2,014
edits
Changes
Jump to navigation
Jump to search
Line 45:
Line 45: − + − +
→The average as a "balance point": fixed dash(es)
:One weight is 6 inches to the left of the average
:One weight is 6 inches to the left of the average
:The other weights are 2 and 4 units to the right of the average
:The other weights are 2 and 4 units to the right of the average
The distance of the weight on the left&dmash;6 inches;equals the total of the distances of the weights on the right.
The distance of the weight on the left — 6 inches — equals the total of the distances of the weights on the right.
It can be shown that this is always true. The ''sum of the distances''<ref>i.e. the absolute magnitude of the difference</ref> between the average and each of the numbers above it is always equal to the sum of the distances between the average and each of the numbers below it.
It can be shown that this is always true. The ''sum of the distances''<ref>i.e. the absolute magnitude of the difference</ref> between the average and each of the numbers above it is always equal to the sum of the distances between the average and each of the numbers below it.
Compare this to the median. In the case of the median, the ''count'' of the numbers above the median equals the count of the numbers below the median.
Compare this to the median. In the case of the median, the ''count'' of the numbers above the median equals the count of the numbers below the median.
==Weighted averages==
==Weighted averages==