Question

find the standard deviation for the group of data items. 17, 18, 18, 18, 18, 19 the standard deviation is (simplify your answer. round to two decimal places, as needed)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{17 + 18+18+18+18+19}{6}=\frac{108}{6}=18$.

Step2: Calculate the squared differences

For \(x = 17\): \((17 - 18)^2=(- 1)^2 = 1\)
For \(x = 18\) (four times): \((18 - 18)^2=0^2 = 0\) (each)
For \(x = 19\): \((19 - 18)^2=1^2 = 1\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{1+0 + 0+0+0+1}{6}=\frac{2}{6}\approx0.33\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{s^{2}}=\sqrt{\frac{2}{6}}\approx0.58\)

Answer:

\(0.58\)