. Using the line of best fit I will look for a correlation to show me the relationship between the Attendence (%)
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From graph 1 we can see that there is a positive correlation between the IQ results and students' total key stage 2 results. The graph suggests that if a person has a higher IQ their total key stage 2 results will be higher; this is what I had to show for this hypothesis. Graph 1 show a sample of just 50 students randomly selected, so I could extend the sample which may make it more accurate or repeat it with different students to back up the result.
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Both numbers of the product are even. I got this by dividing the main number by 2 and then multiplying it by itself again to get maxi product. Number Product 16,0 16x0=0 15,1 15x1=15 14,2 4x2=8 13,3 13x3=39 12,4 12x4=48 16 12.5,3.5 12.5x3.5=43.75 11,5 11x5=55 11.5,4.5 11.5x4.5=51.75 10,6 10x6=60 10.5,5.5 10.5 x5.5=57.75 9,7 9x7=63 9.5,6.5 9.5x6.5=61.75 8,8 8x8=64 8.5,7.5 8.5x7.5=63.75 7,9 7x9=63 I have stopped my table because the answers of the product are now starting to be repeated.
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SAMPLE SIZE: Taking a fixed percentage out of the 1183 students uses a sample size. For example 10% is taken from the whole school. You would end up with 118 students. On the other hand a percentage sample can be taken if the school is divided in strata. For example, if 10% is taken from every year group: Year group Total number of students Sample of 10% 7 282 282 x 0.1= 28.2 8 270 270 x 0.1 = 27 9 261 261 x 0.1 = 26.1 10 200 200 x 0.1 = 20 11 170 170 x 0.1 = 17 From this we learn how many pupils need to be taken from each year group.
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- Connect the motor to the power supply keeping the voltage at a constant 6. - Then measure the time, current, mass, and the voltage (constant). Prediction:- I predict that when the mass increases, the efficiency will increase to a maximum and then decrease. This is because with no weight the motor will consume energy just to turn and do no useful lifting, giving 0% efficiency. When the weights are too heavy the weights will not lift at all, the motor will then heat up, and there will be 0% efficiency too.
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