Question

find the standard deviation for the given data. round to one more decimal place than the original data
3,5,6,6,8,1

oa. 28
ob. 76
oc. 25
od. 54

Explanation:

Step1: Calculate the mean

The data set is \(3,5,6,6,8,1\).
The mean \(\bar{x}=\frac{3 + 5+6+6+8+1}{6}=\frac{29}{6}\approx4.83\)

Step2: Calculate the squared - differences from the mean

\((3 - 4.83)^{2}=(-1.83)^{2}=3.35\)
\((5 - 4.83)^{2}=(0.17)^{2}=0.03\)
\((6 - 4.83)^{2}=(1.17)^{2}=1.37\)
\((6 - 4.83)^{2}=(1.17)^{2}=1.37\)
\((8 - 4.83)^{2}=(3.17)^{2}=10.05\)
\((1 - 4.83)^{2}=(-3.83)^{2}=14.67\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{3.35 + 0.03+1.37+1.37+10.05+14.67}{6 - 1}\)
\(s^{2}=\frac{30.84}{5}=6.17\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{6.17}\approx2.5\)

Answer:

C. 2.5