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In the data set below, what is the variance?\newline5,6,3,6,4,9,25, 6, 3, 6, 4, 9, 2\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?\newline5,6,3,6,4,9,25, 6, 3, 6, 4, 9, 2\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=(5−5)2+(6−5)2+(3−5)2+(6−5)2+(4−5)2+(9−5)2+(2−5)2\Sigma(x_i - \text{mean})^2 = (5 - 5)^2 + (6 - 5)^2 + (3 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (2 - 5)^2\newlineΣ(xi−mean)2=02+12+(−2)2+12+(−1)2+42+(−3)2\Sigma(x_i - \text{mean})^2 = 0^2 + 1^2 + (-2)^2 + 1^2 + (-1)^2 + 4^2 + (-3)^2\newlineΣ(xi−mean)2=0+1+4+1+1+16+9\Sigma(x_i - \text{mean})^2 = 0 + 1 + 4 + 1 + 1 + 16 + 9\newlineΣ(xi−mean)2=32\Sigma(x_i - \text{mean})^2 = 32
  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 = 327\frac{32}{7}\newlineVariance σ2\sigma^2 ≈4.6\approx 4.6 when rounded to the nearest tenth.

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