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In the data set below, what is the variance?\newline3,7,9,7,4,2,33, 7, 9, 7, 4, 2, 3\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?\newline3,7,9,7,4,2,33, 7, 9, 7, 4, 2, 3\newlineIf the answer is a decimal, round it to the nearest tenth.\newlinevariance (σ2)(\sigma^2): _____
  1. Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean.\newlineΣ(xi−mean)2=(3−5)2+(7−5)2+(9−5)2+(7−5)2+(4−5)2+(2−5)2+(3−5)2\Sigma(x_i - \text{mean})^2 = (3 - 5)^2 + (7 - 5)^2 + (9 - 5)^2 + (7 - 5)^2 + (4 - 5)^2 + (2 - 5)^2 + (3 - 5)^2\newlineΣ(xi−mean)2=(−2)2+(2)2+(4)2+(2)2+(−1)2+(−3)2+(−2)2\Sigma(x_i - \text{mean})^2 = (-2)^2 + (2)^2 + (4)^2 + (2)^2 + (-1)^2 + (-3)^2 + (-2)^2\newlineΣ(xi−mean)2=4+4+16+4+1+9+4\Sigma(x_i - \text{mean})^2 = 4 + 4 + 16 + 4 + 1 + 9 + 4\newlineΣ(xi−mean)2=42\Sigma(x_i - \text{mean})^2 = 42
  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 = 427\frac{42}{7}\newlineVariance σ2\sigma^2 = 66

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