Question

find the standard deviation for the group of data items. 5, 6, 7, 7, 8, 9 the standard deviation is (simplify your answer. round to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{5 + 6+7+7+8+9}{6}=\frac{42}{6}=7$

Step2: Calculate the squared differences from the mean

For \(x = 5\): \((5 - 7)^2=(-2)^2 = 4\)
For \(x = 6\): \((6 - 7)^2=(-1)^2 = 1\)
For \(x = 7\): \((7 - 7)^2=0^2 = 0\) (twice)
For \(x = 8\): \((8 - 7)^2=1^2 = 1\)
For \(x = 9\): \((9 - 7)^2=2^2 = 4\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{4 + 1+0+0+1+4}{6}=\frac{10}{6}\approx1.67\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{s^{2}}=\sqrt{\frac{10}{6}}\approx1.29\)

Answer:

\(1.29\)