Question

A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed below:69.401, 69.400, 69.402, 69.396, 69.406, 69.401, 69.396, 69.401, 69.405, and 69.404Calculate (a) the line's most probable length, (b) the standard deviation.

Answer 1

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:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{694.012}{10} = 69.4012$

The line's most probable length is 69.4012 meters.

Sum of squares of differences = 0.0001016

$\sigma = \sqrt{\dfrac{0.0001016}{10}} = 0.0032$

The standard deviation is 0.0032 meters.