Now the task is to randomly select the amount of students from each year group. It is important that I take a random sample because this should mean I get a fair set of data.
Selecting randomly can be done on my scientific calculator. In order to do this I pressed the shirt button followed by ran# and this was then multiplied by the number of students in that category.
Year 7 males: ran# x 151
Year 7 females: ran# x 151 + 131
Year 11 males: ran# x 1097
Year 11 females: ran# x 1097 + 86
I repeated this until I had the right number of students in each category. Once this was done I decided to extract the information regarding height and weight and place all the data in the table shown on the next page:
Plan of action
Now that I have collected all the information I am ready to start investigating it. This will be done in a variety of ways. Firstly I will look into the mean, mode, and median of the data. These are all different ways of investigating the middle of a set of data. Also I will be looking at the standard deviation of the data that shows the spread of data. I will also draw up various ways of presenting my data including; scatter diagrams, bar charts, frequency tables and possibly others as well.
By referring back to my hypothesis I said that I thought that as a person’s height increases, so does their weight. This should be quite simple to recognize if I draw up scatter diagrams of the overall sample. The overall sample is looked at because I’m just looking for a common correlation for all of the data. This will be done using excel.
The scatter diagram shows that there is a clear trend between the height and weight of people in Mayfield High School. This shows my first idea to be correct. This graph doesn’t really show any anomalous results because any weight or height that seemed out of proportion I did not include in my investigation, instead I just found another candidate at random.
The next part of my hypothesis suggested that the year 11’s would be heavier and taller on average than the year 7’s.
This can be shown by getting the mean, mode and median for each year group, and also the genders in each year group to see what this shows us.
Weights: (all figures with decimals have been given to 2 decimal places)
Year 11 male mean: 67.71 kg Year 11 female mean: 49.88 kg
Year 11 male median: 67 kg Year 11 female median: 48 kg
Year 11 male mode: 72 kg Year 11 female mode: 48 kg
Year 11 male standard deviation: 9.14 kg Year 11 female standard deviation: 7.75kg
Year 7 male mean: 42.77 kg Year 7 female mean: 45.10 kg
Year 7 male: median: 40 kg Year 7 female median: 44 kg
Year 7 male mode: 38 kg Year 7 female mode: 38 kg
Year 7 male standard deviation: 8.59 kg Year 7 female standard deviation: 6.80 kg
The average weight for the male of year 11 is 67.71kg; its median is very close to this. However it is surprising that the mode is 72kg. I would have thought that this figure would have been closer to the mean. The year 7 males, year 7 females and year 11 females all show more or less the same type of data.
The information clearly shows that the students in year 11 weigh more than the students in year 7. However the boys have a much large variation between year 11 and year 7 than the girls do.
The same thing is now to be done with the heights:
Heights: (all figures with decimals have been given to 2 decimal places)
Year 11 male mean: 1.73m Year 11 female mean: 1.66m
Year 11 male median: 1.75m Year 11 female median: 1.64m
Year 11 male mode: n/a Year 11 female mode: 1.6m
Year 11 male standard deviation: 0.08m Year 11 female standard deviation: 0.10m
Year 7 male mean: 1.48m Year 7 female mean: 1.61m
Year 7 male median: 1.52m Year 7 female median: 1.60m
Year 7 male mode: 1.54m Year 7 female mode: 1.59m
Year 7 male standard deviation: 0.08m Year 7 female standard deviation: 0.10m
From the information above we can seen that the average height of the year 11 males is 1.73m, this is close to the median which is a measure of the middle of the data. The mode was not found for Year 11 males because there was height which occurred more than once. The standard deviation of 0.08m says that there is not much variance in the spread of data which is gathered from the mean of the data. Most of the females in year 11 had a height of 1.6m and their average height was 1.66m, the middle height of the sample was 1.64m. The year 7 males had an average height of 1.48m and the middle height was 1.52m which is more than average. The year 7 female average height was 1.61m and the middle height was just below this at 1.60m, the most common year 7 female height was 1.59m. The standard deviation is actually not that much use.
This set of data is rather interesting. It shows that males in year 11 are taller than those in year 7, and also that the females are. Yet once again the difference between the year groups is wider in the males than the females. A very interesting point is that the year 7 females, according to my sample are actually taller than the year 7 males, something which disagrees with my hypothesis which said that the males in both the year groups being investigated would be heavier and taller.
I‘m now going to draw frequency tables to show the amounts of people with different heights or weights in the two year groups.
Year 11 males and females: Year 11 males and females:
Year 11 males and females: Year 11 males and females:
This may be clearer to read in the form of bar charts. I used excel to produce these.
