Question

Consider two types of measuring devices. The first device has good accuracy, but poor precision and the second device has bad accuracy, but good precision. If you could repeat measurements many times, then which device would ultimately be able to provide better (i.e. closer to the real value) average result? Please explain. (Remember that accuracy describes the systematic error and precision indicates the extent of the random error)

Answer 1

Consider the results of the shots on target A and Target B. When the average distances from the center of each bulls eye are calculated, which of the two averages will come closer to the exact center?

Answer 2

if you repeat measurements many times, then second device having bad accuracy, but good precision would ultimately be able to provide better (i.e. closer to the real value) average result.
like in the case of vernier calipers, if you take a lot of measurement, then average of all measured values would give true value which would be far deeper then the measurement
from a ruler

Answer 3

You cannot make statement about comparing one instrument being accurate but not precise vs one that is inaccurate but precise without stating the degree of accuracy and precision of each. For in general either one might give a reading closer to the true value. But we never know the true value prior to the readings.

Ultimately the assessment of the reading I.e. how close we THINK our measurement is to the true value, is made with a statement of uncertainty of the measurement. This statement of uncertainty based on both knowledge of the accuracy of the instruments and any corrections to readings (the systematic uncertainty) and precision of the readings and any known statistical variations that must be considered (random uncertainty).

The use of the term error is really not a good one when talking about measurements for it connotes a mistake (which we are not suppose to make). Uncertainty connotes lack of knowledge which it really is.