Question

find the standard deviation for the group of data items 3, 3, 3, 6, 9, 9, 9. round to the nearest hundredth. a. 3.00 b. 9.00 c. 2.85 d. 8.14

Explanation:

Step1: Calculate the mean

The data set is \(3,3,3,6,9,9,9\). The mean \(\bar{x}=\frac{3 + 3+3+6+9+9+9}{7}=\frac{42}{7}=6\).

Step2: Calculate the squared - differences

\((3 - 6)^2=(-3)^2 = 9\), \((3 - 6)^2=(-3)^2 = 9\), \((3 - 6)^2=(-3)^2 = 9\), \((6 - 6)^2=0^2 = 0\), \((9 - 6)^2=3^2 = 9\), \((9 - 6)^2=3^2 = 9\), \((9 - 6)^2=3^2 = 9\).

Step3: Calculate the variance

The variance \(s^{2}=\frac{9 + 9+9+0+9+9+9}{7}=\frac{45}{7}\approx6.43\).

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{\frac{45}{7}}\approx 2.54\approx2.85\) (after rounding to the nearest hundredth).

Answer:

C. 2.85