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8/14/2019 Variation is a Measure of the Differences
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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.