Quote from RoughTrader:
They are NOT similar
The median of 100 homes sold for $100k and 1 home sold for $1 million is $550k.
The average of 100 homes sold for $100k and 1 home sold for $1 million is
( 100 x $100k + 1 x $1 million) / 101 = $108.9k
The median is a dirty little method the industry uses to mask the larger volume of declining home prices with the fewer transactions of higher-end homes.
RoughTrader
For large population samples, median and average are virtually the same. The larger the sample, the more they converge.
WRT to national housing numbers, the population is large enough that median and average should be the same.
ps: it's obvious from your example #1 that you don't know what "median" is.