For the following data set,calculate the estimated population standard deviation. 1.72,4.01,2.55,0.67,1.93,2.05,2.69,3.13,1.22,3.84
A)1.0243
B)1.0492
C)1.0797
D)1.1659

Question

Quizplus · Accepted Answer

Using the formula for an estimated population standard deviation, we can find the answer as follows: 
1. Calculate the mean: 
(1.72 + 4.01 + 2.55 + 0.67 + 1.93 + 2.05 + 2.69 + 3.13 + 1.22 + 3.84) / 10 = 2.485 
2. Calculate the deviations from the mean for each data point: 
(1.72 - 2.485) = -0.765 
(4.01 - 2.485) = 1.525 
(2.55 - 2.485) = 0.065 
(0.67 - 2.485) = -1.815 
(1.93 - 2.485) = -0.555 
(2.05 - 2.485) = -0.435 
(2.69 - 2.485) = 0.205 
(3.13 - 2.485) = 0.645 
(1.22 - 2.485) = -1.265 
(3.84 - 2.485) = 1.355 
3. Square each deviation: 
(-0.765)^2 = 0.585225 
(1.525)^2 = 2.325625 
(0.065)^2 = 0.004225 
(-1.815)^2 = 3.292225 
(-0.555)^2 = 0.308025 
(-0.435)^2 = 0.189225 
(0.205)^2 = 0.042025 
(0.645)^2 = 0.416025 
(-1.265)^2 = 1.601225 
(1.355)^2 = 1.836025 
4. Find the sum of the squared deviations: 
0.585225 + 2.325625 + 0.004225 + 3.292225 + 0.308025 + 0.189225 + 0.042025 + 0.416025 + 1.601225 + 1.836025 = 10.9998 
5. Divide the sum by the sample size minus one, then take the square root: 
√(10.9998 / 9) ≈ 1.0797

For the Following Data Set,calculate the Estimated Population Standard Deviation