In a city with three high schools, all the ninth graders took a Standardized Test, with these results:

High SchoolMean score on testNumber of ninth graders

Glenwood

80

288

Central City

95

307

Lincoln High

65

176

The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 80 . Of course, that is incorrect. What is the mean score for all ninth graders in the city? Round to one decimal place.

mean of all ninth grader's scores = 

To find the correct mean score for all ninth graders in the city, you need to calculate the weighted mean, taking into account the number of students in each school.

Here are the steps to calculate the weighted mean:

1. Multiply the mean score of each school by the number of ninth graders in that school to get the total score for each school.
2. Sum these total scores.
3. Divide the sum of the total scores by the total number of ninth graders in the city.

Let's apply these steps:

**Step 1: Calculate the total score for each school.**
\[ \text{Total score for Glenwood} = 80 \times 288 = 23040 \]
\[ \text{Total score for Central City} = 95 \times 307 = 29165 \]
\[ \text{Total score for Lincoln High} = 65 \times 176 = 11440 \]

**Step 2: Sum these total scores.**
\[ \text{Sum of total scores} = 23040 + 29165 + 11440 = 63645 \]

**Step 3: Calculate the total number of ninth graders in the city.**
\[ \text{Total number of ninth graders} = 288 + 307 + 176 = 771 \]

**Step 4: Divide the sum of the total scores by the total number of ninth graders.**
\[ \text{Mean score} = \frac{63645}{771} \approx 82.6 \]

So, the mean score for all ninth graders in the city is:
\[ \text{Mean of all ninth grader's scores} = 82.6 \]

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What is the median score of all ninth graders in the city?
2. How do you calculate the variance of the scores from all three schools?
3. What is the standard deviation of the scores from all three schools?
4. How does the mean score change if one school had significantly more students?
5. What is the mode score for the ninth graders?
6. How do you interpret the distribution of scores among the three schools?
7. How would the mean score change if Glenwood's mean score was 85 instead of 80?
8. How can you visualize the scores of the three schools using a bar graph?

**Tip:** When calculating weighted means, always ensure that each group’s contribution is proportional to its size to avoid errors in the overall average calculation.

Discover how to calculate the mean score of ninth graders in a city using weighted mean calculations. Understand the distribution of scores among three high schools and learn the correct approach to finding the overall average. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation