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For the following set of data, find the population standard deviation, to the nearest hundredth 102,138,107,112,125,91,134,110

For the following set of data, find the population standard deviation, to the nearest hundredth 102,138,107,112,125,91,134,110 102,138,107,112,125,91,134,110

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Q. For the following set of data, find the population standard deviation, to the nearest hundredth 102,138,107,112,125,91,134,110 102,138,107,112,125,91,134,110
  1. Calculate Mean: First, we need to calculate the mean (average) of the data set. To do this, we add up all the numbers and then divide by the number of data points.\newlineCalculation: Mean = (102+138+107+112+125+91+134+110)/8(102 + 138 + 107 + 112 + 125 + 91 + 134 + 110) / 8\newlineMean = 919/8919 / 8\newlineMean = 114.875114.875
  2. Calculate Variance: Next, we calculate the variance. Variance is the average of the squared differences from the Mean. To find the variance, we subtract the Mean from each number, square the result, and then average those squared differences.\newlineCalculation: \newlineVariance = [(102−114.875)2+(138−114.875)2+(107−114.875)2+(112−114.875)2+(125−114.875)2+(91−114.875)2+(134−114.875)2+(110−114.875)2]/8[(102 - 114.875)^2 + (138 - 114.875)^2 + (107 - 114.875)^2 + (112 - 114.875)^2 + (125 - 114.875)^2 + (91 - 114.875)^2 + (134 - 114.875)^2 + (110 - 114.875)^2] / 8\newlineVariance = [(12.875)2+(23.125)2+(7.875)2+(2.875)2+(10.125)2+(23.875)2+(19.125)2+(4.875)2]/8[(12.875)^2 + (23.125)^2 + (7.875)^2 + (2.875)^2 + (10.125)^2 + (23.875)^2 + (19.125)^2 + (4.875)^2] / 8\newlineVariance = [165.765625+534.765625+62.015625+8.265625+102.515625+570.015625+365.765625+23.765625]/8[165.765625 + 534.765625 + 62.015625 + 8.265625 + 102.515625 + 570.015625 + 365.765625 + 23.765625] / 8\newlineVariance = 1832.875/81832.875 / 8\newlineVariance = 229.109375229.109375
  3. Calculate Standard Deviation: Now, we calculate the population standard deviation, which is the square root of the variance.\newlineCalculation: Standard Deviation = 229.109375\sqrt{229.109375}\newlineStandard Deviation ≈15.136\approx 15.136

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