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ICT IN BIOLOGY

STATISTICS

Statistics are useful mathematical tools which are used to analyse data. Perhaps the best known statistic is the average. This is a single figure which is used to represent a set of data.

Averages

There are three types of average:

The median which is the middle value of a range of results.
The mode which is the value that appears the greatest number of times.
The mean which is the sum of all the results divided by the number of results.

Example: in the following set of data: 1; 3; 7; 10; 11; 12; 13; 13; 22; 23; 24

The median = 12 which is the 6th value when they are arranged in order.

The mode = 13

The mean = 139 ÷11 = 12,6

Note that if there are an even number of results the median is calculated by adding the middle two values and dividing by two.
Example: for the series 1; 2; 4; 5; 7; 9 the median = (4+5)/2 = 4.5

If all three averages are approximately the same we can usually assume that the data shows a “normal distribution” and the following tests can be used even for comparatively small samples (n<30).

Sampling

Remember the mean of the sample you have selected is not necessarily the mean of the whole population. Nor is it necessarily true that if the sample means taken from two different populations are different then the population means of each must be different. There is bound to be a natural variation. The tests below test whether the variation you obtain is actually greater than you might expect.

Predicting the Population Mean

We can never be sure that our sample mean is equal to the population mean but we can produce a confidence interval ie two numbers between which we are 95% certain that the population mean lies.

Standard deviation

The standard deviation is a measure of the variation of the results. For data that is evenly distributed each side of the mean (a normal distribution) 68% of the data lies within one standard deviation of the mean.

You can work this out on your TI 83 plus calculator as follows:

Use the key

Press

This gives you the STAT menu.

You will already be in the EDIT menu. Press

This opens a spread sheet

You can see if there is anything stored in the columns of the spread sheet. Check this and if there are data you need to clear it.

To clear the spread sheet

Press
You will be in the EDIT menu. Press
You will get “ClrList”
Press then

You have now cleared column L1
Repeat the process (, , , , etc….) to clear the other columns

To enter data

Press
You will be in the EDIT menu.
Select
This opens a spread sheet
type in the first number, then
second number then
etc

If you are comparing two sets of data do the same thing in column L2

To find out mean, median, standard deviation and more besides!

Press
Use the cursor to move across to the CALC menu
You will find a menu which permits you to calculate a large number of statistical parameters. Most of what we want is in 1:1-Var Stats. The first on the list.
Press
1-Var Stats appears
Press then and
You will get:

(the mean)

S_x (the standard deviation of the sample)

(the standard deviation of a population)

n (the number in the sample)

Scroll down for more!

minX	(the minimum value)
Q₁	(the first quartile)
Med	(the median)
Q₃	(the third quartile)
maxX	(the maximum value)

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