Ex7-2 Observations for the distance between two points are found to be as follows
Set I : 165.485 ± 0.005 m; Set II : 165.465 ± 0.010 m.
(i) State which of these sets of observation is more reliable and why?
(ii) State whether the sets of observation are significantly different or not. Explain
(iii) Find the weighted mean of observation.
Solution :
(i) The standard deviation of Set I is less than that of Set II. Thus, Set I observation is more reliable than Set II.
(ii) Difference between observations in Set I. & Set II is
165.485 – 165.465 = 0.020m
Where s diff. = ± 
= ± 0.01118 m
Thus the difference between the sets of observation in less than 2sdiff (i.e., 0.020 < 0.02236). Therefore sets I & II can be regarded as value measurements of the same quantity and inspection indicates that they can be combined to find the (weights) mean of observations.
(iii) The weighted mean of observations are :
Set |
Mean of Obs. (mi )
|
Standard Deviation ( si ) |
Weight Factor |
Weights (wi) |
wi mi |
I |
165.485 |
± 0.005 |
|
4 |
661.940 |
II |
165.465 |
± 0.010 |
|
1 |
165.465 |
|
|
||||
= 5 
Therefore, The weighted mean value of the distance is 165.481m
