Before I start my coursework assignment I will check the data for any mistakes that have been made. If I can make a sensible correction to incorrect data I will do this but if not, or it is incomplete I will delete the entire record of data for that student.
I will make sure my data is reliable and not biased by making sure that each member of the population is arranged randomly. So that they are not arranged or grouped together in any form before the sample is taken as this could make the sample become biased. Because if you had all the year groups or the males and females grouped together, your random numbers might only select data about just males in year 7 which would not be a good representative sample of all the students in Solent High School. I will also check that it does not systematically overstate or understate the true value of the variable or favour a particular result by going back and checking the data again to see if it is consistent.
The statistical diagrams, charts and graphs I am planning to draw are:
- Scatter diagrams - using ICT, which I hope will show me whether there is any relationship. If there is a relationship there will be positive or negative correlation between the two variables. I will be able to see at a glance the spread of results and see how it relates to my hypotheses.
I will do one scatter diagram for all the students and separate ones for boys and girls. This will help me check if the correlations are better if I separate vthem or leave them all together. I will also draw lines of best fit and use them to make some predictions.
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Box and whisker plot. – using ICT, which I hope me make graphical comparisons between the data sets and to measure the variation within parts of the IQ data set and KS2 data set.
- Cumulative frequency graphs
My list of random numbers
I used excel to find my list of random numbers for my investigation. I typed the formula and then I pressed enter.
This is a very good way of selecting a list of numbers at random to use in my investigation. I was able to use these to make up the list of numbers to select a sample of the data, which represented the population at Solent high school. By using a sample of the students I was able to gain information about the whole population of Solent high school, as the range of data showed
- females,
- males
- students from all year groups
- different levels of intelligence
- different Key Stage two results
These are the corrections I made to the data. I erased these pupils results because the IQ levels are incorrect and they are all missing a science KS2 result.
I have erased this students set of data
Scatter Diagram
There is definite positive correlation in the scatter diagram for all the students. This supports the hypothesis that pupils with higher IQ levels tend to have higher Key Stage 2 results. The scatter diagram produces a very clear distribution of results and a very distinctive picture emerges. Every result can be included into three broad areas, and these groups stand out on the graph. The first group are those people who attained 10 or less in there total KS2 result, this included 16 of the 17 students with the lowest IQ levels within the range of 84-94. These 16 students had an IQ level of no more than 94 and therefore resulting in a strong positive correlation between low IQ and low attainment. The group at the other end of this distribution, with students attaining a total KS2 result of 14 or more included 14 of the 17 students, which shows 82% with an IQ level of 107 or more. This results in another positive correlation of high IQ and high attainment. Another picture also emerges from the distribution, where an attainment level between 11 and 13 for total KS2 results included 22 of the students. These students all had an IQ between about 92- 107. Thereby showing the majority of the sample of 60 students had a range of IQ levels between 92- 107.
Females and males both have positive correlation. Among the males there is one outlier- the boy with an IQ level of 103 but a Total KS2 result of 10. Compared to the other results his IQ level is higher in comparison to his KS2 results.
9.0909 = 9.1 % (answer given in 1 decimal place) of the females attained a KS2 result of 9 or below.
11.4285 = 11.43 % (answer given in 2 decimal places) of the males attained a KS2 result of 9 or below.
Rounded to the nearest whole number this shows 9% of females and 11% of males attained a KS2 result of 9 or below. This does not support my original hypotheses that males have a higher IQ than females. But that there are more males achieving low attainment levels.
From the scatter diagrams line of best fit I can predict a KS2 result from an IQ level or vice versa. I have done this by using a pencil and a ruler to draw a horizontal line across from KS2 result 12 to the line of best fit and then down to the IQ level scale to predict the IQ level of a pupil.
There is not a very striking difference between the two scatter diagrams but it shows the predicted male IQ level for a KS2 result of 12 is 92, therefore slightly higher than the predicted female IQ level for the same grade which is 90.
Box and Whisker
The box and whisker plots show me that the median for males is about 102 for females about 101. This confirms that the males have a slightly higher IQ on average, as stated in the hypothesis. The male IQ levels are more variable since the Interquartile Range of the males is larger. The female has a larger range of 33 compared to a range of 30 for the males the IQ levels are about the same.
- For all the students the range was 117- 84 = 33
- For the male students the range was 116-86= 30
- For the female students the range was 117- 84 = 33
Second Hypothesis
‘Male students have a higher IQ on average than females’
I used excel to find the mean to calculate the mean from the list of numbers
I used the formula ∑x to check the calculation made by the computer.
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Mean for female IQ levels = 100.6818
Mean for male IQ levels = 100.7143
These results for the mean male and female IQ levels do not prove my hypothesis because the results are very similar. The mean of the male IQ is not considerably more than the mean for the females. So it does support the hypothesis that the males have a higher IQ level but it is not a conclusive finding because the results are very similar. If I was to do this investigation again I would use a larger sample of the population as this would make my results more accurate.