https://file.aiquickdraw.com/mathbot/file/1728010998090tkfxr8vx.jpg

To find the mean score for all ninth graders in the city, we need to calculate the **weighted mean** because each school has a different number of students.

The formula for the weighted mean is:

\[
\text{Weighted Mean} = \frac{\sum (\text{mean score of each school} \times \text{number of students in that school})}{\text{total number of students}}
\]

Using the data from the table:

- Glenwood: Mean score = 75, Number of students = 254
- Central City: Mean score = 91, Number of students = 326
- Lincoln High: Mean score = 68, Number of students = 172

### Step 1: Calculate the total score for each school
- Glenwood: \( 75 \times 254 = 19,050 \)
- Central City: \( 91 \times 326 = 29,666 \)
- Lincoln High: \( 68 \times 172 = 11,696 \)

### Step 2: Sum the total scores
\[
19,050 + 29,666 + 11,696 = 60,412
\]

### Step 3: Calculate the total number of students
\[
254 + 326 + 172 = 752
\]

### Step 4: Calculate the weighted mean
\[
\text{Weighted Mean} = \frac{60,412}{752} \approx 80.3
\]

Thus, the mean score for all ninth graders in the city is **80.3**, rounded to one decimal place.

Would you like more details or have any questions?

Here are some related questions:
1. How is a weighted mean different from a simple mean?
2. Why is the mean score claimed by the city's PR manager incorrect?
3. What happens if you average the mean scores instead of using the weighted mean?
4. How would the overall mean change if the number of students in one school increased dramatically?
5. How would the results be affected if we had more schools with different student populations?

**Tip:** In weighted averages, it's essential to account for the relative sizes of the groups you're averaging to get accurate overall results.

In a city with three high schools, all the ninth graders took a standardized test, with the following results: Glenwood (mean score: 75, number of students: 254), Central City (mean score: 91, number of students: 326), Lincoln High (mean score: 68, number of students: 172). The city's PR manager incorrectly claimed the mean score was 78. What is the correct mean score for all ninth graders in the city, rounded to one decimal place?

Learn how to calculate the weighted mean score for ninth graders across three high schools, using data for Glenwood (mean score 75), Central City (mean score 91), and Lincoln High (mean score 68), along with student counts. Solve the problem and find out why the PR manager's claim of a mean score of 78 was incorrect.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation