Question

An angle is observed repeatedly using the same equipment and procedures producing the data below:32 ∘ 37' 00", 32 ∘ 37' 10", 32 ∘ 37' 10", and 32 ∘ 36' 55"Part A Calculate the angle is most probable value.Calculate the angle's most probable value

Calculate the standard deviation.
Calculate the standard deviation of the mean

Answer 1

a) x_average = 34.51077°, b) σ = 2.69°, c) σ = 2.5107°

Step-by-step explanation:

a) The most likely value of a measure is

x_average = ∑
`x_(i)` / 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 = √ (
`x_(i)` -x_average)² / n-1

σ = √ 50.4646 / (8-1)

σ = 2.69

c) the deviation from the mean

σ = | x -
`x_(i)`| / n

σ = 20.08611 / 8

σ = 2.5107