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Mathematical Requirements (Appendix C)

Probability, Sampling, Statistical Tests and Uncertainty: Standard Deviation

  • 3 things to know
  • All units

Overview

Recall questions on Standard Deviation, Range and Percentage Error in Combined Measurements.

What you need to know

Answer each one before you reveal it.

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Key term

Why is standard deviation usually a better measure of dispersion than the range?

Numbers

Calculate the standard deviation of the values 4, 6 and 8.

Key term

Two means have error bars showing one standard deviation, and the bars overlap considerably. What does this suggest?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What does the standard deviation of a set of measurements tell you?

    Model answer

    It measures the spread of the individual values about the mean, with roughly two thirds of a normally distributed set lying within one standard deviation of the mean.

  2. 2

    Calculate the standard deviation of the values 4, 6 and 8.

    Model answer

    The mean is 6, the squared deviations sum to 8, dividing by two gives 4 and the standard deviation is 2.

  3. 3

    Why is standard deviation usually a better measure of dispersion than the range?

    Model answer

    The range depends only on the two extreme values and is badly distorted by a single outlier, whereas the standard deviation uses every value in the set.

  4. 4

    Two means have error bars showing one standard deviation, and the bars overlap considerably. What does this suggest?

    Model answer

    The two sets of data overlap a great deal, so the difference between the means is unlikely to be significant and a statistical test is needed to confirm it.

  5. 5

    How is the uncertainty of a single reading on a millimetre ruler stated?

    Model answer

    It is taken as half the smallest scale division, so ±0.5 mm.

  6. 6

    A volume of 10 cm³ is measured in a cylinder with an uncertainty of ±0.5 cm³. Calculate the percentage error.

    Model answer

    The percentage error is (0.5 ÷ 10) × 100 = 5%.

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