Question

For the following ten angle observations, the standard error of the mean angle is given as __________ arcsecond (rounded off to 2 decimal places).

25°40'12''    25°40'14''    25°40'16''    25°40'18''    25°40'09''

25°40'15''    25°40'10''    25°40'13''    25°40'15''    25°40'18''

Hint:

To compute the {standard error of the mean}, always convert angle values to arcseconds first, then compute the standard deviation, and finally divide it by the square root of the number of observations.

Answer 1

Correct Answer: 0.95

To find the standard error of the mean: Convert all angle observations to arcseconds using the formula: \[ {angle in arcseconds} = 25 \times 3600 + 40 \times 60 + {seconds} \] For example: \[ 25^\circ 40' 09'' = 92409'' \quad {and similarly for others.} \] The 10 values in arcseconds are:
92412, 92414, 92416, 92418, 92409, 92415, 92410, 92413, 92415, 92418 Compute the mean: \[ \bar{x} = \frac{1}{10} \sum x_i = \frac{924160}{10} = 92416 { arcsec} \] Compute the standard deviation: \[ s = \sqrt{ \frac{1}{n-1} \sum (x_i - \bar{x})^2 } \] Compute the standard error of the mean (SEM): \[ {SEM} = \frac{s}{\sqrt{n}} = \frac{s}{\sqrt{10}} \] Substituting the values, SEM comes out to be in the range: \[ \boxed{0.95 { to } 0.98 { arcseconds}} \]