Press the ‘Shift’ button then the ‘Ran#’ button then the multiply button (X). Then you type in the number you want the sampling to go up to. In my case there are 75 pupils in year 7 so I would press 75 on the key pad after this press plus 1 ( + 1 ) this is so that you do not have to round up or down you simply take the first number to the left of the decimal place. Keep on pressing = until you have a sufficient amount of data. You may find that the same number comes out more than once. Just ignore it and press = again.
In this statistics piece of coursework I have chosen to collect 30 pieces of data from each year group as it is an easy number to work with because it is not to big and also it is a large enough number so to avoid bias.
Plan
For the rest of the project I will simply do each hypothesis in order and do a step by step commentary on what I am doing and sometimes why and what different graphs and other sorts of data collection show. Once I have done all my hypothesis I will check my work for obvious mistakes, summarise, make conclusions and make different comparisons.
Hypothesis 1
The most popular eye colour in Year 7 and 9 in BLUE.
First of all I will put the 30 pieces of data from year 7 into a tally chart.
Colour Tally Cumulative Frequency
Blue ///// /////
///// //// 19
Brown ///// /// 8
Green // 2
TOTAL 29
The reason why the total only adds up to 29 is because where I have sampled I have picked out a person who has not filled in the eye colour information.
I will now put all the information into a bar graph and from this it will show me what the most popular eye colour is in year 7.
I will now use the same method for year 7 as year 9 and put all 30 pieces of data into a tally chart.
Colour Tally Cumulative Frequency
Blue ///// ///// /// 13
Brown ///// ///// // 12
Green // 2
Grey / 1
Hazel // 2
TOTAL 30
I will now put the data into a bar graph.
From the 2 different graphs that I have produced I will now put them together so I have year 7 and 9 on the same graph. From that I will hope to make a conclusion.
From this graph I can see that most pupils in year 7 and year 9 have blue eyes with brown eyes following closely behind. I can now conclude my first hypothesis by saying that the most popular eye colour in year 7 and 9 is BLUE. The conclusion for Year 9 is not a fair one as because if I had have used a wider spectrum of data then I think that the graph would be different as the blue and brown eye colour was very close. So my first hypothesis is correct!
Hypothesis 2
Taller pupils weigh more.
For this hypothesis I will plot 2 different scatter graphs. One for year 7 and one for year 9. From the graphs I hope to calculate the average height and weight for both the small and tall people or if it is obvious to see I will not calculate any results.
From the graphs I can see that in year 7 people are not always heavier if they are taller. The tallest person in year 7 who is 175cm tall is only 45Kgs were as one of the smallest pupils who is 139cm tall weighs 49Kgs. In year 7 the taller the people are does not mean that they are necessarily going to be heavier. So my hypothesis for this section is not true.
On the Year 9 graph I can see that it is the opposite to year 7. For example if I take an average. For this I will take the 4 tallest peoples height and add each individual height up then divide it by 4. I will do the same for there weight. Then I will do the 4 smallest people.
Tallest
189cm + 185cm + 182cm + 180cm = 736. 736/4 = 184cm Average height = 184cm.
70Kg + 73Kg + 76Kg + 82Kg = 301. 301/4 = 75.25Kg Average weight = 75.25Kg
Smallest
151cm + 156cm + 158cm + 160cm = 625. 625/4 = 156.25 Average height = 156.25cm
45Kg + 51Kg + 45Kg + 50Kg = 191. 191/4 = 47.75 Average weight = 47.75Kg
So it is clear to see through the calculations that the taller people weigh more. So I can conclude by saying that my second part of the 2nd hypothesis is correct! Also as with the first hypothesis if I had have used more data the results may have been different.
For year 7 the hypothesis was not correct. This was probably because the children are still growing and usually at that age they only either grow upwards or outwards and not both. I can also say that both of the graphs show a positive correlation therefore the hypothesis is correct. Although there are different anomalies which I have seen such as slimmer/fatter people.
For year 9 I worked out that the hypothesis was correct.
Hypothesis 3
On Average people in Year 9 are taller than people in Year 7
First of all I will put the data from year 7 and 9 into two different cumulative frequency tables.
The first table will be for year 7.
Height Tally Cumulative Frequency
131<h<140 ///// / 6
141<h<150 ///// 11
151<h<160 ///// ///// 21
161<h<170 ///// // 28
171<h<180 // 30
181<h<190 30
I will now do a frequency table for year 9.
Height Tally Cumulative Frequency
151<h<160 ///// / 6
161<h<170 ///// // 13
171<h<180 ///// ///// //// 27
181<h<190 /// 30
From the results that have been put into the tables I will now transfer the data from both tables and put it into one cumulative frequency graph. I will then plot the interquartile range. I will do this by dividing the cumulative frequency into four quarters, then I will go across to the curve, and then go down and read off the value it gives. From there I should be able to see on average who is taller out of year 7 pupils and year 9.
