Maths Stats coursework

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Daniel Knevitt 10S        Statistics Coursework        Mr Andrews

Plan

I have stratified randomly students from a fictional school called Mayfield high and from my own (Framingham Earl High). All the sampled people are from year 10. I wanted to sample sixty students altogether but I had to do 61 because that is what my stratified sample came to.

I have sampled the number of hours of TV they watch per week and their key stage 2 SATs results. I emailed all the necessary people from my school and all the Mayfield high data was supplied to me.

I will be using these methods of comparing my data:

Mode – The most common or most popular data value it is sometimes called the modal value.

The mode is most useful when one value appears much more often than any other. If the data values are too varied, then the mode should not be used. It is the only average that can be used for qualitative (not numerical) data.

Median – To find the median of a set of data, put the values in order of size. The media is the middle value.

For larger sets of data the rule is n+1

                                     2

For sets of data that has an even number of values i.e. 10 than the median value is the difference between the 5th and 6th value.

Mean – To find the mean for a set of data you must, find the total of all the values then divide that by the total number of values.

Range – The range of a set of data is the biggest value take away the smallest. This measures the ‘spread’ of the data.

Lower quartile – The lower quartile is one quarter of the way through the data.

The rule is n+1

               4                

Upper quartile – The upper quartile is three quarters of the way through the data.

 The rule is n+1 × 3, or three times the lower quartile.

               4        

Interquartile range – The interquartile range is the upper quartile take away the lower quartile.

Box plots/Box and whisker diagrams – A way of showing the distribution of data. It shows the median and central half of the data. It also shows the range of data. It can be used to compare two or more sets of data.

Spearman’s coefficient of rank correlation – Spearman’s coefficient of rank correlation is a scale from minus one to positive one of which you can tell how strong the correlation of your positive or negative data is. It is measured on a table like this:

 

Scatter graphs – A scatter graph is a diagram that is used to see if there is a connection between two sets of data.

The equation of the line of best fit – The line of best fit is a strait line. The equation of a strait line can be written in the form of y=mx+c.

‘m’ is the gradient of the line.

‘c’ is the point where the line cuts the vertical axis.

To find the gradient choose two points that are far apart on the scatter graph, write down the vertical and horizontal difference between the two points.

Gradient = vertical difference

               horizontal change

Outliers – I will be removing these after I have drawn my box plots prevent myself from having any too extreme values which are mistakes and of which can give not a very accurate mean or Spearman’s coefficient of rank correlation. You class a value as an outlier if it is 1.5 times the interquartile range.

Hypothesis

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In this coursework I will be comparing:

  1. Year 10 boys generally watch more TV than year 10 girls.
  2. Girls total for their Key Stage 2 SATs results are generally higher than boys because they are much better at concentrating.
  3. Framingham Earl SATS results are similar to Mayfield highs results.
  4. People who watch more TV get lower total for their SATS results.

I have gathered my data fairly because I stratified randomly sixty year ten students from Mayfield High and my own using the ‘Random’ button on my calculator. I have sampled seventeen girls and ...

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