Question

It is desired to determine the most probable value of an angle which has been measured at different times by different observers. The values observed were as follows: 74

∘
39
′
45
′′
(measured two times), 74 39'27" (measured four times), and 74 39'35" (measured six times).

Answer 1

To determine the most probable value of an angle measured by different observers, we can use the method of averaging the observed values. Let's calculate the average of the given measurements:

1st measurement: 74° 39' 45" (1 time)
2nd measurement: 74° 39' 45" (1 time)
3rd measurement: 74° 39' 27" (4 times)
4th measurement: 74° 39' 35" (6 times)

To calculate the average, we need to convert all the measurements to a common unit, such as degrees:

1st measurement: 74° 39' 45" = 74 + (39/60) + (45/3600) = 74.6625°
2nd measurement: 74° 39' 45" = 74 + (39/60) + (45/3600) = 74.6625°
3rd measurement: 74° 39' 27" = 74 + (39/60) + (27/3600) = 74.6575°
4th measurement: 74° 39' 35" = 74 + (39/60) + (35/3600) = 74.6597°

Now, let's calculate the average:

Average = (74.6625° + 74.6625° + 74.6575° + 74.6597°) / (1 + 1 + 4 + 6)

Simplifying this expression will give us the most probable value of the angle.