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Year 10 · Statistics & Probability

Standard deviation

Quartiles split ordered data into quarters. The interquartile range (IQR) measures spread; standard deviation measures spread around the mean.

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How to do it

  1. Order the data. The median splits it in two.
  2. Q1 is the median of the lower half, Q3 of the upper half.
  3. IQR = Q3 − Q1.

Worked example

Find the population standard deviation of: 5, 7, 10, 13. Give one decimal place.
Mean = 8.75. Square each difference from the mean, average them (variance = 9.19), then take the square root: 3.0.
Answer: 3.0

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Order the data first, every time.

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