Median

Median

How to find the median of the given data: examples and their solutions.

Example 1

Find the median for the data below: 1, 3, 1, 2, 2, 4, 2.

The median is the middle value of the data.

There are two ways to find the median:

1. Write the data in order
and find the middle value.

2. Cancel the smallest value (1)
and the largest value (4) in pairs.
Repeat the cancelling
until you get the median value.

It's one of the ways to represent the whole data.

Other ways: Average (Mean), Mode

Example 2

Find the median for the data below: 4, 1, 5, 2, 3, 6, 3, 5.

If the middle value are two values, (3, 4)
then the median is the mean of them: (3 + 4)/2.

If the number of the data is an even number,
(in this case, 8)
then the median is the mean of the two middle values.

Example 3

The following table shows quiz scores of 20 students: [Scores(Frequency)] 0(1), 1(1), 2(4), 3(7), 4(5), 5(2) Find the median of the data.

There are 20 students. (20: even)
And 20/2 = 10.

So the median is the mean of 10th and 11th data.
(the middle of 10th and 11th data)

See the frequency table.
If you add up the frequencies from the top,
the cumulative frequency of '2 scores' is 6,
and the cumulative frequency of '3 scores' is 13.

So the scores of 10th and 11th are both 3.

So the median is [(10th) + (11th)] / 2 = [3 + 3]/2.