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In the data set below, what is the variance?\newline5,1,8,5,4,45, 1, 8, 5, 4, 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?\newline5,1,8,5,4,45, 1, 8, 5, 4, 4\newlineIf the answer is a decimal, round it to the nearest tenth.\newlinevariance (σ2)(\sigma^2): _____
  1. Subtract and Square: Now, subtract the mean from each data point and square the result.\newline(5−4.5)2+(1−4.5)2+(8−4.5)2+(5−4.5)2+(4−4.5)2+(4−4.5)2(5 - 4.5)^2 + (1 - 4.5)^2 + (8 - 4.5)^2 + (5 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2\newline= (0.5)2+(−3.5)2+(3.5)2+(0.5)2+(−0.5)2+(−0.5)2(0.5)^2 + (-3.5)^2 + (3.5)^2 + (0.5)^2 + (-0.5)^2 + (-0.5)^2\newline= 0.25+12.25+12.25+0.25+0.25+0.250.25 + 12.25 + 12.25 + 0.25 + 0.25 + 0.25\newline= 25.525.5
  2. Calculate Sum of Squared Differences: Finally, divide the sum of squared differences by the number of data points to find the variance.\newlineVariance σ2\sigma^2 = 25.56\frac{25.5}{6}\newlineVariance σ2\sigma^2 = 44.2525\newlineRound to the nearest tenth.\newlineVariance σ2\sigma^2 ≈4.3\approx 4.3

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