Suppose a 7-nearest-neighbors regression search returns {7, 6, 8, 4, 7, 11, 100} as the 7 nearest y values for a given x value. What is the value of that minimizes the L1 loss function on this data? There is a common name in statistics for this value as a function of the y values; what is it? Answer the same two questions for the L2 loss function.

I found the answer here: https://www.chegg.com/homework-help/questions-and-answers/machine-learning-knn-learning-suppose-7-nearest-neighbors-regression-search-returns-7-6-8--q20044779

But, I do not understand the answer. I've tried looking up what h hat is and how it corresponds to L1 and L2 and what L1 and L2 are but I do not understand. Thanks.