use the tabl to answer the question
Value| -3|-2|-1|0|1|
Total Observations| 1|2|3|2|1
calculate the standard deviation of the dataset round your answer to the nearest hundreth
The standard deviationis what?
To calculate the standard deviation, we first need to calculate the mean of the dataset:
Mean = (-3*1 + -2*2 + -1*3 + 0*2 + 1*1) / (1+2+3+2+1) = (-3 - 4 - 3 + 0 + 1) / 9 = -9 / 9 = -1
Next, we calculate the variance of the dataset:
Variance = [(1 * (-3+1)^2) + (2 * (-2+1)^2) + (3 * (-1+1)^2) + (2 * (0+1)^2) + (1 * (1+1)^2)] / 9
Variance = [(1 * 4) + (2 * 1) + (3 * 0) + (2 * 1) + (1 * 4)] / 9
Variance = (4 + 2 + 0 + 2 + 4) / 9
Variance = 12 / 9
Variance = 1.33
Finally, the standard deviation is the square root of the variance:
Standard Deviation = √1.33 ≈ 1.15
Therefore, the standard deviation of the dataset is approximately 1.15.