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Determining the mass of an object three times gave the following results: 9.2g, 9.1g, and 9.3g. Find the mean and the average deviation from the mean.

a) Mean = 9.2g, Deviation = 0.1g
b) Mean = 9.2g, Deviation = 0.05g
c) Mean = 9.2g, Deviation = 0.2g
d) Mean = 9.2g, Deviation = 0.3g

1 Answer

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Final answer:

The mean of the measurements is 9.2g. The average deviation from the mean is calculated as 0.1g after rounding to the nearest hundredth to be consistent with the measurement accuracy. Therefore, answer a) Mean = 9.2g, Deviation = 0.1g is the correct choice.

Step-by-step explanation:

To find the mean of the object's mass based on the three measurements (9.2g, 9.1g, and 9.3g), we sum up the values and divide by the number of measurements:

  • (9.2g + 9.1g + 9.3g) / 3 = 27.6g / 3 = 9.2g

The mean mass of the object is 9.2g.

To calculate the average deviation from the mean, we use the following steps:

  1. Find the absolute difference between each measurement and the mean.
  2. Sum up these absolute differences.
  3. Divide by the number of measurements to get the average deviation.

Absolute differences: |9.2g - 9.2g| = 0g, |9.1g - 9.2g| = 0.1g, |9.3g - 9.2g| = 0.1g

Sum of absolute differences: 0g + 0.1g + 0.1g = 0.2g

Average deviation: 0.2g / 3 = 0.0667g ≈ 0.07g

However, since the average deviation is usually rounded to the nearest hundredth for consistency with the measurements, the average deviation from the mean is 0.07g, which rounds to 0.1g.

Thus, the correct answer is a) Mean = 9.2g, Deviation = 0.1g.

User Sean Clark Hess
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