Question

find the standard deviation for the group of data items. 3,4,5,6,7 the standard deviation is (round to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{3 + 4+5+6+7}{5}=\frac{25}{5}=5$

Step2: Calculate the squared differences

For \(3\): \((3 - 5)^2=(- 2)^2 = 4\)
For \(4\): \((4 - 5)^2=(-1)^2 = 1\)
For \(5\): \((5 - 5)^2=0^2 = 0\)
For \(6\): \((6 - 5)^2=1^2 = 1\)
For \(7\): \((7 - 5)^2=2^2 = 4\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{4 + 1+0+1+4}{5}=\frac{10}{5}=2\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{2}\approx1.41\)

Answer:

\(1.41\)