**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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