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

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

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