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In the data set below, what is the variance?\newline4,4,1,8,4,9,54, 4, 1, 8, 4, 9, 5\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?\newline4,4,1,8,4,9,54, 4, 1, 8, 4, 9, 5\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=(4−5)2+(4−5)2+(1−5)2+(8−5)2+(4−5)2+(9−5)2+(5−5)2\Sigma(x_i - \text{mean})^2 = (4 - 5)^2 + (4 - 5)^2 + (1 - 5)^2 + (8 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (5 - 5)^2\newlineΣ(xi−mean)2=(−1)2+(−1)2+(−4)2+(3)2+(−1)2+(4)2+(0)2\Sigma(x_i - \text{mean})^2 = (-1)^2 + (-1)^2 + (-4)^2 + (3)^2 + (-1)^2 + (4)^2 + (0)^2\newlineΣ(xi−mean)2=1+1+16+9+1+16+0\Sigma(x_i - \text{mean})^2 = 1 + 1 + 16 + 9 + 1 + 16 + 0\newlineΣ(xi−mean)2=44\Sigma(x_i - \text{mean})^2 = 44
  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 = 447\frac{44}{7}\newlineVariance σ2\sigma^2 ≈6.3\approx 6.3 (rounded to the nearest tenth)

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