Friday, 23 May 2014

The concept of normal distribution about a mean. Understanding mean and standard deviation as measures of variation within a sample. Candidates will not be required to calculate standard deviation in questions on written papers. Candidates should be able to analyse and interpret data relating to interspecific and intraspecific variation.

When figures get larger towards the mean with no bias left or right, the graph will have this shape:
The shape is known as a bell curve and the distribution of values is called 'normal distribution'.
If a graph has normal distribution, then 68% of the results will be within 1 standard deviation and 95% of results will be within 2 standard deviations:

Standard deviations are a measure of accurate data is; the scattering of data around the mean.

The more centrally (around the mean) scattered they are then the more accurate the data is. If data is really spread out and there is only a small proportion of the data that is near the mean then it will have a large standard deviation, and will not be good data to draw conclusions from.

To work out standard deviation you add together all the deviations and then divide this by the number of values minus one.

To work out a deviation, first find the mean then subtract the it from a value. This answer needs to be squared to eliminate negative numbers. Do this for each value and then add them up. Divide this number by the number of values minus one. Find the square root.

You don't actually need to be able to do this according to the mark scheme, but it would seem wise to learn it.

For example, if I have 1, 2 and 3 and I want to work out the standard deviation I first find the mean
This is done by adding up all the values and dividing by the number of values you have (3):
1+2+3= 6
Next you need to subtract the mean from each value and square the answer:
1-2= -1
-1 squared= 1
2-2= 0
0 squared= 0
3-2= 1
1 squared= 1
Then add together all these answers:
1+0+1= 2
Now divide this by the number of values (3) minus one:
2/2= 0
Now find the square root of this:
the square root of 0= 0
So here one standard deviation is zero.

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