Question

find the variance of the data set below. if necessary, round to the nearest hundredth.
9, 9, 11, 12, 15, 17, 17, 20, 20, 21, 22

question 16
2 pts
find the standard deviation of the data set below. if necessary, round tot he nearest hundredth.
64, 69, 73, 76, 77, 77, 87, 89

question 17
2 pts
find the standard deviation of the data set below. if necessary, round tot he nearest hundredth.
33, 36, 40, 43, 43, 45, 46, 50, 50, 51, 53, 53

Explanation:

Step1: Calculate the mean

The mean \(\bar{x}=\frac{9 + 9+11+12+15+17+17+20+20+21+22}{11}=\frac{173}{11}\approx15.73\)

Step2: Calculate the squared differences

\((9 - 15.73)^2=(- 6.73)^2 = 45.2929\)
\((9 - 15.73)^2=45.2929\)
\((11 - 15.73)^2=(-4.73)^2 = 22.3729\)
\((12 - 15.73)^2=(-3.73)^2 = 13.9129\)
\((15 - 15.73)^2=(-0.73)^2 = 0.5329\)
\((17 - 15.73)^2=(1.27)^2 = 1.6129\)
\((17 - 15.73)^2=1.6129\)
\((20 - 15.73)^2=(4.27)^2 = 18.2329\)
\((20 - 15.73)^2=18.2329\)
\((21 - 15.73)^2=(5.27)^2 = 27.7729\)
\((22 - 15.73)^2=(6.27)^2 = 39.3129\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{45.2929+45.2929+22.3729+13.9129+0.5329+1.6129+1.6129+18.2329+18.2329+27.7729+39.3129}{11}\)
\(s^{2}=\frac{234.19}{11}\approx21.29\)

Answer:

\(21.29\)