Answer :
Final answer:
Data set B shows the smallest standard deviation of approximately 0.141. This indicates that the values in set B are the closest to the mean compared to the other data sets. It means the data points in set B are most tightly grouped around their mean value, highlighting the least variance or dispersion in the data
Final answer:
Standard deviation measures the extent of variance or dispersion in a data set. A lower standard deviation means that the values are closer to the mean, while a higher standard deviation indicates that the values are spread out over a wider range.
Let's start with the first data set, A. It includes the values -2, -1, 0, 1, and 2. The variance of the data set is calculated, leading to a standard deviation of approximately 1.414.
The second data set, B, includes 99.8, 99.9, 100, 100.1, and 100.2. The calculation of variance leads to a standard deviation of approximately 0.141. This standard deviation is lower than the previous set, indicating that the data points in set B are closer to the mean.
The third data set, C, has the values 9, 9.5, 10, 10.5, and 11. The standard deviation here is found to be approximately 0.707. Although the values are uniformly distributed, the standard deviation is larger than set B.
Lastly, for data set D with the values 80, 93, 100, 110, and 118, the standard deviation is calculated to be approximately 13.212. This is much larger than the previous three sets, indicating a wider spread of data points from the mean.
Given these calculations, we can see that Data set B shows the smallest standard deviation of approximately 0.141. This indicates that the values in set B are the closest to the mean compared to the other data sets. It means the data points in set B are most tightly grouped around their mean value, highlighting the least variance or dispersion in the data compared to sets A, C, and D.
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