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  • Level: GCSE
  • Subject: Maths
  • Word count: 6320

Compare the connection between weight and hours spent watching TV, and IQ and TV watched.

Extracts from this document...

Introduction

Nirmal Vadgama 11.T

Ms Aslam

Introduction: I will be investigation several factors from the results obtained from my questionnaire asked in Dunraven High School this will be secondary data. I will also compare one hypothesis to Mayfield High School to see if I get similar results. The hypotheses I have decided to compare is the connection between weight and hours spent watching TV and IQ and TV watched. I am looking for the stronger connection between them this will be primary data

Hypothesis: I am interested in investigating:

  • The comparison of Key Stage 2 results in Dunraven high school and to see which haven similarities with each other (more correlation between Maths and Science than Maths and English or Science and English),
  • If female brunettes have a higher IQ than blonde females
  • If the number of hours watched per week affects a person’s weight.

I predict that there will be a stronger correlation between maths and science than maths and English or science and English. I also predict that boys are better at Maths and Science while girls are better at English. The reason why is because I have noticed this over the years, and would like to explore these factors to prove my point. I think that female brunettes are not necessarily more intelligent however; I do believe that the lower quartile of brunettes IQ will be greater than the lower quartile of blondes. I think that the heaviest person in my sample will have the most number of hours T.V watched and also, the higher the persons IQ, the less TV they will watch. I also think that there will be a stronger connection between the weight and the hours of TV watched.

image00.pngimage01.png

...read more.

Middle

213

9

100

47

Yr8

22

9

106

50

31

24

102

50

43

25

106

51

68

90

103

45

76

14

96

44

85

10

101

65

175

17

101

47

242

24

117

42

269

14

100

43

Yr9

15

13

90

60

21

30

100

49

35

20

100

42

41

50

99

52

53

26

100

48

63

10

98

54

89

8

100

47

124

8

98

41

249

15

94

50

Yr10

4

16

91

70

14

10

100

51

53

3

112

50

65

5

131

50

71

18

87

50

250

17

103

57

187

7

113

80

Yr11

18

40

108

47

28

20

91

73

44

18

110

67

52

20

101

50

71

14

103

52

116

35

97

60

I then drew stem-and-leaf diagrams for each column so that I could order the data and I could get a rough idea of the skew and so that I could find the median, the upper quartiles, the lower quartiles and the mode:

TVIQ

Stem

Leaf

Stem

Leaf

0

3 5 5 7 8 8 9 9

8

7

1

0 0|0 2 2 3 4 4 4 4 4 5|5 6 7 7 8 8 8 9

9

0 1 1 4 6 7 8 8 8|9

2

0 0|0 4 4 5 6

10

0 0 0 0 0 0 0 0 0|1 1 1 2 3 3 3 3 3 4|6 6 6 8

3

0 5

11

0 0 2 3 7

4

0

12

5

0

13

1

6

0= Mode

7

| = Lower quartile

8

| = Median

9

0

| = Upper quartile

Weight

Stem

Leaf

4

0 1 2 2 3 3 4 5 5 5|5 7 7 7 7 8 9 9

5

0 0|0 0 0 0 0 0 1 1 2 2|4 7

6

0 0 5 7

7

0 3

8

0

9

10

11

12

13

14

0

From the stem-and-leaf diagrams I can see that both TV and weight seem to be positively skewed which may suggest a correlation because they have roughly the same shape of distribution. Also I can see that in both the weight and TV data there is one single data value that is quite a lot bigger than the rest (outliers) and there is also an outlier in the IQ data but it is not as far away as in the other two. From the stem-and-leaf diagrams I can also see that the IQ data seems to be negatively skewed, but only slightly. And it also seems to be closer to the same shape as the TV data which may mean that TV and IQ have a stronger correlation which is the opposite of what I hypothesized.

Using the stem-and-leaf diagrams I found the median, the mode, the upper quartile and the lower quartile of each set of data:

Median

Mode

UQ

LQ

TV

15

14

20

10

IQ

100.5

100

105

98.5

Weight

50

50

53

45

I then found the inter-quartile range by subtracting the lower quartile from the upper quartile:

TV: 20-10      =10

IQ: 105-98.5  =6.5

Weight: 53-45=8

I then drew up a box plot for each set of data to get a clear view of how the data was spread using this information:

See graph paper 1 attached.

From the box plots I can see that the IQ data is positively skewed. It also has quite a small range compared to the other two data groups. The weight data could be either positively skewed or negatively skewed from the box plot and it has a very large range, the biggest out of the three. The TV data is almost symmetrical but it was a very big range even though most of the data is spread quite evenly otherwise. The TV and weight seem to be of a more similar shape than the IQ and TV. The range is so large for both TV and weight because of outliers. I then found out the outliers by finding all values greater or lower than 1.5 times the IQR:

TV: IQR=10x1.5=15        LQ=10-15=-5 - no small outliersUQ=20+15=35 40, 50 and 90

IQ: IQR=6.5x1.5=9.75        LQ=98.5-9.75=88.75 – 86        UQ=105+9.75=114.75 – 117 and 131

Weight: IQR=8x1.5=12        LQ=45-12=33 – no small outliers        UQ=53+12=65 – 67, 70, 73, 80 and 140

From this I can see that weight has the most outliers so it is the least accurate and the most spread out. This may make it difficult to compare it with TV because the outliers will affect the calculations.

I then drew up histograms for each set of data to see the shape of distribution clearly. To draw the histograms I needed to find out the frequency density, which is the frequency, divided by the class width. I chose classes of equal intervals of 10 except for the last class in each set because of the outliers:

Class

Frequency

Class Width

Frequency Density

0<x<10

8

10

8/10= 0.8

10<x<20

20

10

20/10= 2

20<x<30

7

10

7/10= 0.7

30<x<40

2

10

2/10= 0.2

40<x<100

3

60

3/60= 0.05

TV:

IQ:

Class

Frequency

Class Width

Frequency Density

80<x<90

1

10

1/10= 0.1

90<x<100

10

10

10/10= 1

100<x<110

23

10

23/10= 2.3

110<x<120

5

10

5/10= 0.5

120<x<140

1

20

1/20= 0.05

Weight:

Class

Frequency

Class Width

Frequency Density

40<x<50

18

10

18/10= 1.8

50<x<60

14

10

14/10= 1.4

60<x<70

4

10

4/10= 0.4

70<x<80

2

10

2/10= 0.2

80<x<150

2

70

2/70= 0.03

...read more.

Conclusion

There are many other factors which affect my results because if for instance a person with a high IQ watches a lot of TV they might be watching information programs so it depends on what type of TV is watched as well as the hours spent watching. Also someone may watch a lot of TV but they may also play a lot of sport, which might help them to stay fitter and weigh less so the data is very inconclusive. I may have been able to get more conclusive results if I had been able to use a larger sample, but because I am working alone with a limited amount of time I could only use a fairly small sample. Also the data I used was secondary data which I did not collect myself. The data may have been inaccurate or even false because there were some ridiculous quantities within the sample that might not have been correct. If I were to get more accurate results I would collect the data myself, although this would take a long time if I want to collect a large enough sample to make the investigation worthwhile.

I think it would be interesting to investigate the link between IQ and key stage 3 results and the link between amount of TV watched and key stage 3 results because it would be interesting to see if TV helps pupils to get better marks or stops them. I think it would also be interesting to investigate the link between weight and height because I think there should be quite strong positive correlation between the two.

...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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