Investigating diversity

In a nutshell

Diversity can be investigated using new technology that provides insights at a molecular level. Variation can be investigated using mean and standard deviation.

Evolutionary relationships 

Technological advances have led to improvements in classification and the determination of evolutionary relationships. These advanced technologies allow scientists to more accurately estimate genetic diversity in a population.

Variation

Definition

Variation refers to the differences that exist between individuals of the same species or different species. There are different ways you can work out variation between samples and within samples.

Random sample

When studying variation of large populations, it would be too time-consuming to collect data from every individual. Therefore, scientists use samples as a model for the whole population. 

As the sample is used to make inferences about the whole population, it must be representative. To do this, the sample should be picked randomly and all results should be analysed using statistical tests. Both of these methods prevent bias and ensure the variation isn't due to chance.

Mean 

The mean, or the average, of the values can then be calculated to indicate if there is variation between samples.

Normally, there will be values either side of the mean, this creates a bell-shaped graph known as the normal distribution. A normal distribution is symmetrical around the mean. 

Standard deviation

Whilst the mean tells you about variation between samples, the standard deviation tells you about variation within a sample. A large standard deviation means the values in the sample vary a lot and the opposite is true for small standard deviations. 

The formula for standard deviation is:

​$$s=\sqrt{ {\sum (x-\overline x)^2}\over n-1}$$

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Example

Using the table, calculate the standard deviation of head circumferences of four newborn babies.

Work out the mean ($$\overline x$$):

$${{35 + 42+ 34+ 36} \over 4 }= 36.75$$

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Work out $$(x-\overline x)^2$$ for each baby:

​$$A: (35-36.75)^2 = 3.0625 \newline B: (42-36.75)^2 = 27.5625 \newline C: (34-36.75)^2 = 7.5625 \newline D: (36-36.75)^2 = 0.5625 \newline$$

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Find the sum: 

​$$3.0625+27.5625+7.5625+0.5625=38.75$$

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Divide by $$n-1$$:

$${38.75\over 4-1 }=12.91 \.{6}$$

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Square root:

​$$\sqrt{12.91\.{6}} =3.59$$​ 

​$$\underline{Therefore,\ the\ standard\ deviation\ of\ head\ circumference\ is\ 3.59\ cm.}$$​​