Question

1. Provide an example of a data set whose histogram you would expect to be skewed to the left. Explain why you would expect the histogram to be skewed left.

2. A report on US annual income states both the mean and the median. Which measure of center do you think is larger, the mean or the median? Which would better represent US annual income? Explain.

Answer 1

1. Histogram skewed to left means a higher amount of data concentrated at the start yet the average is high because the value having larger values contributes more due to their size.

Consider, the average population per country of the World where, most of the countries constitute a small amount of population, reducing the value of median, where as the mean is high because of the population of India and China. While plotting most of the countries will lie at left ( lower side ) but the size of India and China will increase the mean.

2. In US annual income both the mean and the median are given because there a few people who are extremely rich that would drag the mean up much higher than it would be where as it would not affect the median very much.

Hence, median is smaller than that of mean.

Also, the extremely rich people work as an outlier here, ( statistically ) and median is the central tendency less affected by outliers. Therefore, median income is the better measure in case of US annual income data.