Respuesta :
Answer:
a) x_average = 34.51077°, b) σ = 2.69°, c) σ = 2.5107°
Explanation:
a) The most likely value of a measure is
x_average = ∑ [tex]x_{i}[/tex] / n-1
The angle measurements are in the Sixty Base System, to simplify the calculations let's reduce the measurements
1° = 60 min
1 min = 60 s
Table 1
Angle angle converted (x-x_average) (x-x_average)²
32 32,000 2,51077 6.3040
37 00” 37,000 2,48923 6.1963
32 32,000 2,51077 6.3040
37 10” 37.00277 2.492 6.2101
32 32,000 2,51077 6.3040
37 10” 37.1667 2.6559 7.0538
32 32,000 2,51077 6.3040
36 55” 36.9167 2.4059 5.7884
With this values in degree the calculation is easier
x_average = (32 + 37 + 32 + 37.00277 + 32 + 37.1667 + 32 + 36.9167) / 8
x_average = 276.08617 / 8
x_average = 34.51077
b) We look for the standard deviation
σ = √ ([tex]x_{i}[/tex] -x_average)² / n-1
σ = √ 50.4646 / (8-1)
σ = 2.69
c) the deviation from the mean
σ = | x -[tex]x_{i}[/tex]| / n
σ = 20.08611 / 8
σ = 2.5107
