Yes it is.
give 82% of the population an obesity of 30% = 24.6
give 18% an obesity of 54% = 9.72
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34.32% overall
37% of Mississippi's 2.9M population is black, or 1.07M people, leaving the remaining 1.83M white.
Women, of all races, comprise 51% of the state's population, or 1.48M people. What percentage of women in MS are black I don't know, but if it mirrors the overall state population, it would be 37% of that 1.48M people (548k people). This leaves 932k white women in MS. White women's obesity prevalence is 32.2%... or 300k white obese women.
53% of women in MS voted Republican in 2012.
Men, of all races, comprise 49% of the state's population, or 1.42M people. What percentage of men in MS are black I don't know, but if it mirrors the overall state population it would be 37% of that 1.42M people (525k people). This leaves 895k white men in MS. White men's obesity prevalence is 20.3%... or 185k white obese men. 58% of men in MS voted Republican in 2012.
As for obese black women and obese black men, they would.. according to the math above and figures from CDC I posted, be 320k and 110k respectively.
Total obese white: 485k people
Total obese black: 440k people
59% of voters in MS in 2012 were white, 36% were black.
As you can see, MS being the reddest state and fattest is because white obese outnumbers black obese by 10%... which is almost exactly the percentage by which Republicans won the state. Black women are why the total obesity numbers between black/white are off by only 10%, but at only 37% of the state's population they are not why the state is reddest and fattest.