light detection system: Response different from power bank and computer system Hello friends

I'm working on a light detection system for the higher secondary summer term project, for which I'm using a simple Arduino board, Adafruit 16-Bit ADC, an LDR with some resisters, a 5V USB power source either the computer USB 2.0 port or a mobile power bank 5V-500mA/1A/2.1A, a USB mobile charging cable (not the data cable) and a Bluetooth module to communicate with Arduino system, an android or a computer (different from Arduino power source) to record the data.

The difference in maximum and minimum response is very poor when replacing the power source from the computer USB to power bank USB. With the same environmental and experimental conditions, the response goes from 50000 to 45000 counts (the changes in response are 5000 counts) with the power bank. For the same situations, the response goes from 50000 to 5000 counts (the changes are 45000) with the computer power source which is more suitable but it's better to use a small power supply. 

How can I get the better and stable response? Kindly help me to solve out this issue. Thank you.
Based on limited knowledge of the design and limited knowledge of the requirements here are 3 possible reasons.  More may exist.


The USB 2.0 definition stats such a port provide 0.5A of current.  Some devices limit the current as a precaution.  Therefor the battery may provide more current then the USB source.  The type of USB source was not specified and no voltage measurement data was provided.
How fast does the device need to react to a change in light level?  A light-dependent resistor or LDR can have a latency of as much as a second with respect to light level changes.
With regards to the 16 bit ADC.  What precautions have been made with regards to precisely controlling the ADC's voltage reference?  Any fluctuation can cause large errors.  What precautions have been made with regards to filtering out the ADC's random noise?  For example, many ADCs only have a fraction of their resolution if averaging is not used.