# My hypothesis is that the Maths and Science results will be related because I think if a male/female is good at Maths he/she will also be good at Science.

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Introduction

For my second piece of coursework, I have being given 300 pieces of original data about students in an unknown school. This data includes year, gender, class and test results in English, Maths, Science and French. This data is too big to manage so I have decided to take a random sample of 30 students from each year. 15 females and 15 males.

I will look at each year group in turn and from there I will create a table of the numbers contained in each class, in each year group.

Year | Gender: Male | Female | Class |

8 | 14 | 12 | A |

8 | 14 | 11 | B |

8 | 13 | 8 | C |

8 | 14 | 10 | D |

8 | 9 | 15 | E |

Total | 56 | 64 | 120 in year 8 |

Year | Gender: Male | Female | Class |

9 | 10 | 17 | A |

9 | 10 | 16 | B |

9 | 12 | 5 | C |

9 | 6 | 4 | D |

Total | 42 | 38 | 80 in year 9 |

Year | Gender: Male | Female | Class |

10 | 5 | 20 | A |

10 | 16 | 10 | B |

10 | 14 | 10 | C |

10 | 13 | 12 | D |

Total | 48 | 52 | 100 in year 10 |

Check: -

Year 8 = 120

Year 9 = 80

Year 10 = 100

Total 300

Now I am going to select the 15 males and 15 females systematically.

My hypothesis is that the Maths and Science results will be related because I think if a male/female is good at Maths he/she will also be good at Science.

I am going to draw scatter graphs and frequency tables to see if there is a correlation between the Maths and Science.

Middle

0

95

0 × 95

0

I decided to use scatter graphs because they are the easiest diagrams to draw when comparing the Maths and Science results.

I have drawn a line of best fit because it allows me to predict a mark if a student misses a test.

Example:

A student in year 10 scored 60 in a recent maths test, but he/she missed a science test the day after. I predict that the student would score 63 in his/her science test if he/she were there.

I do this my going to the maths scores for Year 10 in my scatter graph and going to 60 and would then go up in a line and I would hit the line of best fit and go across and the mark is 63.

After looking at the graph for Year 8, I found that their marks were tightly packed together, which shows strong positive correlation.

After looking at the Year 9 and 10, I found that both their marks were tightly packed together, which again shows strong positive correlation.

I am going to examine each year group in turn and draw frequency tables for each year group and subject.

## Smallest and Largest values

Year 8 | Year 9 | Year 10 | |||

Maths | Science | Maths | Science | Maths | Science |

41 | 43 | 36 | 41 | 30 | 35 |

43 | 48 | 42 | 44 | 39 | 38 |

44 | 48 | 43 | 47 | 40 | 41 |

47 | 49 | 43 | 47 | 43 | 42 |

52 | 50 | 44 | 47 | 45 | 43 |

52 | 53 | 47 | 50 | 45 | 44 |

52 | 55 | 49 | 51 | 48 | 46 |

52 | 55 | 50 | 51 | 48 | 48 |

54 | 56 | 52 | 51 | 50 | 50 |

55 | 58 | 54 | 52 | 52 | 52 |

56 | 59 | 55 | 52 | 53 | 52 |

56 | 61 | 56 | 53 | 57 | 53 |

57 | 62 | 57 | 54 | 57 | 56 |

59 | 62 | 58 | 54 | 58 | 57 |

60 | 62 | 59 | 56 | 60 | 60 |

60 | 62 | 59 | 56 | 61 | 62 |

61 | 63 | 62 | 57 | 62 | 65 |

62 | 65 | 63 | 59 | 63 | 65 |

62 | 66 | 63 | 59 | 64 | 65 |

64 | 66 | 64 | 59 | 66 | 65 |

65 | 70 | 65 | 62 | 67 | 66 |

65 | 70 | 67 | 64 | 68 | 68 |

67 | 71 | 70 | 64 | 68 | 69 |

68 | 72 | 72 | 68 | 70 | 72 |

68 | 74 | 72 | 69 | 70 | 72 |

68 | 76 | 74 | 70 | 71 | 74 |

73 | 78 | 75 | 70 | 74 | 80 |

75 | 80 | 76 | 71 | 76 | 82 |

78 | 80 | 80 | 76 | 76 | 83 |

83 | 90 | 80 | 78 | 79 | 84 |

My results so far have confirmed my first hypothesis, which is that Maths and Science are closely linked.

