Types of variation, causes and calculations

In a nutshell

Variation occurs between different species and individuals of the same species. It is influenced by both genetic and environmental factors. When investigating variation of a sample you must calculate the mean and standard deviation.

Variation

Definition

Variation is the differences that exist between individuals. There are two types of variation: intraspecific and interspecific.

Type of variation	Definition	Example
Intraspecific	Variation within a species.	Species of the Eurasian magpie show variation in length, wingspan, colour and beak size.
Interspecific	Variation between different species.	Species of the Eurasian magpie will be a different colour to the European robin.

Continuous variation

Variation can be continuous: this means individuals in a population vary within a range and there are no distinct categories.

Biology; Classification and evolution; KS5 Year 12; Types of variation, causes and calculations — Height occurs over a continuous range.

Examples

Animal	Humans can be any height/mass within a range.
Plant	Plants such as trees can have any number of leaves within a range.
Microorganism	A bacterial flagella can have any length within a range.

Discontinuous variation

Variation can also be discontinuous: this means there are distinct categories that individuals can fall into.

Biology; Classification and evolution; KS5 Year 12; Types of variation, causes and calculations — Eye colour is a discrete category.

Examples

Animal	Human can either be blood group A, B, AB or O.
Plant	Pea pods can either be yellow or green, wrinkled or smooth.
Microorganism	Some bacteria can either produce a colour pigment or not produce a coloured pigment.

Causes of variation

Variation can be cause genetic factors, environmental factors or both.

Factor	Description	Example
Genetic	Different species have different genes, organisms of the same species have different versions of the same genes (alleles). Both of these things make up an organism's genotype and differences in genotypes causes differences in phenotypes. Genetic factors are therefore always inherited.	Blood groups are inherited from parents.
Environmental	Variation can be caused by environmental differences such as climate and lifestyle. Environmental factors can change over the lifetime of an organism.	Regional accents.
Both	Sometimes the environment can influence how genetic factors develop.	Height in humans is determined by genes but diet/nutrient availability affects how tall the person will actually grow.

Mean

When investigating variation, you often take samples of a population. 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.

Biology; Classification and evolution; KS5 Year 12; Types of variation, causes and calculations — 1. Mean height, 2. Bell-shaped curve.

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.

Calculating standard deviation

The formula for standard deviation is:

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

$s$	Standard deviation
$\sum$	Sigma, meaning sum of
$x$	Value in the data set
$\overline x$	The mean
$n$	Number of values.

Example

Using the table, calculate the standard deviation of heights of four different people.

Person	Height ( $m$ )
A	$1.68$
B	$1.84$
C	$1.76$
D	$1.72$

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

${{1.68 + 1.84 +1.76 +1.72} \over 4 }= 1.75$

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

$A: (1.68-1.75)^2 = 0.0049 \newline B: (1.84-1.75)^2 = 0.0081 \newline C: (1.76-1.75)^2 = 0.0001 \newline D: (1.72-1.75)^2 = 0.0009 \newline$

Find the sum:

$0.0049 + 0.0081 + 0.0001 + 0.0009 = 0.014$

Divide by $n-1$ :

${0.014\over 4-1 }=0.0047$

Square root:

$\sqrt{0.0047} \approx 0.068$

$\underline{Therefore,\ the\ standard\ deviation\ of\ the\ heights\ is\ 0.068.}$