Calculate the median of the values two and nine-tenths, five and four-tenths, five and one- tenth, three and seven-tenths, three and four-tenths, one and nine-tenths, six and one-tenth, eight and one-tenth, twelve and four-tenths, two and six-tenths, eight and eight-tenths, five and five-tenths.
When a set of numbers is placed in value order, the median is the value in the middle. Our first step is to take these 12 numbers and place them in value order. That means numbering them from least to greatest or from greatest to least.
Let’s start ordering our numbers. Our smallest value is one and nine-tenths, so we can start with one and nine-tenths. The next value would be two and six-tenths. Next would be two and nine-tenths. Next we’ll have three and four-tenths followed by three and seven-tenths, five and one-tenth, five and four-tenths, five and five-tenths, six and one-tenth, eight and one-tenth, eight and eight-tenths, and finally twelve and four-tenths.
So here’s our list, ordered from least to greatest, of 12 values. If we’re going to divide these 12 values in half, each half would have six values in it, like this. There would be six values on the left and six values on the right, which means there is not one value in the middle.
When we’re dealing with sets that have even numbers like this one, we have to take the two values in the middle, in our case five and one-tenth and five and four-tenths, and find the average. We have to find the middle of five and one-tenth and five and four-tenths. To find the average or mean of these two numbers, we have to add them together, five and one-tenth plus five and four-tenths, and then divide that number by two.
Five and one-tenth plus five and four-tenths equals ten and a half, 10.5. Then we need to divide ten and five-tenths by two. Ten and a half divided by two equals five and twenty-five hundredths, 5.25. Since five and twenty-five hundredths falls in the middle of five and one-tenth and five and four-tenths, it’s the median of these 12 values.