The frequency tables and bar charts help me to see if my hypothesis was correct or not. I said that I believed that in the older year of students that there would be less variation between their heights and weights. According to the frequency tables and bar charts the year 11 students has a smaller variation in terms of height, this is shown because there are less categories in the year 11 table and graph than there is the in the year 7 table and graph for height. This is also backed up by something which is known as the range which is the highest value minus the lowest value.
Year 7 height range: 1.79 – 1.3 = 0.49m
Year 11 height range: 1.81 – 1.53 = 0.28m
This means that my hypothesis regarding height was correct, the older students have less variation in height.
Now I want to see if my hypothesis is correct regarding the weight. By looking at my weight frequency tables and bar chart this implies that there is actually more variation in weight in year 11 than there is in the year 7 students. This is clear because there are more categories in the year 11 frequency table and bar chart. Just to verify this I will look at the ranges for the weights of the year 11’s and year 7’s.
Year 7 weight range: 56 – 32 = 24kg
Year 11 weight range: 72 – 42= 30kg
So even thought my hypothesis was right in saying that the height is less variable in year 11, this is actually the opposite for weight. In essence this means that from this point of view my hypothesis was incorrect.
So far I have investigated the things discussed in my hypothesis and said whether they are correct or incorrect.
The last thing in this section of part one is two draw four scatter diagrams, one for year 11 males weights and heights, one for year 11 females weights and heights and the same for the year 7. This will then have a line of best fit drawn on to it which will mean that a good estimation can be given for either the height or weight when only one of these details is known. (All of these to be produced using excel.)
Year 11 males:
A line of best fit has been drawn. If we are given a weight of 60kg we can predict the height by drawing a vertical line up to the best fit from the point where it says 60. Then a horizontal line should be drawn across. This is what the height would approximately be. The dashed line on the graph shows this. Of course this can be done if a height is given as well. With a weight of 60 kg, a person would be a height of around 1.75m.
The same thing can be done using this graph. If a girl were 1.75m tall then her weight would approximately be 56kg.
This page just gives two scatter diagrams, similar to those above but they are for the year 7’s.
Example: If the weight = 40 kg, the average male in year 7 would be 1.47m tall.
This graph also shows that there is a positive correlation between height and weight for the males of year 7 even though there is still quite a variation between the heights and weights. However interestingly, there are 5 males who have similar heights and weights.
The graph above shows the strongest correlation between height and weight; hence this also means that the year 7 females do not have great variation in terms of each other’s heights and weights.
Example: If height was = to 1.75 m, using the line of best fit it can be seen that the weight would = 52 kg
Conclusion of part one
In this investigation I have seen that there is a very strong correlation between heights and weights, in both year groups, for both genders. However there was a much stronger correlation for the year 7’s, especially the females. This actually means that there is much more variation in heights and weights in year 11 than in year 7, this goes in against my hypothesis which said that I thought the year 11’s would have less variation in heights and weights. This is incorrect. I also said that I thought that in all cases, the males would weigh more and also be taller. By looking at the mean heights and weights I can see if this is correct or not:
Mean:
year 7 male weight: 42.77 kg year 7 female: 45.10 kg
year 7 male height: 1.48m Year 7 female: 1.61m
year 11 male weight: 67.71 kg year 11 female mean: 49.88 kg
year 11 male height: 1.73m year 11 female mean: 1.66m
Surprisingly in year 7 the females average for height and weight is more than the males. This may have been down to picking very tall and heavy females at random in the beginning. This means my hypothesis was incorrect here as well. But in year 11 the male average height and weight was bigger than the females. Perhaps it would have been a better idea to take a larger sample size, to reflect a bigger picture.
Overall though I do believe this investigation went quite well. Other possibilities could have been to investigate the height and weight of students in all the year groups, or even carry out other investigation such as comparing weight with the amount of hours of TV that is watched. I couldn’t have made my results any fairer though because I did a completely random sample, hence there was no biased results. I could have used other diagrams to present my data, however in saying this I think I used the clearest and most precise methods and there would have been no point in including extra diagrams just or the sake of it. Also, I think it would have made more sense to investigate the same number of people from each category because then it would have been even fairer as you will have been contrasting the same number of people rather than the same percentage of people.
Part two; Investigating left handed people and IQ
In this second part of this coursework I have chosen to investigate the relationship between left handed people and their IQ. There is much speculation whether or not people who are left handed are more intelligent than those who are right handed. I will just be investigating the students in year 10 for this investigation, as a mix in year groups could give an unfair set of results.
Specific task:
I will be investigating the correlation between left handed people and their IQ’s in year 10, and contrast this with the IQ’s of those students who are right-handed. Also I will take it further by seeing if there is any difference in IQ between right or left handed females against that of the males.
Hypothesis:
I believe that there will be no correlation between left handed people and IQ. This is because I think that the old wives tale, which says left-handed people are more intelligent, is nonsense. I also believe that there will be approximately the same IQ’s shown with males and females whether they are right or left handed.
