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Mayfield High School Maths Coursework

Extracts from this document...

Introduction

Mayfield High School Maths Coursework

My Hypothesis

        My first hypothesis which I have chosen to test is:-

THE HIGHER THE KS2 RESULTS OF STUDENTS, THE HIGHER THE IQ RESULTS ARE.

I have chosen this particular hypothesis because many students who tend to have a high IQ, have a high KS2 result too. I have also chosen this hypothesis because, many students at my school who have a high IQ tend to do well in their KS2 exams and get a high grade and therefore I would like to find this out for my-self.

        The data which I will be using to find out if my hypothesis is right or wrong will be from Mayfield High School. All the data that I will need will be provided for me at school on the computers. This data will include a range of different information on students from years 7-11.

Sampling

        For my hypothesis I will be choosing a sampling size. I have chosen my sample size to be 50, as it will be more accurate. Also using the sample size of 50 will give me a wider range of data and therefore help me with my hypothesis more. There are various samples, which can be used.

...read more.

Middle

99

4

4

4

100

4

4

4

92

3

3

3

92

4

3

3

96

3

3

3

106

5

5

5

103

5

4

4

100

4

4

4

103

4

4

5

100

4

4

4

98

4

4

5

92

3

3

4

My Graph

        From my samples I am going to create a graph. I have decided to do a scatter graph because; it will make it easier for me to see if my hypothesis is correct. It will make it easier for me see this, as all my points will be plotted on the graph and therefore it will give me a better understanding of my results and also a clear view of my correlation line. Below is my graph:-

image22.png

From the graph you can see that my hypothesis is correct. This is because as the IQ results are going higher, so are the KS2 results going higher. I think this because, the clever you are, the more intelligent you are, as you know many things and you can gain more marks. However, from the graph you can see that there is a strong positive correlation. We can see this because, as the KS2 results are going higher, the IQ goes higher too.

...read more.

Conclusion

                              Σxy     Σx  Σy

                             ------ - ----  ----

                                n        n      n

---------------------------------------------------------image05.pngimage06.png

          Σx²       Σx   ²                    Σy²       Σy    ²image07.pngimage08.png

        ------ -   ----          X          -----  -   -----    

n           n                           n          n          

Σ

SD =         Σ χ ²             Σ χ       ²        
               -------    -     -------                

         n                  n  

SD =         Σ y ²               Σ y          ²      
               -------    -      -------                

         n                  n  

Top of Yxy: - 21732      5125        98

                      -------  -  -------  x  ------ = 434.64 – (102.5 x 1.96) = 233.74

                       50            50           50

Bottom of Yxy: -

image09.png

    527838          5125     ²image11.png

  ------------  -    ---------      =  7.105631569image12.png

       50                 50        

                                        10556.74 – 10506.25 =    50.49

image13.png

  1. 98    ²

-------  -    -----     = 3.773380447

  50            50           image14.png

image15.png

                      18.08 – 3.8416 =    14.2384

Yxy = 2.33.74 / (7.105631569 x 3.773380447)

 Yxy = 2.3374 / 26.81225123

Yxy = 0.086900573

Yxy = 0.1 (1 D.P)

Conclusion

Conclusion for my product moment correlation coefficient

        From working out the standard deviation, I have concluded that my regression line has no correlation. This is because my end result which I got after working out the standard deviation my regression line was 0.0869… This therefore, shows that my regression line has no correlation. However, I am able to tell that my regression line is a positive because it is not a negative number. This shows that my hypothesis was correct, but it was not strongly proved, as my regression line was not a perfect correlation.

Overall, from the whole hypothesis I found that the higher the IQ results a student has and more likely they are going to have a higher KS2 result too. You are able to see this on my graph earlier in the work. This therefore proves my hypothesis to be correct.

...read more.

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