Can you help me calculate the standard deviation of the data set. Round to nearest tenth. Please
{20,35,41,48,79,83,83,97,120}
To calculate the standard deviation of the data set {20, 35, 41, 48, 79, 83, 83, 97, 120}, follow these steps:
1. Find the mean of the data set:
Mean = (20 + 35 + 41 + 48 + 79 + 83 + 83 + 97 + 120) / 9
Mean = 606 / 9
Mean = 67.3
2. Subtract the mean from each data point and square the result:
(20 - 67.3)^2 = 2339.29
(35 - 67.3)^2 = 1034.49
(41 - 67.3)^2 = 689.64
(48 - 67.3)^2 = 373.29
(79 - 67.3)^2 = 136.89
(83 - 67.3)^2 = 246.49
(83 - 67.3)^2 = 246.49
(97 - 67.3)^2 = 880.89
(120 - 67.3)^2 = 2207.29
3. Find the sum of all the squared differences:
2339.29 + 1034.49 + 689.64 + 373.29 + 136.89 + 246.49 + 246.49 + 880.89 + 2207.29 = 7108.66
4. Divide the sum by the number of data points minus 1 (which in this case is 8):
7108.66 / 8 = 888.58
5. Take the square root of the result:
Standard deviation = √888.58 ≈ 29.8
Therefore, the standard deviation of the data set {20, 35, 41, 48, 79, 83, 83, 97, 120} is approximately 29.8 (rounded to the nearest tenth).