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Extracts from this document...

Introduction

Joe hughes   maths coursework

Assessment-

Strand 1a   planning  5

1b  collecting 5

Strand 2a  Analysis  10

presentation

diagrams

2b  calculations 10

Strand 3 interpretations 10

total-40

• Structured work
• Clear diagrams
• Accurate calculations
• Reasons & explanations

Structured work

• introduction
• Question/hypothesis
• Sampling
• Display data
• Comparisons
• Correlation
• conclutions

Clear diagrams

Accurate calculations

• Pie charts
• Grouped frequency table
• histograms
• cumulative frequency plots-box and whisker-IQR
• Stem and leaf
• Frequency distributions
• Standard deviations
• Scatter graphs- equation of line-correlation-spearmans rank correlation co efficient

1.   Objective

To collect analyse and compare the heights and weights of boy and girl pupils in the year 10 and 11 at mayfield high school.

If i have time i would like to investigate any statistical relationships betwwen IQ level and height and or weight.

2. Plan

> My investigation is to take a representational sample of data from the 370 year 10 and year 11 pupil database provided and to use statistical methods to quantitively analyse relationships between years and genders.

> My priorety will be height, then weight then IQ data.

>i will tabulate my findings and where possible present that in graphical form for easy interprotations.

3. Specific aims

>To collect a resonable sample of pupil data, using a suitable sampling method.

>To compare gender differences for height using histogram and frequency polygon graphs, and by finding the range and three averages for each sub-group.

>To construct boy/girlheight cumulative frequency graphs for a box and whiskers group distrobution comparisons using inter quartile ranges.

Middle

5. collecting data

The data is secondary ( not primary because i would need to collect that myself) and is part of the whole mayfiled high school (with lots of fields) available on the internet.

This table shows the number of boys and girls for the two years in which I am interested in.

Since i am interested in gender, heights, weights, and IQ only, the remainder of the fields (except names) can be filtered out.

However this would still leave me with masses of data so in order to reduce this to a manageable style, i will take

sampler.

I will randomly pick samples from the spread sheet using the stratified random sample method. To avoid bids and ensure that pupils from different years and gender groups are equally represented.

My sample should be in excess of 109 to be realistic, but not so high, go to calculations too complex. I will comprimise 15%

which gets me the following numbers.

My sample data is as shown attached.

6. Representing data

The pie chart below shows the proportional breakdown of year 10 and 11 boys girls, based on.

I have decided to start by comparing boy/girl height. since height is a continuous variable i will need to produce tally tables with grouped class intervals for this purpose.

Conclusion

I will draw two scatter graphs, one for year 10, and one for year 11.

These two graphs show a good possative linear

correlation between height and weight, which

backs up my second hypothesis. the lines of

best fit can be drawn, to pass as close as possible

to all parts- although there are exceptional values which fall outside the general trend.

Whilst i could find the predicted height form weigh or vice versa using my graphs, it might be simpler to have an equation.

Any straight line has an equation, Y=MX+C When C is the vertical axis intercept.

M is the gradient or shape of the line.

the equations of my lines are-

Boys H =MW+C

Girls H =MW+C

I can use these to make a prediction e.g for boys weight _______ height______

girls weight________ height______

at first glance it appears that _______ have better correlation, ie less offsets, from my lines of best fit.

however i would like to quantify this- using spearmans rank correlation coefficient. this will be ranged from 0 for correlation to 1 for points and straight line (perfect correlation)

To reduce my correlations on year 11 first boys I will eventually do for all sub sectors.

Boy name height-rank and weight-rank  d d2

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girls name height-rank and weight-rank d d2

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12         This quantities my ''gut feeling'' since it shows boys with _____ correlation and girls with _____ correlation. (see statistics textbook page 176)

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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