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In the data set below, what is the variance?\newline4,6,4,8,8,8,44, 6, 4, 8, 8, 8, 4\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?\newline4,6,4,8,8,8,44, 6, 4, 8, 8, 8, 4\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=(4−6)2+(6−6)2+(4−6)2+(8−6)2+(8−6)2+(8−6)2+(4−6)2\Sigma(x_i - \text{mean})^2 = (4 - 6)^2 + (6 - 6)^2 + (4 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 + (4 - 6)^2\newlineΣ(xi−mean)2=(−2)2+(0)2+(−2)2+(2)2+(2)2+(2)2+(−2)2\Sigma(x_i - \text{mean})^2 = (-2)^2 + (0)^2 + (-2)^2 + (2)^2 + (2)^2 + (2)^2 + (-2)^2\newlineΣ(xi−mean)2=4+0+4+4+4+4+4\Sigma(x_i - \text{mean})^2 = 4 + 0 + 4 + 4 + 4 + 4 + 4\newlineΣ(xi−mean)2=24\Sigma(x_i - \text{mean})^2 = 24
  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 = 247\frac{24}{7}\newlineVariance σ2\sigma^2 ≈3.4\approx 3.4 (rounded to the nearest tenth)

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