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

Variance of the given data = 31.143

Step-by-step explanation:

Variance,
`\sigma^2=(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 =
`(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=(1)/(n) \sum_(i=1)^(n)(x_i-\mu)^2=(218)/(7) =31.143`

So variance of the given data = 31.143