this is the data, solve: Number of Accidents ABCDEFGHBefore modification

5

7

6

4

8

9

8

10

After modification

3

7

7

0

4

6

8

2

To solve this problem, we can compare the number of accidents before and after the modification to analyze the effect of the modification. Here's the process:

### 1. **Calculate the Total Number of Accidents**
- **Before Modification**: Add the values of A, B, C, D, E, F, G, H before the modification.
- **After Modification**: Add the values of A, B, C, D, E, F, G, H after the modification.

### 2. **Calculate the Mean Number of Accidents**
- **Before Modification**: Compute the average number of accidents before the modification.
- **After Modification**: Compute the average number of accidents after the modification.

### 3. **Calculate the Reduction in Accidents**
- **For each point (A, B, C, D, E, F, G, H)**: Subtract the number of accidents after the modification from the number of accidents before the modification.

### 4. **Interpret the Results**
- Analyze the change in the number of accidents after the modification.

Let's calculate these values.

#### Step 1: Total Number of Accidents

- **Before Modification**: \( 5 + 7 + 6 + 4 + 8 + 9 + 8 + 10 = 57 \)
- **After Modification**: \( 3 + 7 + 7 + 0 + 4 + 6 + 8 + 2 = 37 \)

#### Step 2: Mean Number of Accidents

- **Before Modification**: \( \frac{57}{8} = 7.125 \)
- **After Modification**: \( \frac{37}{8} = 4.625 \)

#### Step 3: Reduction in Accidents

For each point (A to H):
- **A**: \( 5 - 3 = 2 \)
- **B**: \( 7 - 7 = 0 \)
- **C**: \( 6 - 7 = -1 \) (increase)
- **D**: \( 4 - 0 = 4 \)
- **E**: \( 8 - 4 = 4 \)
- **F**: \( 9 - 6 = 3 \)
- **G**: \( 8 - 8 = 0 \)
- **H**: \( 10 - 2 = 8 \)

### Results:
1. The total number of accidents reduced by \( 57 - 37 = 20 \) after the modification.
2. The average number of accidents decreased from 7.125 to 4.625.
3. The reduction in accidents varies by point, with the most significant decrease at point H (8 fewer accidents).

### Conclusion:
The modification led to a significant overall reduction in accidents, indicating a positive impact on safety.

Would you like more details on any of these calculations or interpretations?

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**Relative Questions:**
1. How can we statistically test whether the reduction in accidents is significant?
2. What other factors could influence the number of accidents before and after the modification?
3. How can we visualize the reduction in accidents for each point?
4. What would be the impact of outliers on the average number of accidents?
5. How does the standard deviation change before and after the modification?

**Tip:** When comparing data before and after an intervention, consider both the overall change and the variation at each data point to fully understand the impact.

Number of Accidents ABCDEFGH Before modification 5, 7, 6, 4, 8, 9, 8, 10. After modification 3, 7, 7, 0, 4, 6, 8, 2

Explore how to analyze the number of accidents before and after modifications. Learn how to calculate the total and mean number of accidents, and understand the reduction in accidents through data analysis. Suitable for students in Grades 5-8.

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