Question

find the variance of the data. 78, 45, 73, 66, 61, 67 (overline{x}=65) variance ((sigma^{2})=?)

Explanation:

Step1: Calculate each data point minus the mean

$$\begin{align*} 78 - 65&=13\\ 45 - 65&=-20\\ 73 - 65&=8\\ 66 - 65&=1\\ 61 - 65&=-4\\ 67 - 65&=2 \end{align*}$$

Step2: Square the results from Step1

$$\begin{align*} 13^{2}&=169\\ (-20)^{2}&=400\\ 8^{2}&=64\\ 1^{2}&=1\\ (-4)^{2}&=16\\ 2^{2}&=4 \end{align*}$$

Step3: Find the average of the squared results (since it's population variance, divide by \(n = 6\))

$$\begin{align*} \sigma^{2}&=\frac{169 + 400+64 + 1+16+4}{6}\\ &=\frac{654}{6}\\ & = 109 \end{align*}$$

Answer:

\(109\)