use the tabl to answer the question

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?

Answer 1

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.