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Variation

Variation is a measure of the

differences between members ofthe same species.

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Where does variation come from?

Genetic origin: human blood group, eye

colour, Cepea shell colour

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Environmental factors e.g. spoken

language, ability to play a musical

instrument

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Combinationofbothofthese

e.g. height, weight, intelligence,

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Variation can be continuous or

discontinuous

Continuous: no clear demarcation

between groups, such as height, hair

colour, weight. Any groupings are

calculated artificially.

Discontinuous: each group is clearly

different, with no link between them, such

as blood group, gender, tongue-rolling

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Normal Distribution

Many forms of variation follow a pattern

called the normal distribution.

A mean value is calculated from the data.

The frequency of each data value is

plotted on a graph.

This pattern is symmetrical about themean, and the data values nearest to the

mean have the highest frequencies.

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So the graph has this shape:

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Investigating Variation

Hypothesis: Americans are fatter than

Europeans.

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There are two possible strategies to testthis hypothesis:

1. Weigh every American and every

European and compare the means of thedata.

2. Weigh some from each group (samples)

and test whether the samples aresignificantly different.

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Strategy 1 would take too much time and

be very difficult to complete, so Strategy 2

is the only reasonable option.

Samples must be taken in such as way as

to ensure randomness (avoiding bias)

and reliability (to reduce the effect of

anomalies).

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If the Americans really are fatter than

Europeans, we would say that they come

from a different population, one which

has a mean weight that is significantlyhigher than the mean weight of the

European population.

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That conclusion would be fine if you really

had measured every American and every

European, but if you have taken a sample

there will be anomalies and extremeresults.

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You need to be able to decide whether the

anomalies are

part of the normal spread of the data,

errors that have occurred as a result offaulty

technique or equipment

or whether the difference is more significant

(and the original hypothesis may be wrong).

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Standard Deviation

Standard deviation is a mathematically

calculated measure of the spread of the

data. Each data point is compared to the

mean value and the differences used tocalculate a single figure.

The greater the value of the standard

deviation, the greater the spread of thedata about the mean.