Find the median for the set of data in this table.
First, let’s talk about each category. The amount is the data that we’re talking about. The tally is the number of times that amount occurs, represented with tally marks. And the frequency is the numerical representation of the tally marks.
In this list, the number 15 occurs seven times, the number 35 occurs eight times, the number 50 occurs once, 75 occurs four times, and 90 occurs five times. The median is the middle of a sorted list of numbers. Our list is sorted from least to greatest. But to find the middle, we need to know how many total values there are. To do that, we’ll add up the frequency. Seven plus eight plus one plus four plus five equals 25.
Now, we need to ask, what is the halfway point of 25? Another way to ask that would be to say “what is 25 divided by two?” 25 goes into two one time. One times two equals two. Two minus two equals zero. Bring down our five. How many times does two go into five? Well, two times two equals four. Five minus four equals one. If we take our remainder of one and place it over our divisor of two, we can recognize that 25 divided by two is 12 and a half.
If we start at the beginning of our ordered list and move forward 12 and a half spaces, we’ll find the median: one, two, three, four, five, six, seven, eight, nine, 10, 11, 12. 12 and a half falls here. It falls between 35 and 35. Well, halfway between 35 and 35 is still 35.
The median of this data would be 35.