Answer :
To determine which data set has the smallest standard deviation, we need to compare the standard deviations for each set.
The standard deviations for the given data sets are as follows:
1. Data set [tex]\([1, 1, 2, 2, 3, 3]\)[/tex] has a standard deviation of approximately 0.8165.
2. Data set [tex]\([1, 3, 5]\)[/tex] has a standard deviation of approximately 1.6330.
3. Data set [tex]\([0, 1, 5, 6, 9, 10]\)[/tex] has a standard deviation of approximately 3.7156.
4. Data set [tex]\([1, 1, 1, 1, 2, 2, 2, 2]\)[/tex] has a standard deviation of 0.5.
By comparing these values, the data set [tex]\([1, 1, 1, 1, 2, 2, 2, 2]\)[/tex] has the smallest standard deviation, which is 0.5. Therefore, this is the data set with the smallest standard deviation.
The standard deviations for the given data sets are as follows:
1. Data set [tex]\([1, 1, 2, 2, 3, 3]\)[/tex] has a standard deviation of approximately 0.8165.
2. Data set [tex]\([1, 3, 5]\)[/tex] has a standard deviation of approximately 1.6330.
3. Data set [tex]\([0, 1, 5, 6, 9, 10]\)[/tex] has a standard deviation of approximately 3.7156.
4. Data set [tex]\([1, 1, 1, 1, 2, 2, 2, 2]\)[/tex] has a standard deviation of 0.5.
By comparing these values, the data set [tex]\([1, 1, 1, 1, 2, 2, 2, 2]\)[/tex] has the smallest standard deviation, which is 0.5. Therefore, this is the data set with the smallest standard deviation.
