Discussion
If the standard deviation of an observation is ± 10 m, then the most probable error would be:
Answer: A
The most probable error is 6.745 m.
For normally distributed errors, the probable error (the value with an even chance of being exceeded) is 0.6745 times the standard deviation:
\[ \begin{aligned} E_p &= 0.6745\,\sigma \\ &= 0.6745 \times 10 = 6.745\ \text{m} \end{aligned} \]
0.6745 m is the multiplier applied to a standard deviation of 1 m instead of 10 m. 10 m is the standard deviation itself, and 20 m is twice it, roughly the 95% confidence limit, not the probable error.
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