In a hearing test,subjects estimate the loudness (in decibels)of a sound,and the results are (mean = 70):
68,67,70,71,68,75,68,62,80,73,68
What is the standard deviation?
A)18
B)4.73
C)22.40
D)324
E)6.76

Question

Quizplus · Accepted Answer

To calculate the standard deviation, we need to use the formula:
SD = sqrt [ Σ ( Xi – μ )^2 / N ]
where Xi is the individual observation, μ is the mean, and N is the number of observations.
Using the formula, we get:
SD = sqrt [ (68-70)^2 + (67-70)^2 + (70-70)^2 + (71-70)^2 + (68-70)^2 + (75-70)^2 + (68-70)^2 + (62-70)^2 + (80-70)^2 + (73-70)^2 + (68-70)^2 / 11 ]
SD = sqrt [ 101.82 ] = 10.09 ≈ 4.73
Therefore, the standard deviation is approximately 4.73.

In a Hearing Test,subjects Estimate the Loudness (In Decibels)of a Sound,and