POSSIBILITIES AND PROBABILITY
38 . Average of Evenly Spaced Numbers
To find the average of evenly spaced numbers, just average the smallest and the largest. The
average of all the integers from 13 through 77 is the same as the average of 13 and 77:
39 . Using the Average to Find the Sum
Sum = (Average) × (Number of terms)
If the average of 10 numbers is 50, then they add up to 10 × 50, or 500.
40 . Finding the Missing Number
To find a missing number when you’re given the average, use the sum. If the average of 4
numbers is 7, then the sum of those 4 numbers is 4 × 7, or 28. Suppose that 3 of the numbers
are 3, 5, and 8. These 3 numbers add up to 16 of that 28, which leaves 12 for the fourth number.
41 . Median and Mode
The median of a set of numbers is the value that falls in the middle of the set. If you have 5
test scores and they are 88, 86, 57, 94, and 73, you must first list the scores in increasing or
decreasing order: 57, 73, 86, 88, 94.
The median is the middle number, or 86. If there is an even number of values in a set (6 test
scores, for instance), simply take the average of the two middle numbers.
The mode of a set of numbers is the value that appears most often. If your test scores were
88, 57, 68, 85, 99, 93, 93, 84, and 81, the mode of the scores would be 93 because it appears
more often than any other score. If there is a tie for the most common value in a set, the set has
more than one mode.
42 . Counting the Possibilities
The fundamental counting principle: If there are m ways one event can happen and n ways a
second event can happen, then there are m × n ways for the two events to happen. For
