Standard Deviation Statistics Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardDataset A: {5, 5, 5, 5}. Dataset B: {2, 4, 6, 8}. Without full calculation, which has a larger standard deviation and why?
Solution
- 1 Step 1: Dataset A has all identical values (mean = 5), so every deviation is 0. Standard deviation = 0.
- 2 Step 2: Dataset B has values spread around the mean (), with deviations of โ3, โ1, 1, 3.
- 3 Step 3: Since B has non-zero deviations and A has all-zero deviations, B has the larger standard deviation.
Answer
Dataset B has the larger standard deviation. Dataset A has .
Standard deviation is zero only when all values are identical. Any variation among values produces a positive standard deviation.
About Standard Deviation
Standard deviation is a measure of how spread out data values are from the mean, representing the typical distance of data points from the average. A small standard deviation means data clusters tightly around the mean; a large one means data is widely spread.
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