Compute $\mathrm { s } ^ { 2 }$ and s for the data set: -3,-1,-4,-3,1,-3
A) 2.24 ; 1.5
B) 1.87 ; 1.37
C) 3.37 ; 1.83
D) 32.3 ; 5.68

Question

Quizplus · Accepted Answer

The variance ($\mathrm { s } ^ { 2 }$) and standard deviation (s) for a sample can be calculated using the formulas for sample variance and standard deviation. First, find the mean of the data set: $\frac{-3 - 1 - 4 - 3 + 1 - 3}{6} = \frac{-13}{6} = -2.17$. Then, calculate the sum of the squared differences from the mean: $\sum (x_i - \bar{x})^2 = (-3 + 2.17)^2 + (-1 + 2.17)^2 + (-4 + 2.17)^2 + (-3 + 2.17)^2 + (1 + 2.17)^2 + (-3 + 2.17)^2 = 3.37$. Divide by $n-1$ (where $n$ is the number of data points) to get the variance: $\frac{3.37}{6-1} = 3.37$. The standard deviation is the square root of the variance: $\sqrt{3.37} = 1.83$.

Compute s2\mathrm { s } ^ { 2 }s2 And S for the Data Set: -3,-1,-4,-3,1,-3 A) 2

Compute $\mathrm { s } ^ { 2 }$ And S for the Data Set: -3,-1,-4,-3,1,-3
A) 2