Final answer:
To find the standard deviation of the given data, calculate the mean, variance, and standard deviation. The mean is -3, the variance is 2, and the standard deviation is 1.4.
Step-by-step explanation:
To find the standard deviation of the given data, we first need to calculate the mean of the data. The mean is calculated by multiplying each data value by its corresponding probability and summing the results. In this case, the mean is (-6 * 0.2) + (-5 * 0.1) + (-4 * 0.2) + (-3 * 0.2) + (-2 * 0.1) + (-1 * 0.2) = -3.
Next, we calculate the variance by squaring the difference between each data value and the mean, multiplying it by the corresponding probability, and summing the results. The variance is (-6 - (-3))^2 * 0.2 + (-5 - (-3))^2 * 0.1 + (-4 - (-3))^2 * 0.2 + (-3 - (-3))^2 * 0.2 + (-2 - (-3))^2 * 0.1 + (-1 - (-3))^2 * 0.2 = 2.
Finally, the standard deviation is the square root of the variance. In this case, the standard deviation is √2 = 1.4 (rounded to one decimal place).