Question

Initial public offerings $(1.3)$The business magazine Forbes reports that $4567$companies sold

their first stock to the public between $1990$and $2000$The mean change in the stock price of these companies since the first stock was issued was $+111\%$The median change was $-31\%$Explain how this could happen. (Hint: Start with the fact that Cisco Systems stock went up $60,600\%$)

Short answer

The stock price change distribution would be strongly skewed to the right. The few extremely high stock price swings will thus strongly influence the mean, while the median will be relatively unaffected, resulting in the mean being much higher than the median.

Step-by-step solution

Given information

When the mean is substantially higher than the median, it suggests that there are a few extremely large changes in stock values, but the majority of the changes are negative.

Concept

Individuals are purposely subjected to a treatment in order to measure their responses in an experiment.

Explanation

When the mean is substantially higher than the median, it suggests that there are a few very exceptionally high stock price changes, while the majority of the stock price changes are negative. As a result, the distribution of stock price change would be heavily skewed to the right. The mean will then be greatly influenced by the few abnormally high stock price fluctuations, whilst the median will be largely unaffected, resulting in the mean being much higher than the median.