Question

find the standard deviation for the group of data items.
5,5,5,5,7,9
the standard deviation is
(simplify your answer. round to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{5 + 5+5+5+7+9}{6}=\frac{36}{6}=6$

Step2: Calculate the squared differences

For \(x = 5\): \((5 - 6)^2=1\) (occurs 4 times)
For \(x = 7\): \((7 - 6)^2 = 1\)
For \(x = 9\): \((9 - 6)^2=9\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{4\times1+1 + 9}{6}=\frac{4 + 1+9}{6}=\frac{14}{6}\approx2.33\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{s^{2}}=\sqrt{\frac{14}{6}}\approx1.53\)

Answer:

\(1.53\)