Without making any calculations, which data set has the smallest standard deviation?

A. [tex]$1, 1, 2, 2, 3, 3$[/tex]
B. [tex]$1, 3, 5$[/tex]
C. [tex]$0, 1, 5, 6, 9, 10$[/tex]
D. [tex]$1, 1, 1, 1, 2, 2, 2, 2$[/tex]



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.