In this coursework I will be comparing:
- Year 10 boys generally watch more TV than year 10 girls.
- Girls total for their Key Stage 2 SATs results are generally higher than boys because they are much better at concentrating.
- Framingham Earl SATS results are similar to Mayfield highs results.
- People who watch more TV get lower total for their SATS results.
I have gathered my data fairly because I stratified randomly sixty year ten students from Mayfield High and my own using the ‘Random’ button on my calculator. I have sampled seventeen girls and nineteen boys from Mayfield high and thirteen boys and twelve girls from my own. Using the ‘Random’ button on the calculator was the most unbiased way I could think of sampling from my data.
Hypothesis 1
Year 10 boys generally watch more TV than girls.
These are the two sets of data I will be comparing:
Female
Range: 30
Male
Range: 64
As you can see the median, lower quartile, upper quartile and interquartile range have been marked on my results. I have used this information to draw box plots to compare the skew, concentration and to see which group watches more TV.
From these box plots I can tell:
- Men on average watch more TV than girls.
- The ‘Female’ box plots have a positive skew meaning that the people that match more than the median amount of TV are a lot more spaced out.
- The ‘Male’ box plot interquartile range has a negative skew meaning that people who watch less than the median amount of TV per week are a bit more spaced out than those who watch more than the median.
- The extreme upper plot on the male box plot might be a lot higher than it should be because there could have been a mistake in the email I received or a mistake in the data that I have been given. I will remove any outliers when I compare further these sets of data.
- The range for the male box plot is a lot more ‘spread’ compared to the female one, I do not know why this is.
Outliers
I have removed any outliers from my results they are highlighted in green. A value is classed as an outlier when it is 1.5 times the interquartile range. I have worked out that in men table any value below 8.6 or above the value of 57 is classed as an outlier and must be removed. In the female table any value below 4.5 or above the value of 36.75 is classed as an outlier and must be removed but there were no outliers above 36.75 in my data. This is the data that I have been left with.
Male
Range: 44
Range: 27
As you can see I have worked out again the median, lower quartile, upper quartile and the interquartile range again because it has obviously changed. I have used the information that I have been left to draw another box plot.
My new box plot doesn’t tell me a lot more than my last box plots did.
All it showed me that the men’s box plot was a bit more negatively skewed than it showed on the last box plots.
Conclusion
In this investigation I have found out:
- Men on average watch an amount of TV per week 2.179(4sf) times the amount girls do.
- It seams as though girls have other thing to do other than watch TV maybe they see TV as a last resort for boredom whilst boys it might be their first choice of entertainment.
Hypothesis 2
Girls total for their Key Stage 2 SATS results are generally higher than boys because they are much better at concentrating.
These are the two sets of data that I will be comparing:
Female
Range: 6
Male
Range: 6
As you can see the median, lower quartile, upper quartile and interquartile range have been marked on my results. I have used this information to draw box plots to compare the skew, concentration and to see if girls got better SATS results.
From my box plots I can tell:
- The male box plot has a very week negative skew.
- The female box plot has a very week positive skew.
- Men getting above the median total for KS2 SATS results got more similar results to those who get less than the median.
- Women getting below the median total for KS2 SATS results got more similar results than to those who got above.
Although there is an obvious difference between the two box plots they are also very similar because the scale is very small. They are similar because:
- The extreme lower values are exactly the same (both at 9.)
- The extreme upper values are exactly the same (both at 15.)
- The interquartile range on both of the box plots are at 3.
- Both got the same lower quartile (at 11) and upper quartile (at 14) values.
I have worked out that any values above 21 for the total of their KS2 SATS results in both tables is classed as an outlier but there are not any. I have also worked out that any value below 7.3 the total of their KS2 SATS results in both tables is classed as an outlier but there are not any to be removed.
Conclusion
There is not much to conclude from this investigation apart from that I was completely wrong in guessing that girls might get better KS2 SATS results than boys because my box plots show that there is hardily any difference between the boys and girls.
Hypothesis 3
Framingham Earl SATS results are similar to Mayfield highs results.
These are the two sets of data that I will be comparing:
Mayfield High
Range: 9
Framingham Earl High School
Range: 9
As you can see the median, lower quartile, upper quartile and interquartile range have been marked on my results. I have used this information to draw box plots to compare the skew, concentration and to see if Framingham Earl SATS results are similar to Mayfield highs results.
These box plots tell me:
- That Framingham Earl high school has a one mark higher median.
- Framingham Earl high school has a very weak negative skew meaning that people who got less than the median total SATS mark were more spread out than the ones above.
- Mayfield high school has a very week positive skew meaning that all the people that got more than the median total SATS mark were more spread out than the ones below. The people below a total of 12 total SATS mark got similar results.
Conclusion
I conclude that all my predictions were right for this hypothesis but I was anticipating that the Framingham Earl Tests results were a little bit better because Framingham earl high school is a very good school with good teachers. In a way I was right because the median for Framingham Earl was one SAT mark higher than the one of Mayfield high.
Hypothesis 4
People who watch more TV get lower total for their SATS results.
These are the results I will be comparing:
I have prepared two scatter graphs, one on the computer and one by hand just in case I have made any mistakes. I have also drawn a line of best fit.
To work out the line of best fit:
The equation is; y=mx+c
Remember, ‘m’ is the gradient of the line. ‘c’ is the point where the line cuts the vertical axis. ‘y’ and ’x’ are the names of the axis.
To find out the gradient, Gradient = vertical difference
horizontal change
So the equation of my line of best fit is;
y=mx+c
Gradient = vertical difference = 2 _ m= 0.0384615
horizontal change 52
y=0.0384615x+13
Spearman’s coefficient of rank correlation
For this I will need 10 different people to compare, I have chosen the extreme lower and the extreme upper person alphabetically and the lower and upper quartile person alphabetically and the median person. The people I have chosen are highlighted in pink.
Conclusion
I conclude for this hypothesis that watching more TV does affect your total for your KS2 SATS results but only on a very small scale. There are many other factors that can affect your KS2 SATS results. Here are some of those factors:
- What you watch on TV because some programs are educational and are specifically for helping you with your tests.
- Your natural IQ can affect your results because some people are naturally bright and they think in different ways.
- Your upbringing can affect your results because some parents do not believe in SATS tests and they do not encourage their son/daughter to do well in them.