Quantitative Investigations of Variation
Joe Wolfensohn
Teacher
Contents
Recall Questions
This topic requires prior knowledge of maths skills from GCSE. You can test your knowledge on these below.
What is the range and what does it represent?
The range is the difference between the highest and lowest values in a data set. It represents the spread of the data but is affected by extreme values.
How do you calculate the mean, and what does it show?
Add all values and divide by the number of values. It gives the average, showing the central tendency of the data.
What is the mode and when is it useful?
The mode is the value that occurs most frequently. It's useful for categorical data or to identify common traits in populations.
Topic Explainer Videos
Check out this @JoeDoesBiology video that explains quantitative investigations of variation or read the full notes below. Once you've gone through the whole note, try out the practice questions!
What are Quantitative Investigations of Diversity?
- Used to measure genetic and species diversity.
- Involves numerical data collection, often from field studies.
- Helps determine how variation is distributed within and between populations.
Standard Deviation
- Standard deviation (SD) measures the spread of data around the mean.
- A small SD = data points close to the mean (less variation).
- A large SD = data points spread out (more variation).
Standard Deviation in Tables – Example
| Species | Mean Leaf Length (cm) | Standard Deviation (cm) |
| A | 5.2 | 0.4 |
| B | 5.6 | 1.2 |
Interpretation: Species A has smaller SD so has more consistent leaf lengths (less variation).
Standard Deviation on Graphs – Example
- Often shown as error bars on a bar chart or line graph.
- Longer error bars = more variability.
- If error bars do not overlap, the difference is likely statistically significant.
- If error bars do show overlap, the difference is likely due to chance and is not statistically significant.
Graph Example:
| Group | Mean Height (cm) | SD |
| A | 50 | ±9 |
| B | 65 | ±4 |
Here, error bars do not overlap, this supports a real difference and there is likely to be a significant difference between the mean values.
How to Analyse and Conclude from SD
- Compare SDs: Smaller SD suggests less variation in the sample.
- Compare means with SDs:
- If means differ but SDs overlap: difference may be not significant.
- If means differ and SDs do not overlap: difference is likely significant.
- Statistical tests (like t-tests) are needed for confirmation, but SD gives a strong indication.
What Does ±2 Standard Deviations (SD) Mean?
- When data is normally distributed (bell-shaped curve), about 95% of all values lie within ±2 standard deviations from the mean.
- This means if the mean height is 100 cm and SD = 5 cm:
- 95% of values fall between 90 cm and 110 cm (100 ± 2×5).
- It’s a way to show the expected range where most data points lie.
- Scientists use ±2 SD to assess whether results are typical or unusual.
- Why it's useful in biology: If two sets of data have non-overlapping ±2 SD ranges, it suggests the difference is likely significant.
Key Terms
- Mean: Average value of the data set.
- Range: Difference between highest and lowest values.
- Standard deviation: Measure of spread of data around the mean; assesses variation in data.
- Error Bars: Graphical representation of SD.
No answer provided.
Exam Tips
Do not say a smaller SD means “it’s more accurate”—use “less variation in data” or “measurements are more consistent”.
Don't say that no overlap in SD suggests the results are significant, say the difference is significant.
No answer provided.
Scientists measured the height of two plant species in the same habitat. The mean height of Species A was 70 cm (SD = + / - 2), and the mean height of Species B was 75 cm (SD = + / - 6).
Use the information to determine if the difference in height is likely to be significant and explain your answer. (3 marks)
- Species A has a small SD (2 cm), so its height is consistent.
- Species B has a larger SD (6 cm), indicating more variation.
- The mean difference is 5 cm, but SDs overlap (70 ± 2 overlaps with 75 ± 6).
- Therefore, the difference may not be statistically significant based on SD.
Practice Question 1
Try to answer the practice question from the TikTok on your own, then watch the video to see how well you did!
Practice Question 2
If you want to try out another one, check this video out and see how you do!