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  • Level: GCSE
  • Subject: Maths
  • Word count: 5601

Investigation to find any relationships between IQ and key stage 2 results.

Extracts from this document...

Introduction

Aim - To find any relationships between IQ and key stage 2 results.

Hypotheses

1) Students with a high IQ will achieve high mark in their key stage 2 results.

2) Students with a low IQ will achieve a low mark in the key stage 2 results

3) Girls will achieve an overall better result than boys in the key stage 2 result.

4) Girls will on average have a higher IQ level than the boys.

The Data

I will need 40 students to compare and examine in my investigation. To get these students I will randomly choose 20 boys and 20 girls. I have chosen 20 students from each gender because it makes the investigation fairer. I have chosen 40 students overall because it gives a wide range of results to analyse. To record the data I hope to use different tables, charts and graphs. I will use these charts and tables to draw conclusions and the relationship between the students IQ and key stage 2 results.

Choosing Data

To retrieve the data about the students I downloaded the information from the internet. To choose the data that I obtained, I will randomly pick 20 girls and 20 boys by circling  their names and stating their IQ and key stage 2 results.

Results

I choose the following boys to examine -

Name  -  IQ  -  key stage results for English , Maths and Science  -  Average key stage result

  1. Stanley Adams        - 94       -  3-3-4   -  3
  2. Robbin Banks          - 103    -  4-5-4   -   4
  3. James Bentley         - 89       -  3-4-3   -  3
  4. Sammi Block           - 80       -  4-3-4   -  4
  5. Thomas Brown        - 84       - 3-3-3    -  3
  6. Edward Bugress      - 98       - 4-4-4    -  4
  7. Shawn Cook            - 116     - 6-6-6    -  6
  8. Dennis Blake           - 90       - 3-3-3    -  3
  9. Donald Dunne         - 104      - 4-5-4    -  4
  10. Daniel Fisher           - 90        - 3-3-3    -  3
  11. Billy Glintode          - 87        - 3-3-3    -  3
...read more.

Middle

80- 90

-

0

90 - 100

////////

8

100 - 110

//////////

10

110 - 120

//

2

120 - 130

-

0

The IQ level of the girls in the investigation shows me that most the girls have IQ’s between 91 and 110. The other two students have a higher IQ between 111 and 120. There are no girls in the level between 71-90 and 121-130.  

Stem and leaf graph

The stem and leaf diagram is another way of showing the average results of the students. The diagram below shows the IQ levels of the girls. The diagram is shown below -

         7 -

         8 -

         9 - 2, 2, 4, 6, 7

10 -0, 0, 0, 2, 2, 2, 3, 4, 4, 5, 5, 6, 9

        11 - 2, 7

        12 -

The stem and leaf diagram shows that most students have a IQ of about 100 to 109. The table also shows that the other students achieved an IQ between 90-99 and 110-119. The graph also shows that no students have IQ’s of between 70-80 or 120-129.

The graph below is a cumulative frequency graph for the girls. It shows that the average relationship of IQ and the key stage 2 results -

IQ levels

Frequency

< 100

8

100 - 110

18

111 - 120

20

I then calculated the median, lower quartile range, upper quartile, minimum and maximum. The results are as follows -

Median = 102

Lower Quartile = 97

Upper Quartile = 106

Minimum = 91

Maximum =120

Box and whiskers diagram

I then used a box and whiskers diagram to show the range of results. The graph is as follows -

The diagram shows the upper and lower quartile as well as the median.  The box and whiskers diagram is an easy way of finding the median of data. The median in this case is an IQ of 102.  

Joint Boys and Girls IQ

This tally chart shows the IQ levels of each student. However, the chart shows the joint IQ’s of both female and male genders.

IQ levels of student

Tally

Frequency

71 - 80

//

2

81- 90

//////

6

91 - 100

////////////

13

101 - 110

/////////////

14

111 - 120

////

4

121 - 130

/

1

The IQ level of the girls and boys shows that most students have an IQ level of between 81 and 110. The other students have an IQ between 111-130 and 71-80.

