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For the following set of data, find the population standard deviation, to the nearest thousandth. 118,83,54,162,83,42,133

For the following set of data, find the population standard deviation, to the nearest thousandth.\newline118,83,54,162,83,42,133 118,83,54,162,83,42,133

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Q. For the following set of data, find the population standard deviation, to the nearest thousandth.\newline118,83,54,162,83,42,133 118,83,54,162,83,42,133
  1. Calculate Mean: First, we need to calculate the mean (average) of the data set. To do this, we add up all the data points and then divide by the number of data points.\newlineMean = (118+83+54+162+83+42+133)/7(118 + 83 + 54 + 162 + 83 + 42 + 133) / 7\newlineMean = 675/7675 / 7\newlineMean ≈96.4286\approx 96.4286
  2. Calculate Variance: Next, we calculate the variance. To do this, we subtract the mean from each data point, square the result, and then average these squared differences.\newlineVariance = [(118−96.4286)2+(83−96.4286)2+(54−96.4286)2+(162−96.4286)2+(83−96.4286)2+(42−96.4286)2+(133−96.4286)2]/7[(118 - 96.4286)^2 + (83 - 96.4286)^2 + (54 - 96.4286)^2 + (162 - 96.4286)^2 + (83 - 96.4286)^2 + (42 - 96.4286)^2 + (133 - 96.4286)^2] / 7\newlineVariance ≈[(21.5714)2+(−13.4286)2+(−42.4286)2+(65.5714)2+(−13.4286)2+(−54.4286)2+(36.5714)2]/7\approx [(21.5714)^2 + (-13.4286)^2 + (-42.4286)^2 + (65.5714)^2 + (-13.4286)^2 + (-54.4286)^2 + (36.5714)^2] / 7\newlineVariance ≈[465.3061+180.3673+1799.3061+4300.3673+180.3673+2962.4489+1337.5510]/7\approx [465.3061 + 180.3673 + 1799.3061 + 4300.3673 + 180.3673 + 2962.4489 + 1337.5510] / 7\newlineVariance ≈11225.714\approx 11225.714
  3. Calculate Standard Deviation: Finally, we calculate the population standard deviation by taking the square root of the variance.\newlineStandard Deviation = 11225.714\sqrt{11225.714}\newlineStandard Deviation ≈105.9506\approx 105.9506
  4. Round Standard Deviation: We round the standard deviation to the nearest thousandth as requested. Standard Deviation ≈105.951\approx 105.951

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