find the variance of the data. 147, 141, 120, 124, 128 $\bar{x}=132$ variance ($sigma^{2}$) = ?
find the variance of the data. 147, 141, 120, 124, 128 $\bar{x}=132$ variance ($sigma^{2}$) = ?
Answer
Explanation:
Step1: Calculate squared - differences
$(147 - 132)^2=15^2 = 225$ $(141 - 132)^2=9^2 = 81$ $(120 - 132)^2=(- 12)^2 = 144$ $(124 - 132)^2=(-8)^2 = 64$ $(128 - 132)^2=(-4)^2 = 16$
Step2: Find the sum of squared - differences
$225+81 + 144+64+16=530$
Step3: Divide by the number of data points
The number of data points $n = 5$. Variance $\sigma^{2}=\frac{530}{5}=106$
Answer:
$106$