# Mayfield School Mathematics Statistics Coursework

Extracts from this document...

Introduction

Is there a link

between ability in Maths and ability in Science?

Introduction

I would like to know whether there is a link between ability in Maths and in Science in the Year 7, 8 and 9 students at Mayfield High School. My initial thoughts are that there is a link between the two because Maths and Science share some of the same attributes - they both involve formulae, they both require logical ability, and they both use numbers. Furthermore, I think that someone with an interest in Maths will also have an interest in Science, and so will probably work hard at both.

Data Collection

To investigate this link, I will use the Key Stage 2 results from the Mayfield High School database. There are 813 Year 7, 8 and 9 students listed in the database, so to save time I will base my investigation on a sample of 30 of these students.

Bias is anything that occurs when taking a sample that might prevent the sample from being a true representation of its parent population. To avoid bias, I will ensure that my selection of the sample is completely random. To ensure a random selection, I will use a random number generator on my calculator. In the database, the students are numbered from 1 to 813. As the random numbers appear on my calculator, I will record the associated data in two or three tables, once for all 30 students, one just for males and one just for females. I have decided to do this as I suspect that any link between ability in Maths and in Science may also in turn be linked to gender.

Middle

Females

11

9

11

9

9

11

[Table 8: Male/Female Stratified Sample]

Now that I know the number of males and females that I want in my sample of 20 from each year group, I will collect my data. To do so, I will use the same strategy as earlier in my investigation; I will generate the required number of random numbers on my calculator and then record the associated data in a set of tables.

I now have the data shown in appendix C at the rear of this project.

Analysis (2)

To ascertain whether the link between ability in Maths and in Science varies with each year group, I need to identify the strength of the relationship between these subjects in each of the year groups. Looking back through my previous analysis, I therefore feel that the most efficient method to once again adopt is the calculation of the productmoment correlation coefficient for each year group and then compare these.

So, to extend my analysis in such a manner, I will now carry out the required calculations for my new set of data. Below is a table to show the result of my calculations:

Product-Moment Correlation Coefficient | ||||

Year 7 | Year 8 | Year 9 | ||

0.61 | 0.74 | 10.85 | ||

[Table 9: Year 7/ 8/ 9 Product-Moment Correlation Coefficients]

As we know from before, the calculation of the product-moment correlation coefficient is such that it will lie between 1 and -1, with 1

meaning that there is perfect positive correlation, 0 no correlation and -1 perfect negative correlation. From the above values, we can clearly see that, on the basis of a stratified sample of 20, the link between ability in Maths and ability in Science is greater in Year 9, than in Year 8 and in turn, than in Year 7.

Conclusion

5

5

4

5

4

4

4

3

3

4

Appendix B

Calculations For Table 8:

Year 7 Males Stratified Sample = (151/282) x 20 =11

Year 7 Females Stratified Sample = (131/282) x 20 = 9

Year 8 Males Stratified Sample = (145/270) x 20 =11

Year 8 Females Stratified Sample = (125/270) x 20= 9

Year 9 Males Stratified Sample = (118/261) x 20 = 9

Year 9 Females Stratified Sample = (143/261) x 20 =11

Calculations For Tables 1 and 2:

Mixed Maths x | Frequency (f) | fz | fx |

2 3 4 5 | 2 5 13 9 | 4 15 52 45 | 8 45 208 225 |

29 | 116 | 486 |

Mixed Science (y) | Frequency (f) | fy | fy2 |

2 3 4 5 | 2 3 12 12 | 4 9 48 60 | 8 27 192 300 |

29 | 121 | 527 |

Calculations For Tables 3 and 4:

Males Maths (x) | Frequency (f) | fx | fx2 |

2 3 4 5 | 1 2 6 6 | 2 6 24 30 | 4 18 96 150 |

15 | 62 | 268 |

Males Science (y) | Frequency (f) | fy | fy2 |

2 3 4 5 | 1 1 7 6 | 2 3 28 30 | 4 9 112 150 |

15 | 63 | 275 |

Calculations For Tables 3 and 4:

Females Maths (x) | Frequency (f) | fx | fx2 |

2 3 4 5 | 1 3 7 3 | 2 9 28 15 | 4 27 112 75 |

14 | 54 | 218 |

Females Science | Frequency | fy | fy2 |

2 3 4 5 | 1 2 5 6 | 2 6 20 30 | 4 18 80 150 |

14 | 58 | 252 |

## Appendix C

Year 7 | ||

Maths | Science | |

## Males | 4 4 5 4 3 4 5 3 4 5 4 | 4 4 4 4 3 3 5 4 4 5 4 |

## Females | 3 5 4 5 4 4 4 4 5 | 4 5 4 4 4 4 5 4 5 |

Year 8 | ||

Maths | ## Science | |

## Males | 4 4 4 5 5 5 4 4 5 4 5 | 4 3 4 5 5 5 5 4 5 4 5 |

## Females | 5 4 4 5 5 4 4 3 4 | 5 4 4 5 5 4 4 4 3 |

Year 9 | ||

Maths | ## Science | |

## Males | 4 4 4 5 4 4 5 5 4 | 4 3 4 5 4 5 5 5 4 |

## Females | 4 5 5 3 3 4 4 4 3 5 5 | 4 5 4 3 3 4 4 4 3 5 5 |

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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