# Signal to Noise Ratio Calculator

Dataset set x
comma separated input values
Mean  =  14.8333
Standard deviation  =  9.4534
Signal noise ratio (SNR)  =  1.5691
GENERATE WORK

## Signal to Noise Ratio - work with steps

Input Data :
Data set = 3, 8, 10, 17, 24, 27
Total number of elements = 6

Objective :
Find what is signal to ratio calculation for given input data?

Formula :

Solution :
Mean = (3 + 8 + 10 + 17 + 24 + 27)/6
= 89/6
Mean = 14.8333

Standard Deviation σ = √(1/6 - 1) x ((3 - 14.8333)2 + ( 8 - 14.8333)2 + ( 10 - 14.8333)2 + ( 17 - 14.8333)2 + ( 24 - 14.8333)2 + ( 27 - 14.8333)2)
= √(1/5) x ((-11.8333)2 + (-6.8333)2 + (-4.8333)2 + (2.1667)2 + (9.1667)2 + (12.1667)2)
= √(0.2) x ((140.027) + (46.694) + (23.3608) + (4.6946) + (84.0284) + (148.0286))
= √(0.2) x 446.8333
= √89.3667
Standard Deviation σ = 9.4534

SNR = μσ
= 14.83339.4534
SNR = 1.5691

Signal-to-noise ratio is also called as SNR or S/N, is defined as the ratio of signal power to the noise power which measures the original signal corruption. It's a defining factor when it comes to measure the quality of signal in communication channels or mediums. A higher SNR guarantees the clear acquisitions with low distortions and artifacts caused by unwanted noise. The better ratio of SNR cause the better signal stand out, makes the better quality of original signal or transmitted information signals. S/R ratio measurement is commonly used in the field of science and engineering fields. A ratio higher than 1 indicates more signal strength.

## Formula - Signal to Noise Ratio

The below mathematical formula used in statistics to calculate the signal to noise (S/N) ratio to find the quality of signal
SNR = Psignal/Pnoise = μ/σ
where
μ is the signal mean or expected value
σ is the standard deviation calculation of the noise
While working with the field of tele-communications or radio communications or optical communications, sometimes, this SNR ratio may required to design & tweak the circuits. The SNR can be calculated by the above statistics formula, however, this signal to noise ratio calculator may useful to perform & verify such calculations quick as possible to analyze & summarize the statistical data.