Statistics: spread
Mean, variance and standard deviation.
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Spread tells you if numbers are close together or scattered.
Look: Eight numbers around a mean of 5.
✏️ Your turn!
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1Spread of 5, 5, 5, 5?
2Add 10 to every number. Does the spread change?
3Double every number. The spread?
! Careful!
✗Averaging the gaps without squaring (they cancel to 0).
✓Square them first.
✗Forgetting the square root at the end.
✓Variance first, then √ for the standard deviation.
See the whole lesson on one page
Spread tells you if numbers are close together or scattered.
Find how far each number is from the mean, square those gaps, and average them: that is the variance. Its square root is the standard deviation.
Think of it like thisTwo archers both average the centre. One hits close every time; the other is all over the board. Same average, different spread.
- Standard deviation
- A typical distance from the mean.
Solved together
Find the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9.
Mean: add and share.
40 ÷ 8 = 5Square each gap from 5, then add.
9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32Average the squares, then square root.
32 ÷ 8 = 4√4 = 2
AnswerStandard deviation 2.
Now practise it
Kanakku makes new questions on statistics: spread every time. It shows the working and gives a hint when you are stuck.