why did you get the average mass of the ball bearings

You're right to question the relevance of calculating the average mass in this context. In fact, the average mass of the ball bearings is not necessary for finding the average percentage deviation from the standard weight. 

The correct approach focuses solely on the deviation of each individual mass from the standard weight and does not involve the average mass of the measurements. 

Let’s revisit the correct steps without the unnecessary calculation:

### Step 1: Calculate the deviation of each mass from the standard weight.
\[
\text{Deviation} = \text{Standard weight} - \text{Measured mass}
\]
For each mass:
- For 4.15 g: \(5.00 - 4.15 = 0.85 \, \text{g}\)
- For 3.75 g: \(5.00 - 3.75 = 1.25 \, \text{g}\)
- For 4.35 g: \(5.00 - 4.35 = 0.65 \, \text{g}\)
- For 4.85 g: \(5.00 - 4.85 = 0.15 \, \text{g}\)
- For 4.55 g: \(5.00 - 4.55 = 0.45 \, \text{g}\)

### Step 2: Convert these deviations into percentage deviations.
\[
\text{Percentage deviation} = \left(\frac{\text{Deviation}}{\text{Standard weight}}\right) \times 100\%
\]
For each mass:
- For 4.15 g: \(\frac{0.85}{5.00} \times 100 = 17.00\%\)
- For 3.75 g: \(\frac{1.25}{5.00} \times 100 = 25.00\%\)
- For 4.35 g: \(\frac{0.65}{5.00} \times 100 = 13.00\%\)
- For 4.85 g: \(\frac{0.15}{5.00} \times 100 = 3.00\%\)
- For 4.55 g: \(\frac{0.45}{5.00} \times 100 = 9.00\%\)

### Step 3: Calculate the average percentage deviation.
\[
\text{Average percentage deviation} = \frac{\text{Sum of percentage deviations}}{\text{Number of measurements}}
\]
\[
\text{Average percentage deviation} = \frac{17.00\% + 25.00\% + 13.00\% + 3.00\% + 9.00\%}{5} = \frac{67.00\%}{5} = 13.40\%
\]

So, the average percentage deviation from the standard weight is **13.40%**.

Would you like to explore more about this concept or have any other questions?

Here are 5 related questions to explore:
1. How would changing the standard weight affect the percentage deviation?
2. What is the significance of using percentage deviation rather than absolute deviation?
3. How does this calculation relate to concepts like accuracy and precision?
4. How would you determine the maximum possible percentage deviation for this set of data?
5. What role do outliers play in percentage deviation calculations?

**Tip:** When calculating percentage deviations, focus on how each individual measurement compares to the standard or expected value to determine the overall accuracy.

Explore how to calculate percentage deviation in statistics using a detailed example. Learn about the importance of deviation from standard values and its application in accuracy assessment. Suitable for advanced high school students.

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