Question

The following data were obtained for repetitive mass measurements of a 1.000-g standard on a top-loading balance.

0.9991 g 1.0090 g 1.0073 g 0.9935 g

1.0093 g 1.0127 g 1.0067 g 1.0033 g

0.9999 g 1.0045 g 0.9996 g 1.0130 g

1.0058 g 1.0092 g 1.0074 g 1.0068 g

a) Assuming the noise is random, calculate the signal-to-noise ratio for this balance.

b) What is the signal-to-noise if each column of measurements is averaged first?

c) What is the name for this noise reduction approach?

Answer 1

a) Signal/noise ratio = mean value/standard deviation

mean of all values = 1.00544

standard deviation = sq.rt.(sum of all(mean-inidividual value)^2/(16-1)) = 0.00526

Signal/noise ratio = 1.00544/0.00526 = 191.04652

b) When each column is averaged

1.5071    1.00885    1.00525    1.00415

mean = 1.13134

standard deviation = 0.25052

Signal/noise ratio = 1.13134/0.25052 = 4.5160

c) The method for this type of reduction is known as smoothing method.