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Types of variation, causes and calculations

Types of variation, causes and calculations

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Tutor: Jasmine

Summary

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

​​

​sss​​
Standard deviation
​∑\sum∑​​
Sigma, meaning sum of
​xxx​​
Value in the data set
​x‾\overline xx​​
The mean
​nnn​​
Number of values.

Example

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

Person
Height (mmm)
A
​1.681.681.68​​
B
​1.841.841.84​​
C
​1.761.761.76​​
D
​1.721.721.72​​


Work out the mean (x‾\overline xx):

1.68+1.84+1.76+1.724=1.75{{1.68 + 1.84 +1.76 +1.72} \over 4 }= 1.7541.68+1.84+1.76+1.72​=1.75

​​

Work out (x−x‾)2(x-\overline x)^2(x−x)2​ for each person:

​A:(1.68−1.75)2=0.0049B:(1.84−1.75)2=0.0081C:(1.76−1.75)2=0.0001D:(1.72−1.75)2=0.0009A: (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 \newlineA:(1.68−1.75)2=0.0049B:(1.84−1.75)2=0.0081C:(1.76−1.75)2=0.0001D:(1.72−1.75)2=0.0009

​​

Find the sum: 

​0.0049+0.0081+0.0001+0.0009=0.0140.0049 + 0.0081 + 0.0001 + 0.0009 = 0.0140.0049+0.0081+0.0001+0.0009=0.014

​

Divide by n−1n-1n−1:

0.0144−1=0.0047{0.014\over 4-1 }=0.00474−10.014​=0.0047

​​

Square root:

​0.0047≈0.068\sqrt{0.0047} \approx 0.0680.0047​≈0.068​ 


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

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FAQs - Frequently Asked Questions

What is continuous variation?

Continuous variation means individuals in a population vary within a range and there are no distinct categories.

What does the standard deviation tell you about variation?

The standard deviation tells you about variation within a sample.

What is variation?

Variation is the differences that exist between individuals.

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