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zloy xaker
2 months ago
13

A distance AB is observed repeatedly using the same equipment and procedures, and the results, in meters, are listed below:69.40

1, 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.
Mathematics
1 answer:
Zina [12.3K]2 months ago
3 0

Answer:

The most likely length of the line is 69.4012 meters.

The calculated standard deviation amounts to 0.0032 meters.

Step-by-step explanation:

In the problem, the following values are provided:

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 represent data points, \bar{x} is the average, and n indicates the count of observations.  

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

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

The most likely length of the line is 69.4012 meters.

Sum of squares of differences = 0.0001016

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

The calculated standard deviation amounts to 0.0032 meters.

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