In a city with three high schools, all the ninth graders took a Standardized Test, with these results:
| High School | Mean score on test | Number of ninth graders |
| :------------ | :----------------- | :---------------------- |
| Glenwood | 75 | 286 |
| Central City | 94 | 323 |
| Lincoln High | 65 | 164 |
The city's PR manager, who never took statistics, claimed the mean score of all ninth graders in the city was 78. 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 = $\square$
Answer (1)
Calculate the total score for each school by multiplying the mean score by the number of students.
Sum the total scores of all schools to get the combined total score.
Calculate the total number of students by summing the number of students from each school.
Divide the combined total score by the total number of students and round to one decimal place: 80.8 .
Explanation
Calculate total scores for each school First, we need to calculate the total score for each high school. This is done by multiplying the mean score of each school by the number of ninth graders in that school.
Glenwood total score For Glenwood High School, the total score is: 75 × 286 = 21450
Central City total score For Central City High School, the total score is: 94 × 323 = 30362
Lincoln High total score For Lincoln High School, the total score is: 65 × 164 = 10660
Calculate total number of students Next, we need to find the total number of ninth graders in the city by adding the number of ninth graders from each high school.
Total students The total number of ninth graders is: 286 + 323 + 164 = 773
Calculate the overall mean score Now, we calculate the mean score for all ninth graders in the city by dividing the sum of the total scores by the total number of ninth graders.
Overall mean score The mean score for all ninth graders is: 773 21450 + 30362 + 10660 = 773 62472 ≈ 80.81759379042691
Round to one decimal place Finally, we round the mean score to one decimal place, which gives us 80.8.
Examples
Understanding the average performance across different groups is crucial in many real-world scenarios. For instance, a company might want to calculate the average sales performance of its employees across different regions to identify areas that need improvement. Similarly, a sports team might calculate the average performance of its players to optimize team strategy. In education, calculating the overall mean score helps in evaluating the effectiveness of different teaching methods or resource allocation across schools, ensuring equitable opportunities for all students.
