To determine if it's statistically possible for 18 out of 25 students to score above 90 while the class average is 75, we need to consider the implications of these scores on the total sum of all scores in the class.
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Calculate Total Class Score: The average score of the class is 75 for 25 students, so the total score for the class is: \[ \text{Total Score} = \text{Average} \times \text{Number of Students} = 75 \times 25 = 1875. \]
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Calculate Total Score of Students Scoring Above 90: If 18 students score above 90, let's assume for simplicity that each of these students scores exactly 90. Thus, the total score for these 18 students would be: \[ \text{Total Score of 18 Students} = 18 \times 90 = 1620. \]
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Calculate Remaining Score: The remaining 7 students must then account for the remaining score needed to reach the average of 75: \[ \text{Total Score of Remaining 7 Students} = \text{Total Score} - \text{Total Score of 18 Students} = 1875 - 1620 = 255. \]
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Calculate Average Score of Remaining Students: The average score for the remaining 7 students would then be: \[ \text{Average Score of Remaining Students} = \frac{\text{Total Score of Remaining 7 Students}}{\text{Number of Remaining Students}} = \frac{255}{7} \approx 36.43. \]
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Conclusion: This calculation shows that for 18 students to score above 90 while maintaining a class average of 75, the remaining 7 students would need to average around 36.43. While it's mathematically possible for some students to score below average (and even significantly lower), whether this scenario is realistic depends on the context (e.g., the actual distribution of scores). Typically, having 18 students scoring very high while the rest score very low may suggest a skewed distribution but remains statistically possible.
In summary, it is statistically possible under certain conditions, but it would imply that the scores of those 7 students are substantially lower than the average, which may not be typical in many educational settings.