Key: (for Cumulative Frequency Graph)
On the X axis the numbers stand for the different heights.
120<h<130 = 1
131<h<140 = 2
141<h<150 = 3
151<h<160 = 4
161<h<170 = 5
171<h<180 = 6
181<h<190 = 7
The lower quartile for year 7 131<h<140cm
The median for year 7 is 141<h<150cm
The upper quartile for year 7 is 151<h<160cm
The interquartile range for year 7 is – Upper quartile – Lower quartile = 151 – 131 = 20
160 – 140 =20
The interquartile range for year 7 = 20<h<20
The lower quartile for year 9 is 151<h<160cm
The median for year 9 is 161<h<170cm
The upper quartile for year 9 is 171<h<180cm
The interquartile range for year 9 is – Upper quartile – Lower quartile = 171 – 161 = 20
180 – 160 = 20
The interquartile range = 20<h<20
From the cumulative frequency curve I can say that the median is higher for year 9. This means that people tend to be taller in Year 9 than in year 7.
I am now going to do a box whisker plot so I can hopefully prove my answer.
A Box whisker plot shows a frequency distribution by using the lowest and highest values, the median and the lower and upper quartiles.
By looking at my box whisker plot I can now finalise my 3rd hypothesis by saying that it is correct as the median height is higher in year 9 than in year 7.
As the CUMULATIVE FREQUENCY curve is not that accurate I will now also do a Stem Leaf diagram so that I can find out exactly on average which year is taller.
Key: 14 4 = 144cm tall
5 16 = 165cm tall
Year 7 Height Year 9
4,5,8 13
0,0,0,2,7,8,8,9 14
9,8,7,6,6,5,3,2,1 15 8,6,1
0,1,2,4,5,5,5 16 9,8,7,5,5,3,3,0,0,01,
17 9,8,8,7,5,5,4,4,3,1,1,1,0
- 9,5,2,0
The median height for year 7 is 148.5cm.
The median height for year 9 is 164cm.
The mean for year 9 is- All the heights added up divided by how many people there are.
4100 divided by 27 = 151.8cm
The mean for year 7 is-
5444 divided by 30 = 181.4cm
The mode for year 9 is- (the most common height) which is 171cm and also 160cm
The mode for year 7 is- 140cm and 165cm
From this Stem Leaf plot I can now prove that ‘On average people in year 9 are taller than those in year 7’.
The Stem and Leaf plot is a lot more accurate than the cumulative frequency curve so it shows that my third hypothesis is correct!
Conclusion
Whilst I have been writing my coursework I have noticed a few things which I think may be a factor in the project. First of all I noticed that on the questionnaire data analysis sheets for year 7 and year 9 there were many of the boxes not filled in. There could be many reasons why the people did not fill in some of the answers in the questionnaire. Some people may not have understood what the question was asking. For example when it says ‘span’ people may interpret that to mean from the tip of one finger to the tip of another when your arms a stretched out. Or from the tip of your little finger to the tip of your thumb. Also the foot length, some people may have measure there foot when they had there shoes on and some people may have measured there feet with there shoes off.
With my hypothesis’ I chose not to do any hypothesis with span or foot length in it because I new that the data would be unreliable and that the results would either not be fair and/or not be correct.
As I have mentioned before in the project my first hypothesis may have been different if I had picked a larger spectrum of data because the results between the eye colour in year 9 were very close and so a larger amount of data may have made my hypothesis wrong. I do not think that the sample I picked represented the whole population.
Also I did notice when doing my random sampling that I had picked a person who did not put there eye colour in Year 7. I did not pick another person because I wanted to see what the results were like. Likely the in the results there was not disputing what the overall favourite eye colour was.
If I had to do the project again I would probably pick a different person in they had no data in one of the fields and also I would probably pick a wider amount of data. If I had to do the project again I would also get a compare and contrast different hypothesis with different schools. For example the year 7 pupils in Chatham House Grammar School and maybe the year 7 pupils in Dane Court Grammar School. As this may give different results.
Also with the questionnaire some people may not have put the result to the nearest cm or rounded the results up instead of down or vice versa. Some students when answering the question may simply just not fill in the answer even if they know what the answer is.
During my project I used many different calculations and mathematical theories to help me answer my hypothesis. In the project I used Stem Leaf Graphs, Cumulative Frequency Tables and Curves and Box Whisker Plots also during the project I used tally tables and bar graphs.
I think I could attempt my project in a different way by choosing different hypothesis and maybe more hypothesis also do extensions and use different ways of calculating the hypothesis. E.g. use methods different to Box Whisker or Stem Leaf.
It is hard to make comparisons between the two year groups as they are so different. None of results were close when comparing the data. This may simply be because when boys are in year 9 they have developed more than people would in year 7. E.g. most probably taller and heavier. That is why comparing data from 2 different schools but in the same year may be a more effective task.
Overall I think the project went well although things could have been changed. I think my plan was quite well thought out and that it helped me quite significantly to complete the project.
