Question

Calculate the standard deviation of the of the data set, Round to the nearest tenth.
{6, 3, 6, 4, 2, 2, 5, 7}

a. 4
b. 1.8
c. 1.2
d. -3.4

Answer 1

The mean of the data set is (6 + 3 + 6 + 4 + 2 + 2 + 5 + 7)/8 = 4.375

Next, calculate the squared difference from the mean for each number:
(6-4.375)^2 = 4.953125
(3-4.375)^2 = 1.890625
(6-4.375)^2 = 4.953125
(4-4.375)^2 = 0.140625
(2-4.375)^2 = 5.390625
(2-4.375)^2 = 5.390625
(5-4.375)^2 = 0.390625
(7-4.375)^2 = 6.890625

Now, calculate the variance:
(4.953125 + 1.890625 + 4.953125 + 0.140625 + 5.390625 + 5.390625 + 0.390625 + 6.890625)/8 = 3.5234375

Finally, calculate the standard deviation by taking the square root of the variance:
√3.5234375 = 1.9

The standard deviation of the data set is approximately 1.9, so the closest answer choice is b. 1.8.