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  1. 1-1-biological-molecules-carbohydrates
    11 主题
  2. 1-2-biological-molecules-lipids
    3 主题
  3. 1-3-biological-molecules-proteins
    5 主题
  4. 1-4-proteins-enzymes
    12 主题
  5. 1-5-nucleic-acids-structure-and-dna-replication
    8 主题
  6. 1-6-atp-water-and-inorganic-ions
    4 主题
  7. 2-1-cell-structure
    7 主题
  8. 2-2-the-microscope-in-cell-studies
    4 主题
  9. 2-3-cell-division-in-eukaryotic-and-prokaryotic-cells
    8 主题
  10. 2-4-cell-membranes-and-transport
    9 主题
  11. 2-5-cell-recognition-and-the-immune-system
    7 主题
  12. 2-6-vaccines-disease-and-monoclonal-antibodies
    6 主题
  13. 3-1-adaptations-for-gas-exchange
    6 主题
  14. 3-2-human-gas-exchange
    14 主题
  15. 3-3-digestion-and-absorption
    5 主题
  16. 3-4-mass-transport-in-animals
    6 主题
  17. 3-5-the-circulatory-system-in-animals
    4 主题
  18. 3-6-mass-transport-in-plants
    6 主题
  19. 4-1-dna-genes-and-chromosomes
    10 主题
  20. 4-2-dna-and-protein-synthesis
    3 主题
  21. 4-3-genetic-diversity-mutations-and-meiosis
    7 主题
  22. 4-4-genetic-diversity-and-adaptation
    6 主题
  23. 4-5-species-and-taxonomy
    4 主题
  24. 4-6-biodiversity
    9 主题
课 24, 主题 7
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4-6-7-quantitative-investigations-of-variation

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Exam code:7401

Quantitative investigations of variation

  • Quantitative investigations of variation can involve using measures of central tendency such as the mean values and their standard deviations

    • A mean value describes the average value of a data set

    • Standard deviation is a measure of the spread or dispersion of data around the mean

      • A small standard deviation indicates that the results lie close to the mean (less variation)

      • A large standard deviation indicates that the results are more spread out

Graph comparing low and high standard deviation curves in a normal distribution; the low curve is narrow and tall, the high curve is wide and short.
Graph comparing low and high standard deviation curves in a normal distribution

Comparison between groups

  • When comparing the results from different groups or samples, using a measure of central tendency, such as the mean, can be quite misleading

  • For example, looking at the two groups below:

    • Group A: 2, 15, 14, 15, 16, 15, 14; mean = 13

    • Group B: 1, 3, 10, 15, 20, 22, 20; mean = 13

  • Even though both groups have a mean of 13, most of the values in Group A lie close to the mean, whereas in Group B, most values lie quite far from the mean

  • For comparison between groups or samples, it is better practice to use the standard deviation in conjunction with the mean

  • The standard deviations of different data sets can determine whether observed differences are due to real effects or just natural variation

    • If standard deviations overlap, the difference between data sets is not statistically significant

    • If standard deviations do not overlap, the difference is likely statistically significant

Worked Example

A group of scientists wanted to investigate the effects of a specific diet on the risk of coronary heart disease. One group was given a specific diet for 8 weeks, while the other group acted as a control. After 8 weeks, scientists measured the diameter of the lumen of the main artery in the arm of the volunteers. The results of the experiment are shown in Table 1 below:

Mean maximum diameter of lumen of main aterty in the arm (mm)

Experimental group (± standard deviation)

Control group (± standard deviation)

Before experiment

0.69 (± 0.02)

0.71 (± 0.02)

After 8 weeks

0.74 (± 0.03)

0.72 (± 0.05)

Use the standard deviations to evaluate whether the diet had a significant effect. 

[2 marks]

Step one: Find the full range of values included within the standard deviations for each data set

Experimental group before: 0.67 to 0.71mm

Experimental group after: 0.71 to 0.77mm

Control group before: 0.69 to 0.73mm

Control group after: 0.67 to 0.77mm

Step two: Use this information to form your answer

0.67~0.71mm and 0.71~0.77mm overlap

There is an overlap of standard deviations in the experimental group before and after the experiment, so it can be said that the difference before and after the experiment is not significant; [1 mark]

0.71~0.77mm and 0.67~0.77mm

There is also an overlap of standard deviations between the experimental and control groups after the eight weeks, so it can be said that the difference between groups is not significant; [1 mark]

Examiner Tips and Tricks

The standard deviations of a data set are not always presented in a table, they can also be represented by standard deviation error bars on a graph. You will not be required to calculate standard deviations in written papers.

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