Wealth

 

If I Were a Rich Man

The most important men in town would come to fawn on me!
They would ask me to advise them like a Solomon the Wise
"If you please, Reb Tevye..."
"Pardon me, Reb Tevye..."
Posing problems that would cross a rabbi's eyes!
And it won't make one bit of difference if I answer right or wrong
When you're rich, they think you really know!

As the song says, just because you are rich, does NOT mean you really know.

If wealth followed a normal distribution, the wealthiest people would be about twice as rich as the median wealth. This assumes that the mean, average, is equal to the median, the value where 50^th percent are greater and 50^th percent are less. A distribution can still follow at least one of the rules of a normal distribution if the mean is no more than 150% of the median. If the mean exceeds the median by more than that amount, the distribution can not be considered to be normal. But any distribution of an abnormal group can be approximated by the presence of more than one normal subgroup within the larger abnormal group.

For example, in my field of transportation demand forecasting, a trip is characterized by its purpose, for example the commute between home and work, a Home Based Work trip, HBW. If commute trips to work are grouped with commute trips from work, and this combination is sorted by starting trip times, then the median starting time is different than the mean starting time of those trips. However, if the difference between the commute to Work and the commute from Work is maintained, the mean and the median within each subgroup are almost equal as shown below.

It is visually obvious that there are two separate groups by starting time. I.e. the mode of starting time to work is generally about 7:30 AM. The mode of the starting time from work is generally about 5 PM. (if the commute time is on average is about 30 minutes, this also means that the average person is at work from 8 to 5! I guess Dolly Parton was wrong!)  The fact that there are two groups is not surprising. However this same behavior is apparent even when the separation between the two groups is not as obvious, If this same grouping was done for shopping trips from the home,  the duration of shopping does not result in the same separation. The fact that there are two normal subgroups is obscured by the fact that these subgroups were combined. In fact if the same separation is made, shopping trips, when combined are not normal in that the mean is greater than the median, but when they are seperated into the legs, trips, from the home to shopping and the legs, trips, from shopping to the home the normality is evident. There are two normal groups, as shown in the chart on the right, which is masked as in the chart on the left where the starting times of each leg are combined.

It is suggested that any group which is abnormal actually consists of many subgroups, where any one subgroup, such as the rich, may be normal only within its own subgroup. However you should not expect that its wisdom is normal for the larger group, such as the group that also includes the poor.  That rich subgroup might say silly things like, “let them eat cake” or ”the problem with the poor is that they live off their principal, and not their interest.” The rich really are different. But that only means that they are richer, not that they should speak for all of us.