For this set of data, the standard deviation (s) is equal to ______. 104, 116, 95, 121, 87
A) 12.66
B) 14.15
C) 104.60
D) 523

Question

Quizplus · Accepted Answer

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

Mean = (104 + 116 + 95 + 121 + 87) / 5 = 104.6

Next, we need to find the deviations of each data point from the mean:

104 - 104.6 = -0.6 
116 - 104.6 = 11.4 
95 - 104.6 = -9.6 
121 - 104.6 = 16.4 
87 - 104.6 = -17.6

Then, we square each deviation:

(-0.6)^2 = 0.36 
(11.4)^2 = 129.96 
(-9.6)^2 = 92.16 
(16.4)^2 = 268.96 
(-17.6)^2 = 309.76

We add up these squared deviations:

0.36 + 129.96 + 92.16 + 268.96 + 309.76 = 801.2

We divide this sum by n-1 (which is 4 in this case since there are 5 data points) and then take the square root:

s = √(801.2 / 4) = 14.15

Therefore, the standard deviation is 14.15. The answer is B.

For This Set of Data, the Standard Deviation (S) Is