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  • Level: GCSE
  • Subject: Maths
  • Word count: 2387

Comparing IQ at school.

Extracts from this document...

Introduction

Statistics

Hypothesis: I think, that the girls science results are better than the boys science results compared with their IQ, because girls are more intelligent in science than boys in year 11.

BOYS

Number

Science

IQ

1

1019

4

113

2

1020

5

105

3

1026

3

89

4

1033

4

106

5

1036

3

76

6

1027

5

119

7

1068

5

106

8

1065

4

101

9

1077

6

107

10

1075

5

103

11

1066

4

104

12

1122

4

104

13

1138

2

78

14

1135

5

127

15

1128

5

122

16

1043

5

110

17

1057

5

110

18

1085

5

124

19

1095

3

90

20

1086

3

97

21

1081

3

98

22

1076

3

102

23

1090

4

98

24

1130

3

89

25

1141

5

14

26

1124

5

110

27

1146

3

86

28

1140

5

107

29

1156

4

100

30

1157

3

101

GIRLS

Number

Science

IQ

1

1016

4

104

2

1023

4

102

3

1018

4

28

4

1017

4

26

5

1067

4

95

6

1070

4

112

7

1071

4

104

8

1087

3

92

9

1097

3

90

10

1031

4

98

11

1026

4

106

12

1136

5

106

13

1132

4

102

14

1137

5

107

15

1125

4

101

16

1082

3

187

17

1081

5

108

18

1037

3

91

19

1030

6

126

20

1047

4

104

21

1029

4

100

22

1046

5

110

23

1032

5

104

24

1140

4

100

25

1114

3

98

26

1105

4

100

27

1174

4

101

28

1180

4

88

29

1107

4

97

30

1127

4

104

I get these information about the students in Mayfield High School from the grid which shows the whole year 11 students. Altogether there are 84 boys and 86 girls which gives a total of 170 students.

I chose the numbers of boys and girls randomly by throwing two dices at the same time. For example at the boys table, the first number which is 1019.  I threw the two dices and one dice showed 6 and the other showed 3. I add them up and the answer was 9.  On the table of all the year 11 students (boys and girls) the number which starts 9 at the ending was the randomly chosen number.  I chose them all in the same way and the girls

too (up to 30 boys and 30 girls) randomly. Then I write down their science results in one column and their IQ in another column.

First I will calculate the find the frequency for the boys and girls of their science results. To have the results detailed and clear. I will draw a whisker box diagram, scatter graphs and other statistical diagrams to support my frequency results in the table below.

...read more.

Middle

||||||

7

28

5

||||||||||

12

60

6

|

1

6

Σf=30

Σfx=123

Mean ,Using the formula : x =  Σfx

                                                   Σf

                        4

Mode

                        5

Median

                            5

Range

                        4

GIRLS

Science Grade

x

Tally

Number of Students (Frequency)

f

fx

1

0

0

2

0

0

3

||||

5

15

4

||||||||||||||||

19

76

5

||||

5

25

6

|

1

6

Σf=30

Σfx=122

Mean ,Using the formula : x =  Σfx

                                                   Σf

                        4

Mode

                        4

Median

                            4

Range

                        5    

BOYS

IQ

Middle point of the class interval

x

Tally

Number of Students (Frequency)

f

fx

10IQ<20

15

|

1

15

20IQ<30

25

0

             0

30IQ<40

35

0

             0

40IQ<50

45

0

0

50IQ<60

55

0

0

60IQ<70

65

0

0

  70IQ<80

75

||

2

150

  80IQ<90

85

|||

3

255

  90IQ<100

95

||||

4

380

100IQ<110

105

|||||||||||

13

1365

110IQ<120

115

||||

4

460

120IQ<130

125

|||

3

375

Σf=30

Σfx=3000

Mean ,Using the formula : x =  Σfx

                                                   Σf

                        100

Model class

                  100IQ<110      

Median

                        94    

Range

            113            

GIRLS

IQ

x

Middle point of the class interval

x

Tally

Number of Students (Frequency)

f

fx

10IQ<20

15

0

0

20IQ<30

25

||

2

           50

30IQ<40

35

0

             0

40IQ<50

45

0

0

50IQ<60

55

0

0

60IQ<70

65

0

0

  70IQ

...read more.

Conclusion

Bar chart and Histogram

I have drawn the bar chart for Science grade attained among boys and girls, because these are discrete data. Histogram is more appropriate in the case of IQ because these are continuous data. From both these diagrams mean, mode and median can be calculated

Frequency polygon

From the frequency polygon I can find that the more number of boys the have value of IQ (115) than girls.

Stem and Leaf Diagram

I have drawn a stem and leaf diagram because IQ data are continuous and are grouped into class interval.

Stem and leaf diagram for IQ

Boys

Stem

Leaf

F

1

4

1

7

6  8

2

8

6  9  9

3

9

0  7  8  8

4

10

0  1  1  2  3  4  4  5  6  6  7  7

12

11

0  0  0  3  9

5

12

2  4  7

3

Girls

Stem

Leaf

F

2

6  8

1

8

8

2

9

0  1  2  5  7  8  8

3

10

0 0  0  1  1  2  2 4  4  4  4  4  6  6  7  8

3

11

0  2

12

12

6

5

18

7

3

Cumulative frequency table

Science Grade

Cumulative frequency

Boys

Girls

1

0

0

2

1

0

3

10

5

4

17

24

5

29

29

6

30

30

IQ

Cumulative frequency

Boys

Girls

15

1

0

25

0

2

75

3

0

85

6

4

95

10

11

105

23

27

115

27

29

125

30

30

Cumulative frequency graph

Cumulative frequency graph is more appropriate for IQ value rather than science grades.

 Because former are continuous data and latter are discrete data.

Science

Boys

Girls

Range

4

5

Interquartile range

1.8

0.9

IQ  

Boys

Girls

Range

113

100

Interquartile range

22

9

Interquartile range shows better value of dispersion because it eliminates the extreme values there by distorting the statistical inference. The data of the boys are widely dispersed. Range is not appropriate in this instance.

I have drawn Box and Whisker diagrams for  science and IQ.

Summary

The achievement of science grades are better among boys than girls because they have higher value of IQ. The conclusion is based on small samples and further analysis should be made considering larger samples. The samples should also test to show that it represents the true population by sampling techniques.

...read more.

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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