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In the data set below, what is the variance?\newline5,2,1,1,9,3,75, 2, 1, 1, 9, 3, 7\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?\newline5,2,1,1,9,3,75, 2, 1, 1, 9, 3, 7\newlineIf the answer is a decimal, round it to the nearest tenth.\newlinevariance (σ2)(\sigma^2): _____
  1. Calculate Variance: Now, let's do the variance part.\newlineWe need to sum up each (number−mean)2(\text{number} - \text{mean})^2.\newlineSo, (5−4)2+(2−4)2+(1−4)2+(1−4)2+(9−4)2+(3−4)2+(7−4)2(5 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (1 - 4)^2 + (9 - 4)^2 + (3 - 4)^2 + (7 - 4)^2\newlineThat's (1)2+(−2)2+(−3)2+(−3)2+(5)2+(−1)2+(3)2(1)^2 + (-2)^2 + (-3)^2 + (-3)^2 + (5)^2 + (-1)^2 + (3)^2\newlineWhich is 1+4+9+9+25+1+91 + 4 + 9 + 9 + 25 + 1 + 9\newlineSum = 5858
  2. Sum of Squares: Finally, divide that sum by the number of data points to get the variance.\newlineVariance = 587\frac{58}{7}\newlineVariance = 8.2857…8.2857\ldots\newlineRound it to the nearest tenth and we get 8.38.3

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