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  • Level: GCSE
  • Subject: Maths
  • Word count: 3434

I am going to investigate the relationship between the IQ and the Key Stage 2 results within this school. This will help me make and prove different hypothesis using the data I have obtained.

Extracts from this document...

Introduction

8Mayfield High School Maths Investigation The following data was provided for Mayfield High school. Year Group Boys Girls Total 7 151 131 282 8 145 125 270 9 118 143 261 10 106 94 200 11 84 86 170 Total 604 579 1183 I am going to investigate the relationship between the IQ and the Key Stage 2 results within this school. This will help me make and prove different hypothesis using the data I have obtained. The data I have been given presents the Key Stage 2 results in three separate columns, maths, English and science, I will add the three results together to give me one number, this will make them easier to handle. I will first take a random stratified sample of my data throughout the whole school of 100 boys and 100 girls; I will take a sample of 100 as this number allows me to make sufficient conclusions without there being too little to conclude anything or too high that it would take too long. First I will investigate IQ and KS2 results throughout all the years of the school then I will investigate the relationships separately amongst males and females. I will take a random stratified sample. My sample size will be 100. I have chosen to take a stratified sample as this method takes around about the correct proportion of students according to how many there are compared with the rest of the school so the investigation is fair. The total number of students in the school is 1183. In a stratified sample, values are sampled from a particular group in proportion to the group's size within the whole school. Therefore, I will multiply 100 by the number o boys/girls in each 1183 Year group. The table below shows my results. I will now randomly select the correct number of boys/girls from each year group using the random number button on my calculator. ...read more.

Middle

IQ Frequency IQ Cumulative Frequency 70-80 1 70 up to but not including 81 1 81-90 3 70 up to but not including 91 4 91-100 19 70 up to but not including 101 23 101-110 16 70 up to but not including 111 39 111-120 9 70 up to but not including 121 48 121-130 1 70 up to but not including 131 49 131-140 0 70 up to but not including 141 49 IQ (Mixed) IQ Frequency IQ Cumulative Frequency 70-80 2 70 up to but not including 81 2 81-90 7 70 up to but not including 91 9 91-100 35 70 up to but not including 101 44 101-110 35 70 up to but not including 111 79 111-120 19 70 up to but not including 121 98 121-130 1 70 up to but not including 131 99 131-140 1 70 up to but not including 141 100 Fig. 8 is a cumulative frequency graph for IQ. Median LQ UQ IQR Mixed 101.5 95 108 13 Boys 102 95.5 108 12.25 Girls 101 95 108.5 13.5 The box - and - whisker diagrams (fig. 9) provide a very clear comparison of the different measures of spread. The box - and - whisker diagrams show that the boys' IQR is 2 less than the girls' IQR, suggesting that the boys have many results clustered about the median. This proves that the range is unreliable; as if the range was considered alone; we would conclude that the boys have many results spread out around the median. The IQR tells us that this s not the case. 28 girls have an IQ less than the boys' median (102). Therefore, 22 girls or 45% have an IQ above the boys' median. More than half of the girls' IQs are below the boys' median IQ. (Fig. 10) In general, boys have greater IQs (and therefore, greater totals of KS2 results) ...read more.

Conclusion

70 up to and including 121 27 121-130 0 71 up to and including 131 27 131-140 0 72 up to and including 141 27 The cumulative frequency graph shows: Median LQ UQ IQR Mixed 101.5 96 105 9 Boys 102.25 98.5 105 6.5 Girls 97 94 104.5 10.5 The IQR for the year 7 girls is quite a lot larger than that of the boys. This suggests that in year 7 girls' IQs are spread out across the median, while boys' IQs are quite clustered around it. This is quite similar to the results for the whole school. Although, the girls has a smaller range in that case, whereas here the IQR and range are larger than the boys' are. We can easily compare the measures of spread by looking at the box-and-whisker diagrams, fig. 18. There is a positive correlation between IQ and the total of KS2 results, like in the whole school. The higher the IQ a pupil has, the higher the total of their KS2 results. The points on the scatter diagram for girls (fig. 16i) are very slightly less dispersed about the line of best fit than for boys (fig. 6). This means that the correlation is better for girls and that boys' results vary more. This is the same as in the whole school. Again, gender affects the relationship between IQ and total of KS2 results, as the correlation is stronger when boys and girls are considered separately. I think that the relationship, within year 7 is linear. Fig. 19 shows in red how the relationship could be expressed as a curve, but it is extremely similar to the line of best fit. The cumulative frequency curves (fig. 17) show that there more girls with lower IQs than there are boys, even though my sample includes more boys than girls. Again, a larger sample would have been more representative of the school. I chose to ignore an anomalous value because it affected my line of best fit considerably. ...read more.

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