Question

Standard Deviation of the Mean

What is the 50% error of the mean for the angles observed below?

Trial Angle
A 42º 52′ 09"
B 42º 53′ 11"
C 42º 52′ 28"
D 42º 52′ 31"
E 42º 52′ 22"
F 42º 53′ 05"
Express your answer to three significant figures.

View Available Hint(s)

E50=±
E 50 = ±

nothing

sec

Answer 1

Answer: the Standard deviation for the angles is 0.00766°

Explanation:

We first covert the angles to standard angle format.

For A) 42° 52' 09'' we have;

42 + (52/60) + (9/3600)

= 42 + 0.866 + 0.00305 = 42.8685°

Repeating the same procedure for the other angles we have

B) 42. 88605°

C) 42.87377°

D) 42.87461°

E) 42.87211°

F) 42.88438°

Mean of the angles becomes

x' = (42.8685+42.88605+42.87377+42.87461+42.87211+42.88448)/6

x' = 42.87657°

x - x' = 0.00807, 0.00948, 0.0028, 0.00196, 0.00446, 0.00781

NB: x - x' values is the mean angle minus the individual angle. We ignore the minus signs

(x - x') ^2 = 0.000065, 0.0000898, 0.0000784, 0.0000384, 0.0000198, 0.0000609

Variance = ( 0.000065+0.0000898+0.0000784+0.0000384+0.0000198+0.0000609)/6

= 0.000358/6 = 0.0000587.

Standard deviation = square root of variance

SD = 0.0000587^0.5 = 0.00766°