The sample data below shows the number of hours spent by 5 students over the weekend to prepare for Monday's Business Statistics exam. The sample standard deviation of the number of hours spent by the 5 students is closest to:
A)3.6 hours
B)4.1 hours
C)13.2 hours
D)16.5 hours

Question

The sample data below shows the number of hours spent by 5 students over the weekend to prepare for Monday's Business Statistics exam.  The sample standard deviation of the number of hours spent by the 5 students is closest to:
A)3.6 hours 
B)4.1 hours 
C)13.2 hours 
D)16.5 hours

Quizplus · Accepted Answer

To calculate the sample standard deviation, we first need to find the mean:

Mean = (2 + 4 + 5 + 6 + 8) / 5 = 5

Next, we calculate the deviation of each data point from the mean:

Deviation = Data Point - Mean

For example, the deviation of the first data point, 2, from the mean, 5, is:

2 - 5 = -3

We square each deviation:

(-3)^2 = 9 
(-1)^2 = 1 
(0)^2 = 0 
(1)^2 = 1 
(3)^2 = 9

We sum the squared deviations:

9 + 1 + 0 + 1 + 9 = 20

We divide by n-1 (in this case, 5-1=4) and take the square root:

sqrt(20/4) = 2.24

Therefore, the closest choice is B) 4.1 hours.

The Sample Data Below Shows the Number of Hours Spent