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  • Level: GCSE
  • Subject: Maths
  • Word count: 2758

Maths Coursework on IQ

Extracts from this document...

Introduction

Maths Coursework

Statistics

Year 10

Mayfield High School

Lucy Andrews

11SRH

SET 2

Intoduction

My aim is to investigate the relationship between the IQ and Key Stage results of a group of students.  I will show if there is any correlation between;

IQ and Key Stage Results in years 7, 8 and 9

If I find an outlier in any of my graphs, I will try and explain why it is there and see if my line of best fit fits better without it.

I will now conduct a pre-trial to test if there are, in fact, any of there correlations;

MASOOMA ABBAS                (male)                IQ – 101

KS2 – Eng-3                Maths-4                Sci-4

ZAHARA ABBOTT                (female)        IQ – 116

KS2 – Eng-5                Maths-5                Sci-5

image00.pngimage01.png

As you can see from the graphs on the previous page, there is some evidence of a correlation between the IQ and the KS2 results.  This is highlighted by Zahara’s IQ being noticeably higher than Masooma’s.  So too are her Key Stage 2 results.  I can conclude therefore that there is reason for me to continue with my tests.  The findings of the pre-test suggest a possible correlation between the IQ and Key Stage 2 results of these particular students and therefore makes my project worthwhile.

Throughout this coursework, I will be using stratified sampling.  In order to do this, I will divide the population into groups which have something in common.  Simple random samples will then be taken from each group.  The number taken from each group must be proportional to the size of the group.

...read more.

Middle

8

Aldridge

Kristina

3.33

8

Nedpod

Jane

Maria

4.00

8

Paine

Charlie

Bob

4.00

8

Rigby

Peter

Daniel

4.00

8

Mechin

Samantha

Louise

3.67

8

Matthews

David

4.33

8

Walker

David

3.67

8

Banken

Lilly

3.67

8

Blakely

Hayley

Henrieta

4.33

8

Kent

Shabnum

3.67

8

Leonard

Robert

3.67

8

Wood

Andrew

Raphael

4.33

8

Holliwell

Claire

4.33

8

Neelam

Kate

4.33

8

Peter

Zakir

4.33

8

Shane

Paul

4.67

9

Billard

Hailey

Billie

4.67

9

Martin

Lisa

3.67

9

Riters

Arthur

Maxwell

4.00

9

O'Neill

Krisila

Louise

4.00

9

Saleem

Adila

4.00

9

Malone

Kyle

4.00

9

Javi

Ursula

Maria

4.00

9

Sim

Emily

4.00

9

Dixon

Mary

Zeoy

4.00

9

Handergon

Ben

Peter

4.33

9

Vasel

Ricardo

4.00

9

Silverstone

Julie

Margaret

4.67

9

Tootill

William

Alex

4.33

9

Hall

Patrick

Conner

4.33

9

Billard

Hailey

Billie

4.67

9

Calg

Natalie

4.00

7

McMan

Kelly

Sue

4.67

7

Whitworth

Kayleigh

Marie

4.67

7

Connaugton

Nick

Michael

5.00

8

Hanten

Victoria

4.67

8

McMahon

Gaynor

Kimberley

5.00

8

Hall

Laura

5.00

8

Spencer

Kerry

Cassey

4.67

8

Dobson

Anthony

5.00

9

Brown

Caroline

Louise

4.67

9

Lewis

Rosie

Jane

4.67

9

Booth

Gary

4.67

9

Suggat

Bob

4.67

9

Holmes

Abby

Laura

5.00

9

Gorst

Lee

Mark

5.00

9

Langley

Sam

Adam

5.00

9

Munir

Asam

5.00

8

Shaw

Ian

Keith

5.67

9

Jasper

Elizabeth

Heather

6.00

It is clearly evidenced from this table that the Key Stage results of students in the first group are the lowest rising through the groups corresponding with the student’s rising IQ.  Therefore the child with the highest IQ, Elizabeth Jasper scoring 130, also has the highest average Key Stage results of 6.00.

It is obvious that the group 93-107 is much larger than the others.  To rectify this, I am going to split this group into two; 93-100 and 101-107.  This sub-division of the group will make it easier to draw a histogram.

It can be clearly seen from the scatter graphs that as the IQ increases, the Key Stage results also increase.  This shows a strong positive correlation between the two.  Year 9 is an excellent example.  There is one student with a high IQ of 130 and another with a low IQ of 69.  As my hypothesis suggests, the child with the higher IQ has a much higher Key Stage result than the boy with the lower IQ.  This concurs excellently with my earlier hypothesis.

The following histograms show the distribution of IQ and Key Stage results in the sample of the population.  I will have 6 bars.  These will be the groups mentioned earlier.  These groups will not be identical, as in order to detail the histogram I will need to change them as follows;

61.5                -        77.5

77.5                -        92.5

92.5                -        100.5

  1. -        107.5

107.5                -        122.5

122.5                -        131.5

IQ

Class

Class Width

Frequency

Frequency Density (Frequency/Class Width)

62-77

61.5-77.5

61.5-77.5 =16

2

2/16 =0.125

78-92

77.5-92.5

77.5-92.5 =15

10

10/15 =0.67

93-100

92.5-100.5

92.5-100.5 =8

29

29/8 =3.63

101-107

100.5-107.5

100.5-107.5 =7

27

27/7 =3.86

108-122

107.5-122.5

107.5-122.5 =15

15

15/15 =1

123-131

122.5-131.5

122.5-131.5 =9

2

2/9 =0.22

...read more.

Conclusion

Conclusion

I can finally conclude that there is a definite positive correlation between the IQ and Key Stage 2 results of these students.  My early hypothesis maintained that this would be the case.  The data collected and analysed supports this theory.  

The scatter graphs show that the Year 7 students have the smallest range of results and perform nearest to the average as indicated by the R-value.  The histograms indicate that the majority of students have an average IQ and that the same groups have the average Key Stage results.  The Cumulative Frequency Graph further supports this because the line is steep in the area of the average students and shallow in the area of the highest and lowest performers.

Finally, the standard deviation calculations show that there is some difference in the range of variation but that this is difficult to calculate accurately because the two areas are measured differently.

Given an opportunity to investigate further I would have liked to analyse the difference between the results achieved by boys vs. girls.  They might show a higher level for performance by girls.  

I mentioned earlier the issue of age in academic years affecting the figures.  I believe to improve the quality of my calculations it may be better to use actual age instead of academic years in any further work on this subject.

It has definitely been concluded that there is a positive correlation between the IQ of students and their Key Stage results in each class group.

...read more.

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