# Signal to Noise Ratio Formula

To detect the quality of a signal, the signal to noise ratio term is used. Simply, it is the ratio of light signal to the noise signal. Often expressed in decibels, a ratio when is higher than 1 : 1, or greater than 0 *dB*, indicates that the signal is more compared to noise.

Signal to noise ratio is often written as S/N or SNR. In Digital sense, this ratio refers useful information, false information, spam or the things that are off topic or unrelated to the webpage, often regarded as “noise” and how the noise interferes with “signal” made to apt discussions.

The ratio is given as

\[\large SNR=\frac{P_{signal}}{P_{noise}}\]

Where,

$P_{signal}$ is the power of a signal

$P_{noise}$ is the background noise

The signal to noise ratio formula is

\[\large SNR=\frac{\mu}{\sigma}\]

Here,

$\sigma$ is the standard deviation

$\mu$ is the mean of the given data

### Solved example

**Question:** Determine the signal to noise ratio for the following data: 1, 5, 6, 8, 10.

**Solution:**

Find out the mean:

$\mu =\frac{1+5+6+8+10}{5}=6$

Standard deviation of the data given:

$\sigma =\sqrt{\frac{1}{n-1}\sum_{t-1}^{2}\left(x_{1}-\mu\right)^{2}}$

$=\left(1-6\right)^{2}+\left(5-6\right)^{2}+\left(6-6\right)^{2}+\left(8-6\right)^{2}+\left(9-6\right)^{2}$

$=\sqrt{\frac{39}{4}}$

$=\sqrt{9.75}=3.1$