Asked by Alysha Brown on May 09, 2024
Verified
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
Data
Information collected for analysis or reference.
- Deduce the standard deviation for several datasets.
Verified Answer
AL
Austin LutherMay 15, 2024
Final Answer :
B
Explanation :
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.
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.
Learning Objectives
- Deduce the standard deviation for several datasets.