Which data set has the same standard deviation as the data set {1, 1, 3, 5, 8}?

a. {1, 2, 6, 6, 9}

b. {2, 2, 4, 6, 9}

c. {9, 8, 9, 8, 9}

d. {1, 1, 1, 2, 2}

b. {2, 2, 4, 6, 9}

Step-by-step explanation:

The value of standard deviation does not get affected if we add constant number in every observation.

In the given data set if we add 1 in every observation then we will get same value as given in option (b).

Thus, the standard deviation of both the observation is same.

Also, we didn't get other options by addition and subtraction of any constant value.

Further, Standard Deviation is used to measure spread of the data and it is defined as square of the distance between the observation and mean of the distribution.

B. {2, 2, 4, 6, 9}

Because they both follow this sequence:

+0, + 2, + 2, + 3