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In the data set below, what is the variance?\newline2,2,1,8,4,3,12, 2, 1, 8, 4, 3, 1\newlineIf the answer is a decimal, round it to the nearest tenth.\newlinevariance (σ2)(\sigma^2): _____

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Q. In the data set below, what is the variance?\newline2,2,1,8,4,3,12, 2, 1, 8, 4, 3, 1\newlineIf the answer is a decimal, round it to the nearest tenth.\newlinevariance (σ2)(\sigma^2): _____
  1. Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean.\newlineΣ(xi−mean)2=(2−3)2+(2−3)2+(1−3)2+(8−3)2+(4−3)2+(3−3)2+(1−3)2\Sigma(x_i - \text{mean})^2 = (2 - 3)^2 + (2 - 3)^2 + (1 - 3)^2 + (8 - 3)^2 + (4 - 3)^2 + (3 - 3)^2 + (1 - 3)^2\newlineΣ(xi−mean)2=(−1)2+(−1)2+(−2)2+(5)2+(1)2+(0)2+(−2)2\Sigma(x_i - \text{mean})^2 = (-1)^2 + (-1)^2 + (-2)^2 + (5)^2 + (1)^2 + (0)^2 + (-2)^2\newlineΣ(xi−mean)2=1+1+4+25+1+0+4\Sigma(x_i - \text{mean})^2 = 1 + 1 + 4 + 25 + 1 + 0 + 4\newlineΣ(xi−mean)2=36\Sigma(x_i - \text{mean})^2 = 36
  2. Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance.\newlineVariance σ2\sigma^2 = Σ(xi−mean)2N\frac{\Sigma(x_i - \text{mean})^2}{N}\newlineVariance σ2\sigma^2 = 367\frac{36}{7}\newlineVariance σ2\sigma^2 ≈5.1\approx 5.1 (rounded to the nearest tenth)

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