Which of the below data sets has the lowest standard deviation? You do not need to calculate the exact standard deviations to answer this question.0, 1, 3, 3, 3, 5, 60, 0, 0, 100, 200, 200, 2000, 1, 2, 3, 4, 5, 60, 25, 50, 100, 125, 150, 1000
Question
Which of the below data sets has the lowest standard deviation? You do not need to calculate the exact standard deviations to answer this question.0, 1, 3, 3, 3, 5, 60, 0, 0, 100, 200, 200, 2000, 1, 2, 3, 4, 5, 60, 25, 50, 100, 125, 150, 1000
Solution
The standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean (average) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Here are the three data sets:
- 0, 1, 3, 3, 3, 5, 6
- 0, 0, 0, 100, 200, 200, 200
- 0, 1, 2, 3, 4, 5, 6, 25, 50, 100, 125, 150, 1000
Without calculating the exact standard deviations, we can make an educated guess based on the spread of the numbers in each set.
- The first set has numbers that are relatively close together, with the exception of 6.
- The second set has three 0s and three 200s, which are far apart, but within each group the numbers are the same.
- The third set has numbers that are spread out over a much larger range, from 0 to 1000.
Based on this, we can infer that the first data set likely has the lowest standard deviation, as its values are closest together. The third data set likely has the highest standard deviation, as its values are spread out over the largest range.
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