Value −3 −2 −1 0 1 Total Observations 1 2 3 2 1 Calculate the standard deviation of the dataset. Round the answer to the nearest hundredth.
To calculate the standard deviation of the dataset, we first need to find the mean:
Mean = (1*(-3) + 2*(-2) + 3*(-1) + 2*(0) + 1*(1)) / 9
Mean = (-3 - 4 - 3 + 0 + 1) / 9
Mean = -9 / 9
Mean = -1
Next, we calculate the squared differences between each observation and the mean, then sum them up:
(1 - (-1))^2 = 4
(2 - (-1))^2 = 9
(3 - (-1))^2 = 16
(2 - (-1))^2 = 9
(1 - (-1))^2 = 4
Sum of squared differences = 4 + 9 + 16 + 9 + 4
Sum of squared differences = 42
We calculate the variance:
Variance = 42 / 9
Variance = 4.67
Finally, we calculate the standard deviation by taking the square root of the variance:
Standard deviation = √4.67
Standard deviation ≈ 2.16
Therefore, the standard deviation of the dataset is approximately 2.16 rounded to the nearest hundredth.