HP 12C: Statistical Signal to Noise Ratio
Introduction and The Formula
There are many parameters that can be used to measure signal to noise ratio. Today's formula will concentrate on the statistical measurements of univariate (1-variable) data. The signal to noise ratio (SNR) is defined as the inverse of the ratio of the coefficient of variation, or the ratio of the mean to deviation.
SNR = mean / deviation
In the sources listed below (see the Sources section), they define the ratio as:
SNR = mean / standard deviation
However, the sources define standard deviation as:
√( ∑(x_i - mean for i = 1 to n) / (1 - n )
This is the formula for sample standard deviation, and that is the deviation this program will use.
HP 12C Program: SNR
STEP KEY KEY CODE
01 x-bar 43, 0
02 STO 0 44, 0
03 s 43, 48
04 RCL 0 45, 0
05 x<>y 34
06 ÷ 10
07 GTO 00 43, 33, 00
Notes:
1. x-bar displays the mean for both x and y data in their respective stacks. Since we are only interested in the x data, I had to store the mean in R0.
2. Similarly, calling up the s function displays the standard deviation for both x and y.
3. In statistics, only certain registers are available for storing values. The HP 12C stores the following calculations during statistics: R1: n, R2: ∑x, R3: ∑x^2, R4: ∑y, R5: ∑y^2, R6: ∑xy.
Instructions
1. Clear the statistical data registers by pressing [ f ], [ SST ].
2. Enter the data by using [ ∑+ ].
3. Run the program by pressing [ R/S ].
Examples
Note: The HP 12C is set to Fix 4 mode for these examples.
Example 1:
Data: 10, 35, 76, 49, 52, 56
SNR: 2.0883
(Mean: 46.3333, Sample Standard Deviation: 22.1871)
Example 2:
Data: 50, 30, 20, 35, 25
SNR: 2.78000
(Mean: 32.0000, Sample Standard Deviation: 11.5109)
Sources
BYJU'S "Signal to Noise Ratio Formula" BYJU'S Classes. 2021. https://byjus.com/signal-to-noise-ratio-formula/ Last Retrieved March 23, 2021
EasyCalculation.com "How to Calculate Signal to Noise Ratio (SNR) - Tutorial" https://www.easycalculation.com/statistics/learn-signal-to-noise-ratio.php Last Retrieved March 23, 2021
Wikipedia "Signal-to-noise" https://en.wikipedia.org/wiki/Signal-to-noise_ratio Retrieved February 27, 2021
Eddie
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