Investigation:
Even though this task is to investigate correlation between IQ and which hand is used most frequently, I still believe that the numbers of males and females investigated should be the same, just to avoid any bias in the overall results. This doesn’t mean to say that I believe there is any difference between male IQ and female IQ, it’s just a precautionary measure to try to ensure that the results I get at the end are as fair as possible.
I worked all this information out more easily with the use of the sort tool that excel has.
Above there are four different categories, I’ve decided to investigate 15 students from each one, hence having a total sample size of 60 students.
Just as in part one, I will not use my scientific calculator to get the students who I will investigate at random. I pressed shift followed by ran# and then times. Due to the fact I sorted the ks4 part of the spreadsheet by year group, then gender and then right/left handed the numbers of the candidates have changed.
This however will not really make any difference; in fact it will just make the sampling process easier. The random process was done by the formulae listed below:
Year 10 right handed females: ran# x 95
Year 10 left handed females: ran# x 19
Year 10 right handed males: ran# x 201
Year 10 left handed males: ran# x 124
In each of these cases it was likely that on occasions I would get a random number that applied for a different category, this is down to my functions being cumulative. However in these cases I just repeated the random function until I got the correct category.
Here are the results of the random functions:
Of course I had to round when decimals came up on he calculator (which happened 100% of the time).
Plan of action:
Now I have collected my data, I need to use it to investigate the subject at hand and display and say what they show, and why they show it.
Firstly I am going to just investigate right-handed students and their IQ’s and left-handed students IQ’s without bringing gender into it.
The mean IQ for left-handed students in year 10 is: 104.1
The mean IQ for right-handed students in year 10 is: 100
The median IQ for left handed students in year 10 is: 103.5
The median IQ for right-handed students in year 10 is: 101
The mode IQ for left-handed students in year 10 is: 96
The mode IQ for right-handed students in year 10 is: 103
Standard deviation for left-handed students in year 10 is: 11.14
Standard deviation for right-handed students in year 10 is: 8.92
The information above, gives no clear sign that either right handed people or left handed people are more intelligent (hence have a higher IQ). The difference between the mean, median, mode and standard deviation is minimal between right or left handed students. However in saying this for the mean and median the left handed students do have a higher IQ but the most common IQ for left handed students of 96 is lower than that of the right handed students. This doesn’t really show any clear message either way.
However I’m going to draw up frequency tables and bar charts/frequency graphs to see if the data can give a clearer message.
These frequency tables and charts show that the right handed students have less variation in term of their IQ. The left handed students seem to have more extreme ends of the spectrum, hence yes there are left handed people in the sample who have a much higher IQ than that in comparison to the right handed students, but at the same time there are also students who have a much lower IQ than any of the right handed students.
This part of my second investigation is now complete. I cannot really see any clear correlation between what hand people use most frequency and their IQ’s, based on this alone I think that the idea that left handed people are more intelligent than that of right handed people is simply not true.
Now I’m going to basically do the same thing, but this time I’m going to break it down into genders to see if this has any affect any my results.
The mean IQ for male left-handed students in year 10 is: 105.87
The mean IQ for female left-handed students in year 10 is: 102.33
The mean IQ for male right-handed students in year 10 is: 99.4
The mean IQ for female right-handed students in year 10 is: 101.6
The median IQ for male left handed students in year 10 is: 104
The median IQ for female left-handed students in year 10 is: 103
The median IQ for male right handed students in year 10 is: 103
The median IQ for female right-handed students in year 10 is: 100
The mode IQ for male left-handed students in year 10 is: 96
The mode IQ for female left-handed students in year 10 is: 94
The mode IQ for male right-handed students in year 10 is: 103
The mode IQ for female right-handed students in year 10 is: 94
Standard deviation for male left-handed students in year 10 is: 12.16
Standard deviation for female left-handed students in year 10 is: 10.13
Standard deviation for male right-handed students in year 10 is: 7.24
Standard deviation for female right-handed students in year 10 is: 10.49
Once again, as expected from the data above there seems to be no significant variation in IQ due to either gender or which handed the students are. I do not believe that there is any reason to draw up tables or graphs in this section because I can see from the data already that there is no point because there is no correlation appearing.
Conclusion
In conclusion I think this second part probably went better than the first part. This is due to the fact that I had learnt how to carry things out effectively from part one, so when it came to part two it was easy. My hypothesis for this section was correct in all cases because I said that I didn’t believe that IQ was determined by hand uses. In this case I think the sample size was big enough, unlike in part one where I felt a bigger sample would have been more helpful for my investigation. Other investigations that could have been carried out include comparing hair colour with IQ, comparing hair colour and IQ results and many more. All in all, I think my investigation went well, but there could still be improvemens made such as using a wider variety of methods to present my data. Yet in saying this I still think my data was presented precisely and efficiently.
