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In the data set below, what is the variance?\newline8,8,2,9,5,2,18, 8, 2, 9, 5, 2, 1\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?\newline8,8,2,9,5,2,18, 8, 2, 9, 5, 2, 1\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 thing.\newlineWe need to sum up (each number−mean)2(\text{each number} - \text{mean})^2.\newlineSo, (8−5)2+(8−5)2+(2−5)2+(9−5)2+(5−5)2+(2−5)2+(1−5)2(8 - 5)^2 + (8 - 5)^2 + (2 - 5)^2 + (9 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (1 - 5)^2\newlineThat's 32+32+(−3)2+42+02+(−3)2+(−4)23^2 + 3^2 + (-3)^2 + 4^2 + 0^2 + (-3)^2 + (-4)^2\newlineWhich is 9+9+9+16+0+9+169 + 9 + 9 + 16 + 0 + 9 + 16
  2. Sum of Squares: Add 'em all up for the sum.\newlineSum = 9+9+9+16+0+9+169 + 9 + 9 + 16 + 0 + 9 + 16\newlineSum = 6868
  3. Calculate Sum: Finally, divide by the number of data points to get variance.\newlineVariance = Sum7\frac{\text{Sum}}{7}\newlineVariance = 687\frac{68}{7}\newlineVariance = 9.71428571…9.71428571\ldots\newlineRound it to the nearest tenth.\newlineVariance ≈9.7\approx 9.7

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