The Grocer And His Fruits
TECTechnics Classroom   TECTechnics Overview

The Grocer And His Fruits

Suppose a grocer sells 2 apples for 5 cents and 3 oranges for 5 cents. He surmises that the simple arithmetic of selling 5 fruits for 10 cents results in the same average price. In other words, according to him, a sale of 2 apples and 3 oranges have the same average price as a sale of any 5 pieces of fruits for 10 cents.
Is the grocer right? What is the correct average price ?

The string:
S7P6A63 (Multi-Criteria Combination).
The math:

Pj Problem of Interest is of type grouping. Average values result from the summation of a set of values and the division of the total sum by the number of elements in the set. In essence, an average value is a representative of a group. So, problems of average values are grouping problems.
The grocer is not correct. The apropriate average price should be:
Average of the averages of the two price scenarios.
So, correct average price = (5/2 + 5/3)/2 = 25/12 cents.

Math

Blessed are they that have not seen, and yet have believed. John 20:29