Answer:
a) ![\bar X =\frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%5Cfrac%7B736.352%2B736.363%2B736.375%2B736.324%2B736.358%2B736.383%7D%7B6%7D%3D736.359)
b) The sample deviation is calculated from the following formula:
![s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D%7D)
And for this case after replace the values and with the sample mean already calculated we got:
![s= 0.0206](https://tex.z-dn.net/?f=%20s%3D%200.0206)
If we assume that the data represent a population then the standard deviation would be given by:
![\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn%7D%7D)
And then the deviation would be:
![\sigma=0.0188](https://tex.z-dn.net/?f=%20%5Csigma%3D0.0188)
Step-by-step explanation:
For this case we have the following dataset:
736.352, 736.363, 736.375, 736.324, 736.358, and 736.383
Part a: Determine the most probable value.
For this case the most probably value would be the sample mean given by this formula:
![\bar X =\frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%20%5Cbar%20X%20%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
And if we replace we got:
![\bar X =\frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%5Cfrac%7B736.352%2B736.363%2B736.375%2B736.324%2B736.358%2B736.383%7D%7B6%7D%3D736.359)
Part b: Determine the standard deviation
The sample deviation is calculated from the following formula:
![s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D%7D)
And for this case after replace the values and with the sample mean already calculated we got:
![s= 0.0206](https://tex.z-dn.net/?f=%20s%3D%200.0206)
If we assume that the data represent a population then the standard deviation would be given by:
![\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn%7D%7D)
And then the deviation would be:
![\sigma=0.0188](https://tex.z-dn.net/?f=%20%5Csigma%3D0.0188)