To determine the most probable value of the angle, the standard deviation, and the standard error of the mean from the given observations, you can follow these steps:
a) **Most Probable Value of the Angle (Mean):**
To find the mean (average) of the given angles, add up all the observations and divide by the total number of observations.
\[ \text{Mean} = \frac{\sum \text{Observations}}{\text{Number of Observations}} \]
\[ \text{Mean} = \frac{47°26'13" + 47°26'10" + \ldots + 47°26'14"}{11} \]
Calculate the mean using the provided observations.
b) **Standard Deviation:**
The standard deviation measures the dispersion or spread of the observations around the mean. You can calculate it using the following formula:
\[ \text{Standard Deviation} = \sqrt{\frac{\sum (\text{Observation} - \text{Mean})^2}{\text{Number of Observations}}} \]
Subtract the mean from each observation, square the result, sum up these squared differences, divide by the number of observations, and then take the square root of the result to find the standard deviation.
c) **Standard Error of the Mean:**
The standard error of the mean (SE) measures the variability of the sample mean. It is calculated by dividing the standard deviation by the square root of the number of observations:
\[ \text{Standard Error} = \frac{\text{Standard Deviation}}{\sqrt{\text{Number of Observations}}} \]
Substitute the calculated standard deviation into the formula and compute the standard error.
Please perform the calculations using the provided observations to find the most probable value of the angle, the standard deviation, and the standard error of the mean.