Question

Calculate the variance for the data set. Round your answer to the nearest hundredth. Show all of your steps. { 10 , 19 , 21 , 28 , 12 , 20 , 16 }

Answer 1

Answer:

Variance of the given data = 31.143

Explanation:

  Variance, $\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2$, where n is the number of observations, μ is the mean and $x_i$ is the observations made.

   Number of observations, n = 7

   Mean, μ = $\frac{10+19+21+28+12+20+16}{7} = 18$

   $\sum_{i=1}^{n}(x_i-\mu)^2=(10-18)^2+(19-18)^2+(21-18)^2+(28-18)^2+(12-18)^2+(20-18)^2+(16-18)^2\\ \\ \sum_{i=1}^{n}(x_i-\mu)^2=64+1+9+100+36+4+4=218$

  $\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2=\frac{218}{7} =31.143$

  So variance of the given data = 31.143