Question

in the data set below, what is the variance? 3 2 7 5 3 4 if the answer is a decimal, round it to the nearest tenth. variance (σ²):

Explanation:

Step1: Calculate the mean

The data - set is \(3,2,7,5,3,4\). The mean \(\bar{x}=\frac{3 + 2+7+5+3+4}{6}=\frac{24}{6}=4\).

Step2: Calculate the squared - differences

\((3 - 4)^2=(-1)^2 = 1\), \((2 - 4)^2=(-2)^2 = 4\), \((7 - 4)^2=3^2 = 9\), \((5 - 4)^2=1^2 = 1\), \((3 - 4)^2=(-1)^2 = 1\), \((4 - 4)^2=0^2 = 0\).

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{1 + 4+9+1+1+0}{6}=\frac{16}{6}\approx2.7\).

Answer:

\(2.7\)