Three different people weight a standard mass of 2.00 g on the same balance. Each person obtains a reading of 2.32 g for the mass of the standard. These results imply that the balance that was used is precise.
Precision can be defined as the closeness of measured values to each other, for a measuring equipment it is the closeness of the values of readings obtained at different times to each other. It does not necessarily means the measurements are accurate(closeness to the actual value). Therefore, in the case above where three different people measured the same mass on the same balance, and each of them obtained the same value which is different from the standard value. We can say the balance used is precise because the three readings are the same.
This all simply due to the size of the two water bodies question and the your body size in a bath tub the water is small enough to allow the upthrust displace water out if the tub whereas in a lake the water is bigger and your body size is smaller to allow any noticeable upthrust that would cause an overflow
