Why might most students still need extra tutoring even though the average score is above the threshold?

Conditions

• The decision rule relies solely on the class average score.
• The dataset contains a significant outlier.
• The threshold is set at 35.

Reasoning, step by step

1. Calculate the class average including the outlier.
2. Compare the average to the threshold.
3. Examine the individual scores against the threshold.
4. Identify the conflict between the majority's performance and the mean-based decision.

Example

In the sample 15, 20, 25, 20, 100, four students scored below 35. However, the mean is 36, which is above 35, leading to the incorrect conclusion that no extra classes are needed.

Common misconceptions

• Assuming that if the class average is high, most students are performing well.
• Ignoring the distribution of individual data points when making decisions based on the mean.

Watch the explanation

Explore next

• How does replacing the outlier change the decision?
• What is the effect of outliers on regression models?