Sample size: 80 boys:44 girls:36
My sample size is 80. I am using stratified sampling so I need the following number of pupils who wear and don’t wear glasses.
22 boys who wear glasses 22 boys who don’t wear glasses
18 girls who wear glasses 18 girls who don’t wear glasses
I needed to pick these to get a fair and unbiased representation of the overall population. This method is fair as I am taking into account that there are more boys than girls in the overall population. I need to replicate this within my sample.
Some of the data in unreliable because test marks have omissions. To solve this problem I am going to replace these results. When I take my sample if I land on an inaccurate data I will use the one below to replace it and carry on. If I use the data with a mistake in it, it will give inaccurate results.
To take my sample I will roll a dice. The number it lands on is the data number I start on. I will continue to roll the dice and pick the sample in this way. I will stop when I get to the correct number of data I need for my sample. To make it easier for me I have sorted the data in a spreadsheet so they are separated by gender and then whether they wear glasses or not.
The range of my data for year 8 math’s exam results is: 281-67=214
The range of my data for year 9 math’s exam results is: 121-29=92
To find the model groups I found the most common test mark and which group it fitted in.
Model groups for yr 8 math’s exam results from pupils who wear glasses =212<m<235
Model groups for yr 8 math’s exam results from pupils who don’t wear glasses =69<m<92
Model groups for yr 9 math’s exam results from pupils who wear glasses =236<m<259
Model groups for yr 9 math’s exam results from pupils who don’t wear glasses =69<m<82
To find the averages I added up all of the marks and divided by the number of marks.
Mean for yr 8 glasses: 199.46=199
Mean for yr 8 no glasses: 191.25=191
Mean for yr 9 glasses: 83.07=84
Mean for yr 89 no glasses: 74.60=75
Average test mark for a pupil who wears glasses: 141.27=141
Average test mark for a pupil who doesn’t wear glasses: 132.93=133
From the cumulative frequency tables I can create cumulative frequency graphs and then use this information to find the Inter quartile range and the median. To find the inter quartile range I use this equation:
Q3-A1=IQR
Q2=median
By finding these I will be able to create box and whisker plots to compare the spread of the data.
Pie charts can also be created to see the spread of the data and how the sizes of data groups differ.
Conclusions and results
By comparing the pie charts I have found that for the yr 9 math’s result chart the 212<m<235 is the largest group for both glasses and no glasses.
From the yr 8 graphs I have found that the 212<m<235 is also the largest group of data for glasses and no glasses. These groups are both towards the higher end of the groups.
The box and whisker plots show that year 8 pupils who wear glasses has the highest inter quartile range, of 84, compared to rest of the population.
By comparing both the Yr 8 box and whisker plots you can see that pupils who wear glasses have a much higher inter quartile range of 84. A difference of 20 compared with the Yr 8 no glasses box and whisker plot.
The problem I wanted to try and solve was whether glasses have an effect on your overall math’s ability. My results clearly show that pupils who wear glasses have gained high-test results throughout two tests over two years. By calculating the overall averages of both years, I have found that the average mark for pupils who don’t wear glasses is 141 whereas a pupil who doesn’t wear glasses average score is 133.
Separately the results show that during the yr 8 tests pupils who wore glasses had a lower average test mark. One reason for this may be where each individual pupil sits in the class. If a pupil with glasses is sat towards the back of the classroom and unable to read the board then they could miss vital work. If not caught up on this could effect their test marks. The Year 9 test marks show the opposite, that pupils who wear glasses have a higher test mark.
The cumulative frequency graphs show that the curve on graph 1 is more shallow than graph 2. also that the median and upper quartile on graph 1 are much closer together resulting in a small box on the box and whisker plots.
Overall the data doesn’t show a clear pattern. Only when the data for year 8 and 9 are combined does the problem begin to be resolved. My calculations and finding show that wearing glasses does effect your math’s ability but this is only true for one year group in one school. this evidence doesn’t prove this point, it only gives you an idea about what the whole population may be like. It doesn’t prove the theory for the whole country or world.
I believe that my way of taking my sample was unbiased and effective. I had a true accurate figure of pupils in the same proportions as the total population of a year group. If I were to retake my sample I would rid of the anomalies before taking the sample because sometimes as you go through you miss out and then have to change it. I would also sort the data more thoroughly before taking my sample, as it was difficult to relate back to it when finding averages and doing other calculations.
Overall my investigation into glasses has shown that glasses can make a slight difference to a pupil’s math’s ability.
