https://file.aiquickdraw.com/mathbot/file/1730064711421c72wists.jpg

Let’s go over the problem to verify the solution.

### Problem Summary:
- **Given**: The mean of 200 observations is 50.
- **Mistake**: Two observations were wrongly recorded as 92 and 8 instead of 192 and 88.
- **Goal**: Find the corrected mean.

### Solution Steps:
1. **Calculate the Total of All Observations (∑X)**:
   \[
   \text{Mean} = \frac{\sum X}{n} \Rightarrow \sum X = \text{Mean} \times n = 50 \times 200 = 10000
   \]

2. **Calculate the Effect of the Mistakes**:
   - **Incorrect values**: 92 and 8, totaling \(92 + 8 = 100\).
   - **Correct values**: 192 and 88, totaling \(192 + 88 = 280\).

3. **Adjust the Total Sum (∑X)**:
   - Since the incorrect total was 100 and the correct total should be 280, the difference is:
     \[
     280 - 100 = 180
     \]
   - So, the corrected total is:
     \[
     10000 + 180 = 10180
     \]

4. **Calculate the Corrected Mean**:
   \[
   \text{Corrected Mean} = \frac{10180}{200} = 50.9
   \]

### Verification of Work in the Image
The steps shown in the image appear to match this calculation:
- The original mean calculation was correct.
- The adjustment due to the error was calculated as an addition of 180.
- The final corrected mean is shown as 50.9, which is accurate.

### Conclusion
Yes, the solution is correct. The corrected mean is indeed **50.9**.

Would you like more details on any part of this solution, or do you have further questions?

### Related Questions
1. What would be the corrected mean if only one of the observations was incorrect?
2. How would the mean change if the number of observations was different?
3. What is the impact of a smaller versus larger error on the mean in similar scenarios?
4. How would you calculate the median if the data was given in this problem?
5. Can a similar method be applied to adjust for multiple incorrect values in a data set?

### Tip
Always double-check the calculations, especially in cases with multiple observations, as small mistakes can lead to incorrect conclusions.

The mean of 200 observations is 50. Two observations were wrongly recorded as 92 and 8 instead of 192 and 88. Find the correct mean.

Learn how to correct the mean for a dataset with errors. Given a mean of 50 for 200 observations, two incorrect entries (92 and 8) were identified and corrected to 192 and 88. Follow the step-by-step solution to calculate the new mean, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation