Statistical jugglery is common in political statement, instead if majority and minority groups' per capita income has been reported, it would have been more meaningful statement to know differences in earnings, though per capita income itself hides more than it reveals.

The average is a bad indicator of a "typical income". It is well known that some people have extraordinary high incomes, dragging the average to higher values. You may thus calculate an average income of, say, 2000$ per month, bot actually the vast majority of the people have an income of less than 1000$ per month.

Better indicators would be the median or even the mode of the incomes.

Sepcifically:

1: No obvious flaws. However, "income" has to be well defined. And, as said above, the average is not a good "typical value". Also, the source of the information should be clear: how trustworthy is the information about the income? If it is based on some polls: is it (un)biased? Who payed?

2: Use the median or mode. Give some indication of uncertainties or ranges (e.g. interquartile ranges, interdecentile ranges).

3: No. Abuse is intentional. The average might be useful for some purposes. It is not very useful as a measure of a "typical income". *If* the publication used it to indicate something like "typical incomes", then it is a kind of abuse, in my eyes...

Thank you both Mohammad and Jochen for your comments. How about the composition of percentages? Would that affect the biasness?

First, one has to determine population in each group, then total income of all persons or national income then calculate what is share of each group according to the percentages given and compare it in ratio form with majority absolute income income or median, or preferably mode of income is imposable to work out as it is also impossible to know incomes of all individuals and in most cases distribution of population by income brackets (groups) is lacking otherwise it is possible to calculate median or modal income of all groups.

What do you mean by "composition of percentages"?

15% and 12% versus the rest.

Mohammad, can you make up a concrete example please?

Yes, I can after some time.

Thanks Brian for a long response. However, frankly, with all due respect, I could not understand what you are talking about. I would appreciate it if you could summarize it and respond the questions raised directly.

The problem that I find with that statistics is assuming that there are just two minorities and the other minorities are contemplated as part of the majority. This may skew any posterior analysis on income this may be that these two minorities have some factors in common that may be the cause of income disparity but as it stands a conclusion that can be drawn is minority-> income disparity.

Using averages is not wrong in itself but it brings the image of a normal distribution. While I am not an economist, I would be careful with this since some heavy tailed distributions might better fit the bill in such modeling and since no additional information was given I might arrive at an image of a perfectly symmetrical distribution. more information needs to be provided so that a proper interpretation of the data is given.

Thanks very much Arturo for your comments. I think, as Jochen mentioned, mean may not be a good measure for salary comparison. In a company whose CEO receives several millions of dollars a year versus a janitor who receives less than $20,000, the average makes no sense. Also, I am not sure if incresing the number of minority classes would make a difference in response to my questions. However, I am yet concern if the composition of the population could be a determining factor.

Averages can be misleading, but often a bigger problem - and perhaps a problem here - are matters of who and what is included and who and what is not. For example, are children included? are retirees included? Are social security and disability payments included? Or just money from paychecks? Dividends? By including/excluding different categories you can generate a wide range of results. So, clearing stating what i in and what is out is essential.

Thanks David for your comments. So, when statement says the average household income could be quite misleading. Thus, what is a proper way expressing household income for different classes and categories in a population?

The average household income is very misleading because of the wide spread in the distribution. This hides the large numbers of poor people that exist in every ethnic group. David Abbott also brings the crucial point of who is or isn't included in the statistics. The prison population is generally excluded from the statistics. This is important because the prison population removes from the statistics a large number of low-income people and its ethnic distribution is different than that of the general population. Without this artificial effect (where prisoners don't count), we would more clearly see the huge gap that persists to this day in the average earnings of ethnic groups that have historically been victimized by discrimination.

As they say, there's "lies, damned lies, and statistics".

To tentatively answer your question "what is a proper way expressing household income for different classes and categories in a population?" I would say: Maybe grouping households by income, and then characterizing the ethnic composition of each income group would be more informative?

Thanks very much Marzia for your comments. I agree with you regarding exclusion and the rest. However, I have problem grouping and comparisons. This way we may not include all in the comparisons. Perhaps, I am not understanding what you mean by grouping.

Aliakbar,

If you're looking for a simple answer, then using the MEDIAN household income (instead of the MEAN) will already be a huge improvement - agree?

You can also use other quantiles, such as the 10th percentile (i.e., the value below which lie 10% of households, with 90% above it).

But you need to correct somehow for the prison population, since the numbers are too huge to ignore. Staggering, in fact. When you remove from the statistics such huge numbers of the poorest people from specific ethnic groups, you have 2 effects: (1) the apparent statistics of their ethnic group look much better than they are in reality, and (2) the real statistics of that ethnic group are prevented from actually improving (due to the life-long burden of having a criminal record, and of kids being raised without their dad). In other words, you make things worse while making them look better.

You can try to introduce a correction to account for the artificial effect in (1) by re-including the imprisoned population in the statistics with some plausible estimate of their earnings.