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  • Level: GCSE
  • Subject: Maths
  • Word count: 1652

Investigation in to the relationships between IQ results, Key stage 2 results and gender in secondary school students

Extracts from this document...

Introduction

98308.doc

Maths Coursework – Statistics

Introduction

We are going to investigate the relationships between IQ results, Key stage 2 results and gender in secondary school students. The school that we are using to gather information for our sample from, Mayfield, is a fictitious high school. However, the data that is presented is still based on a real school and real students.

Hypothesis

I predict that this investigation will prove that girls are more intelligent than boys. There are plenty of surveys that show that key stage 2 results are higher for girls than boys. Although these surveys may be questionable, as there would be some exceptions.

Plan

By comparing the differences between the 3 factors, for girls and boys, we will be able to determine which gender is more intelligent.

We will be using a random sample of 100 students – 50 boys and 50 girls. These 100 students will be selected randomly from year 7. We will then use this sample to analyse the information and make judgements about it. We will make graphs and charts to show our results, which we will use to draw our conclusions on our information.

...read more.

Middle

8

26

16

0

Percentages

0%

16%

52%

32%

0%

Mark (m)

M < 2

M < 3

M < 4

M < 5

M < 6

Cumulative frequency

0

8

34

50

50

For the boys’ Key stage 2 results, you can see from the graph that all three subjects were very close in the results that the students achieved. All three subjects had the same average level for the boys.

As you can see from the cumulative frequency table of results, most of the boys achieved a level 4 in all three subjects, which shows that the majority of boys do not excel in one particular subject.

The following table shows the chart with which I worked out class widths and frequencies for the histogram that shows the results for the boys’ IQ.

Class interval

Class width

Frequency

Frequency density

70 < m < 90

20

2

0.1

90 < m < 105

15

33

2.2

105 < m < 110

5

10

2

110 < m < 120

10

5

0.5

I decided to use these class intervals for the construction of this histogram because they were most appropriate. The first class width started at 70 because from the information that I had gathered previously did not show any boys that were achieving below this mark in their IQ. As there were not many people who were getting between 70 and 80 for their IQ results, I decided to make the interval slightly wider to 70 – 90 points.

I used the next interval because there were quite a few people who would be put into this interval. I thought it best to have one overall interval that held the majority of students.

I chose a small interval again for the next two because it seemed that they did not contain many students.

The average IQ result for the boys was 99.

The next thing we did was to find the average for the Girls’ Key stage 2 results.  Here is what we found:

English

5 + 5 + 5 + 5 + 5 + 5 + 4 + 4 + 4 + 4 + 5 + 4 + 4 + 5 + 4 + 4 + 3 + 3 + 4 + 3 + 5 + 5 + 4 + 5 + 4 + 4 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 4 + 5 + 3 + 5 + 4 + 4 + 5 + 3 + 5 + 5 + 5 + 5 + 4 + 5 + 5 + 5 + 4     = 215

215 = 4.3

50

Mean average girls’ English result is level 4

Maths

6 + 4 + 5 + 5 + 4 + 5 + 4 + 4 + 4 + 4 + 5 + 4 + 3 + 5 + 4 + 4 + 3 + 3 + 4 + 3 + 5 + 5 + 4 + 5 + 4 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 3 + 4 + 4 + 4 + 5 + 3 + 5 + 4 + 5 + 4 + 5 + 5 + 5 + 5 + 4     = 210

  1. = 4.2

      50

Mean average girls’ Maths result is level 4

Science

5 + 5 + 5 + 5 + 4 + 5 + 4 + 4 + 4 + 4 + 6 + 4 + 4 + 5 + 5 + 4 + 3 + 4 + 5 + 3 + 4 + 5 + 4 + 5 + 4 + 4 + 3 + 4 + 4 + 5 + 5 + 4 + 4 + 5 + 5 + 4 + 4 + 5 + 4 + 5 + 3 + 5 + 5 + 5 + 4 + 5 + 5 + 5 + 6 + 5     = 223

  1. = 4.56

 50

Mean average girls’ Science results is level 5

However, although the mean averages for the girls’ results say that the majority of girls are achieving level 4 in their key stage 2 results, if you compare this with the mode averages, then we get slightly different results.

The mode averages suggest that the majority of girls are achieving level 5 in their key stage 2 exams. (Excluding the maths results with which the average would still be level 4). The following tables show this:

Percentage and cumulative frequency tables for the girls’ Key stage 2 Results

English

Mark ( M )

2

3

4

5

6

Frequency

0

7

21

22

0

Percentages

0%

14%

42%

44%

0%

...read more.

Conclusion

Conclusion

The results that we gathered in general show that the girls from our sample are more intelligent that the boys. The girls are achieving higher key stage 2 results and higher IQ results. It is also true that the girls must put more effort into their studies in order for them to be achieving higher marks, and are therefore learning more rapidly because of this. I would like to stress that there were a few boys in our sample who did achieve above the average mark for their gender, but this was only a minority. The girls’ majority of results proved to be higher than the boys.

Therefore in conclusion, I would like to state that this does not always mean that girls are better than boys or vice versa, but that the majority of the girls would work harder to achieve good results than the boys.

Vseymour-hunt        Page         5/9/2007

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This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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