## Second hypothesis

I will now investigate the differences in gender may effect the marks in a particular subject like Maths.

Again to further my investigate, I am going to use Stem and Leaf diagrams to compare female marks with male marks. A Stem and Leaf diagram consists of numbers, which themselves made up the bars, like in a bar chart. I have already systemically chosen a sample of 30 students from each year group, again 15 females and 15 males.

By doing this it avoids bias and will represent the complete data given. A Stem and Leaf diagram is used to display data in order of size. It can also be used to find the mode, median, lower quartile, upper quartile and interquartile range.

### Year 8 Maths

Females | Males | ||||||||||

30 | 40 | 50 | 60 | 70 | 80 | 30 | 40 | 50 | 60 | 70 | 80 |

43 | 52 | 60 | 73 | 41 | 52 | 60 | 78 | 83 | |||

52 | 62 | 75 | 44 | 55 | 61 | ||||||

52 | 64 | 47 | 56 | 62 | |||||||

54 | 65 | 59 | 67 | ||||||||

56 | 65 | 68 | |||||||||

57 | 68 | 68 |

Stem and Leaf

Females | Stem | Males | ||||||||||

30 | ||||||||||||

3 | 40 | 1 | 4 | 7 | ||||||||

7 | 6 | 4 | 2 | 2 | 2 | 50 | 2 | 5 | 6 | 9 | ||

8 | 5 | 5 | 4 | 2 | 0 | 60 | 0 | 1 | 2 | 7 | 8 | 8 |

5 | 3 | 70 | 8 | |||||||||

80 | 3 |

Females | Males | |

Mean | 59.3 | 60 |

Median | 60 | 60 |

Mode | 52 | 68 |

Range | 32 | 42 |

Conclusion

59.9

58.6

Median

64

58

Mode

45, 70

48, 57

Range

37

49

From this set of results I have noticed tat the girls in year 10 are better than the boys at Maths. For example the girls have achieved a higher mode, which is 45, 70 and the boys mode was 48, 57. They also had a higher mean and median.

I am now going to construct Box and Whisker diagrams, these will show the distribution of data.

First of all I will find the biggest and smallest values. Then I will put Year 8, 9 and 10 Maths and Science marks in order of size, starting from the smallest to the biggest, from here I will need to obtain each year groups median and lower and upper quartiles.

This box shows the Mean for each year group.

Year | Maths Mean | Science Mean |

8 | 60 | 63 |

9 | 60 | 58 |

10 | 59 | 57 |

From the results in the table above I can see that the means are quite close together.

#### Year 8

Maths | Science | |

Median | 60 | 62 |

Lower Quartile | 52 | 55 |

Upper Quartile | 67 | 71 |

Lowest Value | 41 | 43 |

Highest Value | 83 | 90 |

#### Year 9

Maths | Science | |

Median | 59 | 56 |

Lower Quartile | 50 | 51 |

Upper Quartile | 70 | 64 |

Lowest Value | 36 | 41 |

Highest Value | 80 | 78 |

#### Year 10

Maths | Science | |

Median | 61 | 62 |

Lower Quartile | 48 | 48 |

Upper Quartile | 68 | 69 |

Lowest Value | 30 | 35 |

Highest Value | 79 | 84 |

From the box plots I can see that Year 8 are slightly better at maths and science than Year 9 and 10.

Year | Maths Mean | Science Mean |

8 | 60 | 63 |

9 | 60 | 58 |

10 | 59 | 57 |

From the results above

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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