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  1. Yes! These correlations probably need to be included. Not reporting data that doesn't fit your hypothesis is a failure of rigorous research methodology and an ethics issue. Depending on the significance of these correlations your study may require significant redesign or at least analysis of possible study shortcomings. You should probably do some analysis of variance between different demographics to determine if simple random sampling is even appropriate, or if you need some form of sample stratification to achieve a reasonable statistical confidence interval. (Since you did not mention your data collection method, I am assuming you use random sampling and could not measure every member of the population.) Also, make sure to plot the data to visually see if it looks like a straight line relationship between the demographic and the variable. Correlation only captures linear relationships, and not more complex relationships like the bell curve of human IQ. 1) This sort of preliminary correlational analysis is very common and a good way to begin validating data quality. 2) Yes, even if there is truly no significance this is part of your study design and data collection method. It shows what your data sample looks like. 3) This belongs in the discussion/conclusion, and possibly not results depending on the level of detail you want to get into. Ask your supervisor what they think, they can probably give you better guidance on how to handle this difficult question. You didn't give a lot of details about your research, so this answer could be way off base.
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