# AVERAGE, MEDIAN, AND MODE

1. Average or Arithmetic Mean

To find the average of a set of numbers, add them up and divide by the number of numbers.

Sum of the terms

Average                        =         Number of terms

To find the average of the five numbers 12, 15, 23, 40, and 40, first add them:

12 + 15 + 23 + 40 + 40 = 130. Then divide the sum by 5: 130 / 5 = 26.

2. Using the Average to Find the Sum

Sum = (Average) X (Number of terms)

If the average of ten numbers is 60, then they add up to 10 X 60, or 600.

3. Finding a Missing Number

To find a missing number when you’re given the average, use the sum.   If the average of four numbers is 7, then the sum of those four numbers is 4  X  7, or 28.   Suppose that three of the numbers are 3, 5, and 8. These three numbers add up to 16 of that 28, which leaves 12 for the fourth number.

4. Median

The median of a set of numbers is the value that falls in the middle of the set. If you have five 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 (six test scores, for instance), simply take the average of the two middle numbers.

5. Mode

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.

6. Standard Deviation

Standard Deviation is a complex statistical measure, but for the test you mainly need to know that the it is the measure of how spread out a group of numbers are.  For example, the numbers {0, 10, 20} have a Standard Deviation of about 8.17 while the numbers {9, 10, 11} have a Standard Deviation of about 0.82.   Both have an average of 10, but because the first group was more “spread out” it had a higher Standard Deviation.