VG2
statistikk
Quiz
What is standard deviation?
Standard deviation measures how spread out the numbers in a dataset are around the mean.
While the mean tells us the middle value, standard deviation tells us how much the numbers vary around this centre. A small standard deviation means the numbers are clustered together — a large one means great spread.
σ = √( Σ(xᵢ - x̄)² / n )
Where x̄ is the mean, xᵢ is each individual value and n is the number of values.
Step by step:
1. Calculate the mean x̄
2. Subtract the mean from each value: (xᵢ - x̄)
3. Square each deviation: (xᵢ - x̄)²
4. Sum all squared deviations
5. Divide by n
6. Take the square root
1. Calculate the mean x̄
2. Subtract the mean from each value: (xᵢ - x̄)
3. Square each deviation: (xᵢ - x̄)²
4. Sum all squared deviations
5. Divide by n
6. Take the square root
Example
Dataset: 2, 4, 4, 4, 5, 5, 7, 9
x̄ = 40/8 = 5
Sum of squared deviations = 32
Variance = 32/8 = 4
σ = √4 = 2
Sum of squared deviations = 32
Variance = 32/8 = 4
σ = √4 = 2
Interpretation: σ = 2 means the values are on average 2 units away from the mean of 5.
Statistics is the science of learning from data — and standard deviation is one of its most important teachers.
— Karl Pearson (1857–1936)
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What does standard deviation measure?
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