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For the following set of data, find the population standard deviation, to the nearest hundredth.\newline139,126,51,61,77,109,112139, 126, 51, 61, 77, 109, 112\newline

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Q. For the following set of data, find the population standard deviation, to the nearest hundredth.\newline139,126,51,61,77,109,112139, 126, 51, 61, 77, 109, 112\newline
  1. List data set & calculate mean: List the data set and calculate the mean (average).\newlineThe data set is: 139,126,51,61,77,109,112139, 126, 51, 61, 77, 109, 112.\newlineTo calculate the mean, sum all the values and divide by the number of values.\newlineMean = (139+126+51+61+77+109+112)/7(139 + 126 + 51 + 61 + 77 + 109 + 112) / 7\newlineMean = 675/7675 / 7\newlineMean ≈96.43\approx 96.43
  2. Subtract mean & square: Subtract the mean from each data value and square the result.\newlineThis step involves calculating the squared differences from the mean for each data point.\newline(139−96.43)2=42.572≈1812.2049(139 - 96.43)^2 = 42.57^2 \approx 1812.2049\newline(126−96.43)2=29.572≈874.6849(126 - 96.43)^2 = 29.57^2 \approx 874.6849\newline(51−96.43)2=−45.432≈2063.8849(51 - 96.43)^2 = -45.43^2 \approx 2063.8849\newline(61−96.43)2=−35.432≈1255.2849(61 - 96.43)^2 = -35.43^2 \approx 1255.2849\newline(77−96.43)2=−19.432≈377.5049(77 - 96.43)^2 = -19.43^2 \approx 377.5049\newline(109−96.43)2=12.572≈158.0849(109 - 96.43)^2 = 12.57^2 \approx 158.0849\newline(112−96.43)2=15.572≈242.5249(112 - 96.43)^2 = 15.57^2 \approx 242.5249
  3. Sum squared differences: Sum the squared differences.\newlineSum = 1812.2049+874.6849+2063.8849+1255.2849+377.5049+158.0849+242.52491812.2049 + 874.6849 + 2063.8849 + 1255.2849 + 377.5049 + 158.0849 + 242.5249\newlineSum ≈7784.1743\approx 7784.1743
  4. Divide by data values: Divide the sum of squared differences by the number of data values to find the variance.\newlineSince we are calculating the population standard deviation, we divide by the total number of data points, which is 77.\newlineVariance =7784.1743/7= 7784.1743 / 7\newlineVariance hickapprox1112.0249 hickapprox 1112.0249
  5. Find standard deviation: Take the square root of the variance to find the population standard deviation.\newlineStandard Deviation = 1112.0249\sqrt{1112.0249}\newlineStandard Deviation ≈33.35\approx 33.35

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