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For the following set of data, find the sample standard deviation, to the nearest thousandth. pected Value 96,63,83,78,55,96,114,52 Calculate Measure of Dispersion Normal Distribution - Find Z Score Normal Distribution - Empirical Rule Normal Distribution - Find Area Normal Distribution w/ Population Size Calculator Javon Thomas Log Out Copy Values for Calculator Open Statistics Calculator Answer Attempt 1 out of 20 Submit Answer

For the following set of data, find the sample standard deviation, to the nearest thousandth.96,63,83,78,55,96,114,52 96,63,83,78,55,96,114,52

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Q. For the following set of data, find the sample standard deviation, to the nearest thousandth.96,63,83,78,55,96,114,52 96,63,83,78,55,96,114,52
  1. List Data Set: List the given data set and verify its correctness.\newlineThe given data set is: 96,63,83,78,55,96,114,5296, 63, 83, 78, 55, 96, 114, 52.\newlineWe need to ensure that all values are correctly listed and there are no duplicates or missing values unless intentionally repeated.
  2. Calculate Mean: Calculate the mean (average) of the data set.\newlineTo find the mean, sum all the values and divide by the number of values.\newlineMean = (96+63+83+78+55+96+114+52)/8(96 + 63 + 83 + 78 + 55 + 96 + 114 + 52) / 8\newlineMean = (637)/8(637) / 8\newlineMean = 79.62579.625
  3. Subtract and Square: Subtract the mean from each data value and square the result.\newlineThis step is part of calculating the variance, which is the average of the squared differences from the Mean.\newlineSquared differences: \newline(96−79.625)2=268.515625(96 - 79.625)^2 = 268.515625\newline(63−79.625)2=277.515625(63 - 79.625)^2 = 277.515625\newline(83−79.625)2=11.390625(83 - 79.625)^2 = 11.390625\newline(78−79.625)2=2.640625(78 - 79.625)^2 = 2.640625\newline(55−79.625)2=608.015625(55 - 79.625)^2 = 608.015625\newline(96−79.625)2=268.515625(96 - 79.625)^2 = 268.515625\newline(114−79.625)2=1180.515625(114 - 79.625)^2 = 1180.515625\newline(52−79.625)2=767.015625(52 - 79.625)^2 = 767.015625
  4. Sum Squared Differences: Sum the squared differences.\newlineSum of squared differences = 268.515625+277.515625+11.390625+2.640625+608.015625+268.515625+1180.515625+767.015625268.515625 + 277.515625 + 11.390625 + 2.640625 + 608.015625 + 268.515625 + 1180.515625 + 767.015625\newlineSum of squared differences = 3384.1253384.125
  5. Calculate Variance: Divide the sum of squared differences by the sample size minus one to get the sample variance.\newlineSince we have 88 data points, we divide by 77 (n−1n-1 for a sample standard deviation).\newlineSample variance = rac{3384.125}{7}\newlineSample variance = 483.44642857483.44642857
  6. Calculate Standard Deviation: Take the square root of the sample variance to get the sample standard deviation.\newlineSample standard deviation = 483.44642857\sqrt{483.44642857}\newlineSample standard deviation ≈21.986\approx 21.986
  7. Round Standard Deviation: Round the sample standard deviation to the nearest thousandth.\newlineRounded sample standard deviation = 21.98621.986

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