In a rating of the satisfaction with their instructor, 13 students gave the following scores from a scale of 1 to 5 (mean = 3):
3, 2, 1, 1, 5, 5, 4, 3, 3, 2, 4, 3, 3

-What is the standard deviation?
A)3
B)4
C)1.291
D)1.667
E)2.779

Question

In a rating of the satisfaction with their instructor, 13 students gave the following scores from a scale of 1 to 5 (mean = 3):
3, 2, 1, 1, 5, 5, 4, 3, 3, 2, 4, 3, 3

-What is the standard deviation?
A)3
B)4
C)1.291
D)1.667
E)2.779

Quizplus · Accepted Answer

The standard deviation is a measure of the amount of variation or dispersion of a set of values. It tells us how much the values deviate from the mean. In this case, we are given a set of values and their mean, and asked to calculate the standard deviation. Using the formula for standard deviation, we get:

Standard deviation = sqrt[(sum of (xi - x)^2)/n]

where xi is each individual value in the set, x is the mean, and n is the number of values in the set.

Calculating this for the given set of values, we get:

Standard deviation = sqrt[((2-4)^2 + (4-4)^2 + (4-4)^2 + (4-4)^2 + (6-4)^2)/5]

= sqrt[(4 + 0 + 0 + 0 + 4)/5]

= sqrt[8/5]

= 1.791

None of the choices given matches this value exactly, so we need to choose the closest one. The closest choice is C, 1.291, which is off by about 0.5 but is the closest approximation to our calculated value. Therefore, the best choice is C.

In a Rating of the Satisfaction with Their Instructor, 13