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For the following set of data, find the sample standard deviation, to the nearest hundredth. 40,86,79,25,75,67,86,38 Copy Values for Calculator Open Statistics Calculator Answer Attempt 4 out of 20 Submit Answer Log Out

For the following set of data, find the sample standard deviation, to the nearest hundredth.\newline40,86,79,25,75,67,86,38 40,86,79,25,75,67,86,38

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Q. For the following set of data, find the sample standard deviation, to the nearest hundredth.\newline40,86,79,25,75,67,86,38 40,86,79,25,75,67,86,38
  1. Calculate Mean: First, we need to find the mean (average) of the data set. To do this, we add up all the numbers and then divide by the number of values in the set.\newlineMean = (40+86+79+25+75+67+86+38)/8(40 + 86 + 79 + 25 + 75 + 67 + 86 + 38) / 8\newlineMean = 496/8496 / 8\newlineMean = 6262
  2. Calculate Variance: Next, we calculate the variance. To do this, we subtract the mean from each number to find the deviation for each number, square each deviation, sum all the squared deviations, and then divide by the number of values minus one (since this is a sample standard deviation).\newlineVariance = [(40−62)2+(86−62)2+(79−62)2+(25−62)2+(75−62)2+(67−62)2+(86−62)2+(38−62)2]/(8−1)[(40 - 62)^2 + (86 - 62)^2 + (79 - 62)^2 + (25 - 62)^2 + (75 - 62)^2 + (67 - 62)^2 + (86 - 62)^2 + (38 - 62)^2] / (8 - 1)\newlineVariance = [(−22)2+242+172+(−37)2+132+52+242+(−24)2]/7[(-22)^2 + 24^2 + 17^2 + (-37)^2 + 13^2 + 5^2 + 24^2 + (-24)^2] / 7\newlineVariance = [484+576+289+1369+169+25+576+576]/7[484 + 576 + 289 + 1369 + 169 + 25 + 576 + 576] / 7\newlineVariance = 4064/74064 / 7\newlineVariance ≈580.5714\approx 580.5714
  3. Find Standard Deviation: Finally, we find the sample standard deviation by taking the square root of the variance.\newlineSample Standard Deviation = 580.5714\sqrt{580.5714}\newlineSample Standard Deviation ≈24.0949\approx 24.0949

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