Maths Coursework - Statistics Mayfield High School

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                                                                                                               Sonal Halai 11Q

Maths Coursework – Statistics

Mayfield High School

Introduction

My investigation will be based on information from Mayfield High School, a fictitious school. I will use a wide range of mathematical techniques to present my data and findings in different ways. I will explore two different hypotheses for this piece of coursework.

Hypothesis 1

I believe that ‘Girls are more intelligent than boys’. I predict that this investigation will prove that girls are more intelligent than boys. There are plenty of surveys that show that key stage 2 results are higher for girls than boys. With this hypothesis I will also investigate whether ‘IQ results are directly proportional to Key Stage 2 results’. I believe that as the IQ result increases the Key Stage 2 result will also increase.

Plan

By comparing the differences between two factors, for girls and boys, I will be able to determine which gender is more intelligent. The two factors I will compare are IQ results and Key Stage 2 results.

I will be using a random sample of 100 students - 50 boys and 50 girls. These 100 students will be selected randomly from year 7. I will then use this sample to analyse the information and make judgements about it. I will make graphs and charts to show my results, which I will use to draw my conclusions on my information. I will use cumulative frequency curves, frequency polygons and histograms to present my data.

To draw a cumulative frequency curve I will first need to make a cumulative frequency table. The cumulative frequency indicates how often a result was obtained which was less than or equal to a stated value in a collection of data. To draw a cumulative frequency curve for a set of grouped data you plot the upper boundary of each class of data against the cumulative frequency for that class. The cumulative frequency always goes on the vertical axis.

A frequency polygon is a line graph which shows the shape of a grouped frequency distribution. To draw a frequency polygon you plot the class mid-values against frequency.

A Histogram is just a bar chart where the bars can be of different widths. The height of the bar does not matter but the area. The vertical axis is always frequency density which can be worked out by:                                                                    

                           Frequency density= frequency/class interval width

The likely outcome for this hypothesis is that girls are in fact more intelligent than boys.

        For my second investigation I will take a quota sample of a 100 pupils from year 7. A quota sample is where you pick a sample which as far as possible reflects the whole population by having the same proportion of males and females, in this case. I will present my findings in a scatter graph because from it I will be able to find out if there is a relationship between IQ results and Key Stage 2 results.

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Processing

In order to obtain my sample, I did some stratified random sampling. This means that I took 50 boys and 50 girls form year 7, but used the random numbers generator on my calculator to pick which students would be selected for my sample. I did this so that the information I gathered would not be bias in any way.

The first thing I did was to find out the average mark from the key stage 2 results for boys and girls. I was left with the following results:

Mean results - boys KS2.

English

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