Answer:
The line's most probable length is 69.4012 meters.
The standard deviation is 0.0032 meters.
Step-by-step explanation:
We are given the following in the question:
69.401, 69.400, 69.402, 69.396, 69.406, 69.401, 69.396, 69.401, 69.405, 69.404
Formula:
where
are data points,
is the mean and n is the number of observations.
![Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Ctext%7BSum%20of%20all%20observations%7D%7D%7B%5Ctext%7BTotal%20number%20of%20observation%7D%7D)
![Mean =\displaystyle\frac{694.012}{10} = 69.4012](https://tex.z-dn.net/?f=Mean%20%3D%5Cdisplaystyle%5Cfrac%7B694.012%7D%7B10%7D%20%3D%2069.4012)
The line's most probable length is 69.4012 meters.
Sum of squares of differences = 0.0001016
![\sigma = \sqrt{\dfrac{0.0001016}{10}} = 0.0032](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cdfrac%7B0.0001016%7D%7B10%7D%7D%20%3D%200.0032)
The standard deviation is 0.0032 meters.