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# Mayfield High School Maths coursework

Extracts from this document...

Introduction

In this assignment I will be aiming to determine whether there is a connection between IQ and Key Stage 2 results. To establish whether there is a relationship,

I will be analysing data collected from Mayfield High School. The data that I am using ranges from students from year 7-9. There are 812 students at Mayfield School which gives me too much data, so I will use excel to filter it. I have only chosen the numerical data which are IQ and key stage 2 results. If I hadn’t filtered the data, there would have been too much to analyse, some of it irrelevant to my hypothesis and I wouldn’t have been able to examine the data accurately. Data such as hair colour had to have been left out because I am only looking at quantative data not qualitative data. I only need numerical data, which I can narrow down using maths statistics. I have included reference numbers, and have purified the data. The reference number will be important because I will use ran # on the calculator to generate numbers. I have used reference numbers, to get a range of results using random stratified sampling. This type of sampling will give me a number, which I will locate through my reference numbers that will have the random IQ’s and Average Ks2 results. An average key stage 2 result was generated so I can compare one number with the IQ, rather than comparing 3 numbers with the IQ which will give me a range of outcomes rather than just one. Therefore by using an average Key stage 2 result, it can be compared with the IQ easier. At the end of this investigation I will right a conclusion on the outcome of my results, and state whether my hypotheses where correct.

Middle

I have chosen the hypothesis “Boys are more intelligent than girls”, because this will enable me to find summary statistics such as the mean, median, mode, range and standard deviation. These statistics will therefore allow me to compare genders directly and obtain accurate results. For example, if the boys have a higher mean than the girls, than this suggests that the boys are more intelligent than girls which will therefore prove my first hypothesis correct. I am going to use the IQ scores to measure intelligence because it is used worldwide. The IQ will be the dependent variable, because IQ usually dictates the Key stage 2 result.

The reason why I chose the second hypothesis is because it will allow me to work out a bi-variate analysis, and I will be able to produce lines of best fit and scatter diagrams.

I will analyse my first hypothesis which is “Boys are more intelligent than girls” by finding out the following data;

I will draw Cumulative frequency (C.F) curves to enable me to find upper and lower quartiles, Inter Quartile Range (IQR) and also find the median. The drawing of the C.F curve will help me to draw the box plot. I am going to work out the mean, median and mode to compare the genders. I will produce a stem and leaf diagram to group the data, and make it easier to read and to give me a visual idea about the spread of the data. I will draw a box-and-whisker diagram to show the minimum and maximum values, the upper and lower quartiles and the medians for my data, as well as showing the spread and indicating skewness.

Conclusion

n

= √321992 – 101.6132

IQx | X2 |

∑x | ∑x2 |

= | = |

31

= √321992 – 10325.20177

31

= 7.85 (to 2 d.p)

IQ | Frequency |

70 ≤ IQ < 80 | 1 |

80 ≤ IQ < 90 | 1 |

90 ≤ IQ < 100 | 3 |

100 ≤ IQ < 110 | 4 |

110 ≤ IQ < 120 | 1 |

120 ≤ IQ < 130 | 1 |

The C.F curve will enable me to compare IQ’s on the same graph, and will help me to answer the following probability question,

“What is the probability a boy or girl has an IQ over 100?”

I will now draw a stem and leaf diagram to group the data, and make it easier to read and to give me a visual idea about the spread of the data.

From my stem and leaf diagram I can see that thee are three modal pointswhich are 97, 100 and 107.

“The higher the IQ the higher the average Key stage 2 result”

I will examine this hypothesis by drawing scatter diagrams as bi-variate data, finding the line of best fit and calculating the strength of the correlation by working out the PMCC.

I will now draw a scatter diagram for all pupils on the same graph.

On the x axis I will put the IQ because it is the independent variable because the IQ is what controls the Key stage 2 grade.

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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