Problem: The Doran family has 5 children, aged 9, 12, 7, 16 and 13. How old is the middle child?

Solution: Sort the age of the children from the youngest to the oldest, you get:

7, 9, 12, 13, 16

Answer: The age of the middle child is the most average number in the data set, which is 12.

In the above problem, we found the median of a series of 5 numbers.

Definition: The median of a data set is the most average number in the set. The median is also the number in the middle of the set. To find the median, the data must first be arranged in order from minimum to maximum.

To remember the definition of median, just think of the median of a street, which is the most central part of the street. In the previous problem, 12 is the median: it is the number that is in the middle of the whole. There are two children over the age of 12 and two children under the age of 12. Let’s see some other examples.

Gas PumpExample 1: The Jameson family crossed 7 states during the summer vacation. Gasoline prices varied from state to state. What is the median price of gasoline?

\$1.79, \$1.61, \$1.96, \$2.09, \$1.84, \$1,75, \$2.11

Solution: Sorting the data from minimum to maximum, we get:

\$1.61, \$1.75, \$1.79, \$1.84, \$1.96, \$2.09, \$2.11

Answer: The average price of gasoline is \$1.84. (There were 3 states with higher gasoline prices and 3 states with lower prices).

Test CardExample 2: During the first evaluation period, Nicole’s math quiz scores were 90, 92, 93, 88, 95, 88, 97, 87, and 98. What was the average quiz score?

The solution: Sort the data from minimum to maximum, you get it:

87, 88, 88, 90, 92, 93, 95, 96, 98

Answer: The average quiz score was 92. (Four quiz scores were higher than 92 and four lower).

In each of the above examples, there is an odd number of entries in each data set. In example 1, there are 7 numbers in the data set; in example 2, there are 9 numbers. Let’s see some examples where there is an even number of entries in the data set.

MarathonExample 3: A marathon was completed by 4 participants. What was the median time of the race?

2.7 hours, 8.3 hours, 3.5 hours, 5.1 hours

Solution: Sorting the data from minimum to maximum, we get:

2.7, 3.5, 5.1, 8.3

Since there is an even number of elements in the data set, we calculate the median by taking the average of the two most average numbers.

3.5 + 5.1 = 8.6

Answer: The average race time was 4.3 hours.

BonusExample 4: The salaries of 8 employees working for a small company are listed below. What is the median salary?

\$40,000, \$29,000, \$35,500, \$31,000, \$43,000, \$30,000, \$27,000, \$32,000

Solution: Sorting the data from minimum to maximum, we get:

\$27,000, \$29,000, \$30,000, \$31,000, \$32,000, \$35,500, \$40,000, \$43,000

Since there is an even number of elements in the data set, we calculate the median by taking the average of the two most median numbers.

\$31,000 + \$32,000 = \$63,000

Answer: The average salary is \$31,500.

Summary: The median of a data set is the most average number of the set. The median is also the number in the middle of the set. To find the median, the data must be arranged in order from minimum to maximum. If there is an even number of elements in the data set, then the median is found by taking the average of the two median numbers.