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Question\newlineWatch Video\newlineMemory usage: \newline132MB132\text{MB}\newlineFor the following set of data, find the sample standard deviation, to the nearest hundredth.\newline68,20,87,61,85,43,7468,20,87,61,85,43,74\newlineCopy Values for Calculator\newlineOpen Statistics Calculator\newlineAnswer Attempt 22 out of 22\newline26962696

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Q. Question\newlineWatch Video\newlineMemory usage: \newline132MB132\text{MB}\newlineFor the following set of data, find the sample standard deviation, to the nearest hundredth.\newline68,20,87,61,85,43,7468,20,87,61,85,43,74\newlineCopy Values for Calculator\newlineOpen Statistics Calculator\newlineAnswer Attempt 22 out of 22\newline26962696
  1. List data set & count: List the data set and verify the number of data points.\newlineData set: 68,20,87,61,85,43,7468, 20, 87, 61, 85, 43, 74\newlineNumber of data points (n):7(n): 7
  2. Calculate mean: Calculate the mean (average) of the data set.\newlineMean = (68+20+87+61+85+43+74)/7(68 + 20 + 87 + 61 + 85 + 43 + 74) / 7\newlineMean = (438)/7(438) / 7\newlineMean = 62.5762.57 (rounded to two decimal places)
  3. Calculate squared differences: Calculate the squared differences from the mean for each data point.\newline(68−62.57)2=29.64(68 - 62.57)^2 = 29.64\newline(20−62.57)2=1805.44(20 - 62.57)^2 = 1805.44\newline(87−62.57)2=595.05(87 - 62.57)^2 = 595.05\newline(61−62.57)2=2.47(61 - 62.57)^2 = 2.47\newline(85−62.57)2=501.76(85 - 62.57)^2 = 501.76\newline(43−62.57)2=383.04(43 - 62.57)^2 = 383.04\newline(74−62.57)2=130.69(74 - 62.57)^2 = 130.69
  4. Sum squared differences: Sum the squared differences.\newlineSum of squared differences = 29.64+1805.44+595.05+2.47+501.76+383.04+130.6929.64 + 1805.44 + 595.05 + 2.47 + 501.76 + 383.04 + 130.69\newlineSum of squared differences = 3447.093447.09
  5. Calculate variance: Divide the sum of squared differences by the number of data points minus one to find the variance (since this is a sample standard deviation).\newlineVariance = 3447.09(7−1)\frac{3447.09}{(7 - 1)}\newlineVariance = 3447.096\frac{3447.09}{6}\newlineVariance = 574.515574.515
  6. Find standard deviation: Take the square root of the variance to find the sample standard deviation.\newlineSample standard deviation = 574.515\sqrt{574.515}\newlineSample standard deviation ≈23.967\approx 23.967 (rounded to three decimal places)
  7. Round standard deviation: Round the sample standard deviation to the nearest hundredth.\newlineSample standard deviation ≈23.97\approx 23.97

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