Question

Measures of Average: U.S. Census Bureau

The U.S. Census Bureau reports the median family income in its summary of census data.

a) Why do you suppose it uses the median instead of the mean?

b) What might be the disadvantages of reporting the mean?

Measures of Variation: MP3 Player Life Span

A company selling a new MP3 player advertises that the player has a mean lifetime of 5 years. If you were in charge of quality control at the factory, would you prefer that the standard deviation of lifespans of the players you produce be 2 years or 2 months? Why?

Answer 1

The U.S. Census Bureau reports the median family income in its summary of census data.

a) Why do you suppose it uses the median instead of the mean?

Income data has a lot of outlier towards the right where few people have really high income which makes the data skewed. So, in the case of skewed data with outliers median is a better estimate.

b) What might be the disadvantages of reporting the mean?

If the data would have been reported as mean than the estimate would be biased towards the right due to skewness in the data set.

A company selling a new MP3 player advertises that the player has a mean lifetime of 5 years. If you were in charge of quality control at the factory, would you prefer that the standard deviation of the lifespans of the players you produce be 2 years or 2 months? Why?

If the mean of two samples is equal than lesser the variability better the estimates.

So, we will prefer te player with a lesser standard deviation that is 2 months