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- Suppose there are two sets of data A and B with the same mean value. If the variance of set A is twice the variance of set B, what can you conclude about the standard deviation of set A c
Suppose there are two sets of data A and B with the same mean value. If the variance of set A is twice the variance of set B, what can you conclude about the standard deviation of set A compared to the standard deviation of set B?
The standard deviation of set A is equal to the standard deviation of set B.
The standard deviation of set A is larger than the standard deviation of set B.
The standard deviation of set A is smaller than the standard deviation of set B.
There is not enough information to determine the relationship between the standard deviation of set A and the standard deviation of set B.
Answers (1)
option B) The standard deviation of set A is larger than the standard deviation of set B.
Variance and standard deviation are related measures of dispersion. If the variance of set A is twice the variance of set B, then the standard deviation of set A will be larger than the standard deviation of set B. This is because the standard deviation is the square root of the variance, so if the variance is larger, then the standard deviation will also be larger. Since the mean values of the two sets are the same, the difference in variance is a reflection of the spread of the data.
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