Question

Find the standard deviation of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary

44,88,40,46,83,47,47,53,52,52,86

Answer 1

For the given data set, the standard deviation is approximately 18.32.

Step-by-step explanation:

To find the standard deviation of a data set, follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Calculate the mean of the squared differences.
4. Take the square root of the mean from step 3 to find the standard deviation.

For the data set 44, 88, 40, 46, 83, 47, 47, 53, 52, 52, and 86:

1. The mean is (44+88+40+46+83+47+47+53+52+52+86)/11 = 58.64
2. Subtract the mean from each data point and square the result:
   • (44-58.64)^2 = 208.27
   • (88-58.64)^2 = 879.13
   • (40-58.64)^2 = 344.88
   • (46-58.64)^2 = 159.97
   • (83-58.64)^2 = 595.48
   • (47-58.64)^2 = 136.03
   • (47-58.64)^2 = 136.03
   • (53-58.64)^2 = 32.09
   • (52-58.64)^2 = 44.76
   • (52-58.64)^2 = 44.76
   • (86-58.64)^2 = 757.53
3. Calculate the mean of the squared differences: (208.27+879.13+344.88+159.97+595.48+136.03+136.03+32.09+44.76+44.76+757.53)/11 = 335.65
4. Take the square root of 335.65 to find the standard deviation: √335.65 ≈ 18.32 (rounded to the nearest hundredth).

Therefore, the standard deviation of the data set is approximately 18.32.