Read the following paragraph carefully and answer the following five questions: In a ninth standard class of 50 students, the teacher administered test to measure achievement of students in Physics and Chemistry, respectively. The mean and SD of the class for the achievement scores in Physics were 50 and 20 , respectively whereas, the mean and SD of the class for the achievement scores in Chemistry were 20 and 5 respectively. One student Rekha scored 30 marks in Physics and 26 marks in Chemistry. Another student Reshma scored 56 marks in Physics and 22.5 marks in Chemistry. Another student Sameer scored 46 marks in Physics and 19 marks in Chemistry. The summary of these scores is given below:S ubject Mean of the class SD of the class Rekha Reshma Sameer Physics 50 20 30 56 46 Chemistry 20 5 26 22.5 19
Who had the best mean score on both tests?
The question asks us to determine which student had the best mean score across both tests administered in Physics and Chemistry. To answer this, we need to calculate the average score for each student by summing their scores in both subjects and dividing by the number of subjects (which is two).
Calculating Individual Student Mean Achievement Scores
The mean score for a student across two subjects is calculated using the formula: $$ \text{Mean Score} = \frac{\text{Score in Physics} + \text{Score in Chemistry}}{2} $$ Let's apply this formula to each student using the scores provided in the summary table.
- Rekha: Rekha scored 30 marks in Physics and 26 marks in Chemistry. Her mean score is calculated as: $$ \text{Rekha's Mean} = \frac{30 + 26}{2} = \frac{56}{2} = 28 $$
- Reshma: Reshma scored 56 marks in Physics and 22.5 marks in Chemistry. Her mean score is calculated as: $$ \text{Reshma's Mean} = \frac{56 + 22.5}{2} = \frac{78.5}{2} = 39.25 $$
- Sameer: Sameer scored 46 marks in Physics and 19 marks in Chemistry. His mean score is calculated as: $$ \text{Sameer's Mean} = \frac{46 + 19}{2} = \frac{65}{2} = 32.5 $$
Comparing Student Mean Scores
Now we have the mean scores for each of the three students:
| Student | Mean Score Across Both Tests |
|---|---|
| Rekha | 28 |
| Reshma | 39.25 |
| Sameer | 32.5 |
Comparing these mean scores (28, 39.25, and 32.5), we can see that Reshma has the highest mean score (39.25) across the Physics and Chemistry tests.
Therefore, Reshma had the best mean score on both tests.
Revision Table: Key Performance Indicators
| Term | Definition | Relevance to the Question |
|---|---|---|
| Mean Score | The average score obtained by summing scores and dividing by the number of tests. | Used to compare overall performance across multiple subjects for individual students. |
| Standard Deviation (SD) | A measure of the spread or dispersion of scores around the mean. | Indicates consistency of scores, not directly used to find the highest average score. |
| Individual Scores | Specific marks obtained by a student in a particular test. | The raw data used to calculate the individual mean scores. |
Additional Information: Understanding Achievement Test Results
Achievement tests like those in Physics and Chemistry are used to measure a student's knowledge or skills in a specific subject area. While individual scores give a snapshot of performance in one test, calculating a mean score across multiple tests provides a more general indicator of overall academic performance over those subjects.
- Importance of Mean: The mean helps to get a single value that represents the typical performance level of a student across different subjects. It smooths out fluctuations that might occur in a single test score.
- Standard Deviation Context: Although the question didn't require using standard deviation (SD), it's important to know that SD tells us how much individual scores vary from the class mean. A smaller SD means scores are clustered closely around the mean, while a larger SD means scores are more spread out.
- Comparing Performance: Comparing individual mean scores allows us to rank students based on their average performance across the evaluated subjects, helping to identify who performed best overall in this specific set of tests.
Important Questions from Data Interpretation
The table shows the monthly expenditure of Saumya. What percent of her monthly salary is she able to save?
Expense Amount Food 5,000 Rent 20,000 Travel 10,000 Clothing 3,000 Miscellaneous 15,000 Savings 7,500 Who had the best score on either test?
Who had the most consistent scores on both tests?
Who had the least consistent scores on both tests?
Who had the poorest score on either test?