Stem and leaf graph

The stem and leaf diagram is another way of showing the average results of the students. The diagram below shows the IQ levels of the girls. The diagram is shown below -

         7 - 4

         8 - 0, 4, 4, 7, 9

         9 - 0, 0, 1, 2, 2, 4, 4, 6, 7, 8

10 -0, 0, 0, 0, 0, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 9

        11 - 0, 2, 6, 7

        12 - 2

This stem and leaf diagram for the boys and girls shows that the average IQ of boys and girls is between 100 and 109. This is the same as when graphs were made separately of boys and girls. However, this stem and leaf diagram also shows that many students also got an IQ of between 90-99. This was also true with the previous diagrams.

The graph below is a cumulative frequency graph for the boys. It shows the average relationship of IQ and the key stage 2 results -

IQ levels

Frequency

< 70

1

< 80    

7

< 90

17

< 100

32

< 110

36

< 120

39

< 130

40

I then calculated the median, lower quartile range, upper quartile, minimum and maximum. The results are as followers -

Median = 93

Lower Quartile = 84

Upper Quartile = 99

Minimum = 70

Maximum =99

From these results, I then formed a Box and whisker diagram. The graph is shown below -

The diagram shows me the upper and lower quartile as well as the median. The box and whiskers diagram is an easy way of finding the median of data. The median in this case is an IQ of 93. The graph above also shows me that the upper quartile is 84 and the lower quartile is 99.  

Bar Charts

English

Level achieved

Frequency

Level 2

1 student

Level 3

8 students

Level 4

20 students

Level 5

6 students

Level 6

2 students

The bar graph is an easy way to show what the 20 students achieved in their key stage 2 results.  The following graph shows the levels each student achieved in English -

This graph shows me that there is a big gap between any other levels and level 4. This shows that most students achieved level 4.  

Bar charts

Maths levels

Level achieved

Frequency

Level 2

1 student

Level 3

15 students

Level 4

19 students

Level 5

8 students

Level 6

3 students

The following graph shows the levels what each student achieved in Maths -

The above graph shows me that the majority of students achieved level 4 in Maths. This shows that most students could have achieved level 3 or 4.

Bar charts

Science levels

Level achieved

Frequency

Level 2

1 student

Level 3

11 students

Level 4

20 students

Level 5

5 students

Level 6

2 students

The following graph shows the levels that each student achieved in Science: -

The above graph shows me that the majority of students got a level 4 in science followed by level 3. I have seen this pattern in the last result and I conclude that the average result for these subjects is level 4.

Bar charts

Average levels

Level achieved

Frequency

Level 2

1 student

Level 3

13 students

Level 4

20 students

Level 5

4 students

Level 6

2 students

...read more.

Conclusion

To prove this I randomly picked 6 students, 3 boys and 3 girls. The students are shown below -

Girls

Samantha Dean        - 112     - 5-5-5     - 5

     Sara Slater                - 96       - 3-3-3     - 3

Jo Hamilton              - 105     - 5-5-4     - 5

Boys

     Matt Hawk               - 74        - 2-2-2    - 2

Stuart Gilroy            - 110      - 5-5-5    -  5

James Mcdonald      - 122      - 5-5-5    -  5

- The girls relationship was true for this rule as when Sara got a level 3 the line of best fit showed she should get an IQ of 96. This was also true with the other two students as Samantha and Jo both got level 5. The line of best fit showed me that at level 5 they should have an IQ of 110.

- This rule was also true for the boys, as Matt who got a low level 2 and therefore should have an IQ of about 70. This rule was also true for both Stuart and James. Both of these students achieved level 5, but they had a very different IQ level. The graph shows me that at a result of level 5 they should have had an IQ of 113. This shows me that James has a very high IQ level.

This proves that there is a positive relationship between the IQ and key stage 2 results.

Bibliography

For this report, I used various sources of information. I used the following to help me prepare this report.

Text Books

GCSE Mathematics – written by A Greer

GCSE Bitesize revision mathematics

People

Mr G Singh    - this person helped me with the report

Miss T Thanawala - this person helped me with some of the graphs.

Electronic

Electronic services also helped me with my report. This included the use of the internet. The websites used to get the information included: -

        -www.edcel.co.uk

        -www.mathsrevision.com

        -www.bbc.co.uk/education

In this report, I also used e-mail and fax services to help with my project.

And thanks to WWW.COURSEWORK.INFO.COM

Deepak Tailor

11GS

Beal High School

...read more.

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