Biodiversity (AQA A-Level Biology): Revision Notes

Quantitative Investigations of Variation

Understanding variation and measurement challenges

Living organisms show remarkable diversity both between and within species. Interspecific variation refers to differences between different species, while intraspecific variation describes differences between individuals of the same species. Even identical twins with the same DNA show variation due to their different experiences throughout life.

Measuring biological variation presents unique challenges for scientists. Unlike measuring non-living objects, biologists cannot simply take a single measurement to characterise a population. For example, you cannot determine the height of all buttercups or count red blood cells in human blood from just one measurement.

This is why biologists must take samples - collections of measurements from individuals selected from the population being studied.

Random sampling principles

Sampling involves taking measurements from individuals selected from the population under investigation. For these measurements to be reliable and representative of the entire population, the sampling process must be carefully designed.

The key principle is that samples should be representative of the population as a whole. However, several factors can compromise this representativeness:

Implementing random sampling

The most effective way to prevent sampling bias is to eliminate human involvement in choosing samples through random sampling. One systematic method involves:

Minimising chance effects

While random sampling reduces bias, chance effects cannot be completely eliminated. However, their influence can be minimised through:

1. Using large sample sizes: The probability that chance will influence results decreases as sample size increases. Sampling 500 individuals gives much more reliable data than sampling only five individuals.
2. Statistical analysis of collected data: Mathematical tests can determine whether observed variation is likely due to chance or represents genuine biological differences. These tests help scientists decide if their results are statistically significant.

The normal distribution curve

When continuous variation data is plotted graphically, it typically produces a normal distribution curve - a symmetrical, bell-shaped pattern. This curve is characteristic of features like human height, where most individuals cluster around an average value with fewer individuals at the extremes.

Sometimes the curve becomes skewed, meaning it shifts slightly to one side, creating asymmetry. In skewed distributions, the mean, mode, and median have different values, unlike in normal distributions where they coincide.

Measures of central tendency

Three key statistical measures describe the central or typical value in a data set:

1. Mean (arithmetic mean): The sum of all sampled values divided by the number of items.

$\text{Mean} = \frac{\text{total of sampled values}}{\text{number of items}}$

This provides an average value and is particularly useful for comparing different samples. However, it gives no information about the range or spread of values within the sample.

1. Mode: The single value that occurs most frequently in the sample. In some data sets, there may be more than one mode if multiple values occur with equal highest frequency.
2. Median: The central or middle value when all measurements are arranged in ascending order. For an odd number of values, this is the middle value. For an even number of values, it's the average of the two middle values.

Standard deviation

Standard deviation is a measure of how widely data values are spread around the mean. It provides crucial information about the variability within a sample.

A small standard deviation indicates that most values cluster closely around the mean (little variety), while a large standard deviation shows that values are more widely spread (high variety).

Calculating standard deviation

The formula for standard deviation appears complex but becomes manageable when calculated step by step:

$\text{Standard deviation} = \sqrt{\frac{\sum(x - \bar{x})^2}{n-1}}$

Where:

• $\sum$ = sum of
• $x$ = measured value from the sample
• $\bar{x}$ = mean value
• $n$ = total number of values in the sample

Step-by-step calculation process:

1. Calculate the mean value ($\bar{x}$) by adding all measurements and dividing by the number of items
2. Subtract the mean from each individual measured value $(x - \bar{x})$
3. Square all these differences $(x - \bar{x})^2$ - remember to square both positive and negative values
4. Add all the squared values together $\sum(x - \bar{x})^2$
5. Divide by $(n-1)$ where $n$ is the number of measurements
6. Take the square root to return to the original units

Significant figures and calculations

When using calculators for standard deviation calculations, you'll often get very long decimal answers. The significance of digits decreases from left to right, so it's normal practice to round answers to an appropriate number of significant figures.