4.6.7 Quantitative Investigations of Variation

Key Concepts

1. Types of Variation:

• Interspecific Variation: Differences between species.
• Intraspecific Variation: Differences within individuals of the same species.

2. Importance of Reliable Data:

• A large sample size is necessary to minimise the effects of chance on results.
• Random sampling reduces bias and ensures a representative dataset.

3. Measurement of Characteristics:

• Measure observable characteristics like size, mass, or shape.
• Analyse genetic information such as DNA base sequences, mRNA, or amino acid sequences.

Statistical Techniques

1. Mean: The average value of a dataset.

• Provides an overall measure of central tendency.

2. Standard Deviation (SD):

• Indicates the spread of data around the mean.
• A small standard deviation suggests low variation, while a large standard deviation suggests high variation.

3. Normal Distribution:

• Data often follows a normal distribution curve (bell-shaped), with most individuals clustering around the mean.
• Used to identify patterns in variation.

4. Comparison of Data:

• Use standard deviations and overlap to assess the significance of differences between groups or species.

Steps in Quantitative Investigations

1. Sampling:

• Use random sampling methods (e.g., quadrats, transects) to avoid bias.
• Ensure a large sample size to make the results reliable.

2. Data Collection:

• Record measurements for the selected characteristic (e.g., height, weight).

3. Statistical Analysis:

• Calculate the mean and standard deviation for the data.
• Analyse the distribution (normal or skewed).
• Compare datasets using overlap of standard deviations.

Key Formula

Standard Deviation (SD):

$$SD = \sqrt{\frac{\Sigma (x - \bar{x})^2}{n - 1}}$$

Where:

• $x$= each value in the dataset.
• $xˉ$= mean of the dataset.
• $n$= total number of values.