To determine which set of data has the smallest standard deviation, we need to understand that standard deviation measures the amount of variation or dispersion in a set of values. The smaller the standard deviation, the closer the data values tend to cluster around the mean (average).
Let's summarize the provided datasets:
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Set 1: 1, 6, 2, 100, 4, 0, 0, 0, 0, 1
- This set has a wide range of values (from 0 to 100), leading to a high standard deviation.
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Set 2: 1, 2, 3, 4, 5, 6, 7, 8, 8, 9
- This set consists of consecutive integers with a few repeating values, indicating lower variability.
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Set 3: 79, 79, 79, 79, 79, 79, 79, 79, 79, 79
- All values are the same (79). Therefore, the standard deviation is 0, indicating no variation at all.
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Set 4: 3, 33, 103, 4, 122, 1, 0, 245, 7, 99
- This set has a wide range of values, from 0 to 245, leading to a high standard deviation.
Given this evaluation:
- Set 3 has all identical numbers (79), resulting in a standard deviation of 0, which is the smallest possible standard deviation.
Therefore, the set of data with the smallest standard deviation is:
79, 79, 79, 79, 79, 79, 79, 79, 79, 79.
3 answers