**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

All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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