Final answer:
To find the standard deviation of a sample, calculate the mean, find each data point's deviation, square them, sum them. The nearest answer choice is (c) 1.94.
Step-by-step explanation:
To find the standard deviation of the sample data set {5, 7, 6, 9, 6, 4, 4, 6, 5, 9, 3}, we follow these steps: Calculate the mean (average) of the data set. Subtract the mean from each data value to find the deviations. Square each deviation to get the squared deviations.
Add all the squared deviations together. Divide this sum by one less than the number of data points (n-1) to get the variance. Take the square root of the variance to get the standard deviation. The calculations are performed as follows:
Mean = (5 + 7 + 6 + 9 + 6 + 4 + 4 + 6 + 5 + 9 + 3) / 11 = 64 / 11 ≈ 5.82. Deviations: (5-5.82), (7-5.82), ... Squared deviations: (5-5.82)^2, (7-5.82)^2, ... Sum of squared deviations ≈ 38.18. Variance = 38.18 / (11-1) = 38.18 / 10 ≈ 3.818. Standard deviation = √3.818 ≈ 1.953.