Precision indicates the level of variation in your measurements when you repeat the same measurement multiple times under the same conditions. High precision means that the measurements are very similar to each other, showing little variation. It's important to differentiate precision from accuracy. While precision is about the closeness of repeated measurements to each other, accuracy refers to how close a measurement is to the true or actual value. It's possible to have high precision but low accuracy if all measurements are consistent but far from the true value.

Precision can be quantified using statistical measures such as the standard deviation or variance within a dataset. A lower standard deviation or variance indicates higher precision, as the data points are more closely clustered around the mean.

To calculate the standard deviation, you first find the difference between each mean value and the overall mean of these means, square these differences, sum them up, divide by the number of samples, and then take the square root of this final value. This standard deviation gives you a quantitative measure of precision.

During deployment planning, it's important to know the expected precision of velocity outputs. Depending on instrument type, and velocity range, each instrument will have single ping precision which is known. With increased number of samples in each output, the precision will improve. 

You can find expected precision for your instrument either in the planning software wizard or in the technical specification. With changing number of samples per output, the precision measure will roughly scale with the calculated standard deviation. 

Below are a few examples from the deployment software*:

Changed Average Interval (s):

Say that your velocity precision is 6.8 cm/s with an average interval of 5 sec.
An average interval to 7 sec will change your precision relatively (5/7)^0.5 ~ 0,84. Resulting in velocity precision of 5,7 cm/s. 

Changed sampling rate (Hz) on output data:

Say that your velocity precision is 3.7 cm/s with 2Hz sampling rate.
With 4Hz sampling rate, your precision will change as a function of the square root of samples, ie (4/2)^0.5 ~1.41. Resulting in velocity precision of 5.2 cm/s. 
With 1Hz sampling rate, your precision will change relatively (1/2)^0.5~0,71. Resulting in velocity precision of 2.6 cm/s.

*keeping a constant measurement load.