Blacks are only 2.7 times as likely to be in poverty. If you were to create some sort of crime/poverty index, in which crime rates are adjusted for poverty, they would still be way more likely to commit crime.
There are almost twice the number of white people below the poverty line as black people in the US. Using the numbers found on Wikipedia, there are about 9.6 million black Americans below the poverty line and 19.2 million white Americans below the poverty line. So, if "irrespective of race, [poor areas] have an increase in violence" then whites would be committing violence at a race twice that of blacks.
Poverty rates are insufficient to explain the differences in crime rate. There are more whites than blacks at every level of income (in absolute numbers), there are twice as many whites in poverty as blacks and yet blacks commit more murders than whites (in absolute numbers).
So we can say with relative certainty that when it comes to crimes like rape and murder which are not committed for economic gain that poverty is not a sufficient explanation.
The link between the two isn't even that particularly strong.
For the years 2006-2011, the Census-ACS provides estimates of the Mean Income, Median Income, and Poverty Rates for each urban center, and we can easily perform the same calculations we did in the racial case. The correlations between the Mean Income and Median Income levels and the various crime categories generally fall in the range of -0.40 to -0.60, being moderately rather than strongly negative. Even the correlation between Poverty Rate and crime—supported by the obvious truism that most street criminals are poor—is hardly enormous, falling between 0.50 and 0.70, and usually well below our racial figures.
What is odd is that Detroit spends roughly $15,000 a year per pupil which is $5,000 more than the national average and $3,000 more per year than the rest of Michigan.
Inner city schools are often more well funded than their rural less diverse counterparts.
The HS graduation rate for black students in Indianapolis is only 62%. That isn't a failure you can attribute to the school system. It is the parents and students who are responsible. No matter how much money is poured into this problem nothing will change.Indianapolis spends roughly $7,800 per student which is $2000 more per student than the state average.
It is the same in Chicago. Per pupil spending in 2011 averaged a staggering 13,432.53. Teachers and administrators in the Chicago public school system enjoy some of the highest salaries in the nation.
Some administrators make over $200k a year. The state average per pupil spending is 11,841.53. Children in rural areas of southern Illinois receive a third less money that what children in Chicago receive.
Of the 5,574 juveniles arrested on CPS grounds in 2010, 74% were African American.