Why can't this problem rely only on the mean to select the graph, but also needs to look at the standard deviation?

Conditions

• The score distributions of both schools are close to normal distributions.
• The problem provides five different normal curve options.

Reasoning, step by step

1. Observe the horizontal positions of the curves in all five options.
2. Note that all options place School A's curve to the left of School B's curve.
3. Realize that the mean alone cannot eliminate any of the options.
4. Recall that the standard deviation determines the width and height of the normal curve.
5. Use the standard deviations (10 for School A, 5 for School B) to compare the shapes of the curves.
6. Eliminate options that do not match the expected width and height differences.

Example

The video states: 'The speaker points out that all five graphs roughly satisfy A on the left and B on the right, so one needs to switch to using standard deviation for discrimination.'

Common misconceptions

• Thinking that the mean is the only parameter that affects the normal distribution graph.
• Assuming that a larger standard deviation results in a taller and narrower curve.

Watch the explanation

Connected concepts

Explore next

• When the standard deviation is larger, does the normal curve become wider or taller?
• How does the magnitude of the standard deviation affect the width and height of the normal distribution curve?
• Why was (A) selected in the end for this problem?