Answer:
The standard deviation is 2.6076809621.
Step-by-step explanation:
The set of values are 2, 4, 7, 8, 9.
The mean of these values are [tex]\frac{2 + 4 + 7 + 8 + 9}{5} = \frac{30}{5} = 6[/tex].
The mean of the squares of the differences of these numbers and the mean is [tex]\frac{(6 - 2)^{2} + (6 - 4)^{2} + (6 - 7)^{2} + (6 - 8)^{2} + (6 - 9)^{2}}{5} = \frac{(4)^{2} + (2)^{2} + (-1)^{2} + (-2)^{2} + (-3)^{2}}{5} = \frac{34}{5} = 6.8[/tex].
In order to get the value of the standard deviation, we need to square-root the value of 6.8.
Hence, the standard deviation of the data set is [tex]\sqrt{6.8} = 2.607680962081[/tex] ≅2.6076809621.
