Question

Four students measured the mass of a piece of metal whose accurate mass is 34.75g. Their results are 34.2g, 33.75g, 35.0g, and 34.69g. Explain whether the results are precise or accurate​

Answer 1

Answer:

The given data are more precise than they are accurate

Explanation:

From the given measurements, we have;

The accurate mass = 34.75 g

The deviations from the accurate measurement is as follows;

34.2 g - 34.75 g = -0.55 g

33.75 g - 34.75 g = -1 g

35.0 g - 34.75 g = 0.25 g

34.69 g - 34.75 g = -0.06 g

For precision measurement, we find the average deviations as follows;

The sum of the deviations = -0.55 g - 1 g + 0.25 g - 0.06 g = -1.36 g

The average deviation = -1.36 g/4 = -0.34 g

For accuracy measurement, we find the average of the absolute deviations as follows;

The sum of the absolute deviations = 0.55 g + 1 g + 0.25 g + 0.06 g = 1.86 grams

The average absolute deviation = 1.86 g/4 = 0.465 g

Therefore, the magnitude of the average deviation is less than the magnitude of the absolute deviations, therefore, the given data are more precise than they are accurate