Arithmetic Mean: Evenly distributes the total among individuals. Can be unrepresentative when measurements are highly skewed right. (e.g. per capita income)
Median: Value dividing distribution into two equal parts. 50th percentile. (e.g. median household income)
Mode: Most frequently observed outcome (rarely reported with numeric data)
The well-chosen average: how not qualifying an average can change the meaning of the data. Before I delve into this, quickly, when I say, average - what comes to your mind? Sum(x1....xn) / N - right? The arithmetic mean. But I said average, not arithmetic average did I? Not many people know that there are 3 averages
Arithmetic average / mean - sum of quantities / number of quantities
Median - the middle point of the data which separates the data, the midpoint when data is sorted
Mode - the data point that occurs the most in a given set of data
And when someone says average, leaving it unqualified, there is a lot of room for juggling. The author mentions a very simple example. If an organization publishes a statistic that the average pay of the employees is $1000, what does this mean? This makes most of us think that almost everyone makes around $2000 - the reader thinks it is the median. But, the corporation can be talking about an arithmetic mean, where the boss might be earning say $10,500 and the rest of the 19 employees earn $500 each - the arithmetic average. Just by not qualifying the average the published fact can be completely twisted out of form from the real facts.The way out - always ask what is the kind of the average that someone is talking about.