. Five small ball bearings are placed on a balance and are found to have the following masses:  4.15 g, 3.75 g, 4.35 g, 4.85 g & 4.55 g. If the standard weight for these coins is 5.00g, find the average percentage deviation of these readings. 

To calculate the average percentage deviation of these readings from the standard weight, we follow these steps:

### Step 1: Calculate the mean (average) mass of the ball bearings.
\[
\text{Mean} = \frac{\text{Sum of all masses}}{\text{Number of ball bearings}}
\]
\[
\text{Mean} = \frac{4.15 + 3.75 + 4.35 + 4.85 + 4.55}{5} = \frac{21.65}{5} = 4.33 \, \text{g}
\]

### Step 2: 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 3: 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 4: 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 of these readings from the standard weight is **13.40%**.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How would the average percentage deviation change if the standard weight was different?
2. What is the significance of the standard deviation in this context?
3. How would you calculate the variance of the given masses?
4. How does the average percentage deviation differ from the mean absolute deviation?
5. What is the impact of one measurement being significantly off on the average percentage deviation?

**Tip:** Remember that percentage deviations can highlight how individual measurements compare to a standard or mean, which can be useful in quality control processes.

Learn how to calculate the average percentage deviation of ball bearings masses from a standard weight of 5.00g. This problem involves calculating means, deviations, and percentage deviations for given mass readings. Suitable for Grades 9-12.

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