Measures of Central Tendency

  1. The house is Bel Air will not dramatically affect the median, but will raise the mean considerably.  The mean will end up being far higher than any of the other houses (but lower than the Bel Air house), which would not be an accurate representation of the prices. Mode would be silly.  Even if two houses have the same exact price, that's pretty meaningless for the group. Median is probably the most informative measure.
  2. The mode of these tests would be 100 because that's the only double score.  That's not quite accurate, as all the other scores are lower.  The mean and the median of this dataset are probably pretty close: either would be a good measure of central tendency.
  3. The mode of these contributions is 20.  That's probably pretty accurate: most people put in $20. The mean and median will be pretty close and both pretty accurate. The 0s will pull the mean down a little artificially, but they will still be fairly close.
  4. The GOOP coat will raise the mean ridiculously. The mode is useless a there are no two coats with the same price (and even if there were, it would just be a coincidence).  The median is the most reasonable measure of central tendency for these data.
  5. Two students must have gotten a 2000, and no other students got the same score.  The mode is a silly measure here. And, probably one or two students got very, very low scores, pulling down the average. 
  6. The student probably got mostly good grades, but he must have gotten a few very low scores, which are dragging the mean down to a D.
  7. There must be a lot of people in Mississippi who earn very little (or nothing) which drags the mean down. The median better captures the middle of this group, but the mean does highlight the existence of some extreme poverty, which you would also want to know.  This is a case when it's important to have both the mean and the median so that you can compare and learn from that comparison.
  8. There must be people in Orange County who earn a lot of money, which drags the mean up.  The median better captures the middle of this group, but the mean does tell you that there are some very high-earning families (or perhaps one or two Bill Gates/Donald Trump types), which is a good piece of data to have. 
  9. Mode is a terrible way to measure a continuous variable like income (categorical variables fit into groups, like 0-$20,000, 20,001-30,000, etc and continuous variables can be any number), because the existence of more than one of the same figure is more a matter of coincidence than a matter of that number saying something important about the dataset as a whole.