Having played around with the data using MS Excel, there are some large errors there which are a lot worse than would be expected from the specification of the pressure transmitter.
How good was the calibration equipment you used to produce these data?
Edit Vlady gave the answer to this as I was typing.
If you are sure that you want to use this data, I can suggest two possible solutions, but if you are not good at software, you will not like either of them!
Both methods involve using an ADC to read the data into a microprocessor. It will have to be a 14/16 bit device (as suggested by RonH) to get the accuracy/resolution you require.
Method 1
Produce a linear equation (y=mx+c) for the data between each pair of calibration points. You will have six equations for your seven data point pairs.
Write the software, which will:
Read the ADC
Compare the voltage with the calibration points
Calculate the pressure using the appropriate equation
Display the pressure.
Method 2
Produce a polynomial equation which fits the data.
Write the software, which will:
Read the ADC
Calculate the pressure using the equation
Display the pressure.
To find a suitable equation for your data, have a look here:
https://www.xuru.org/rt/TOC.asp
There are some online calculators which will do it for you.
JimB