Finding The Median Of Ungrouped Data

Finding the median of ungrouped data is another common measure of central tendency in statistics.

In this lesson, you will learn the formula and the step-by-step method for finding the median of ungrouped data.

BONUS: A link to practice questions on statistics is included at the end of this lesson.

Formula for finding the median of ungrouped data

The formula for finding the median of ungrouped data is to arrange the numbers according to their size, and pick the middle number.

Question on finding the median of ungrouped data

Let’s take an example:

Find the median of the following numbers:

15, 11, 8, 3, 13, 8, 5

STEP 1.

Arrange the numbers according to their size

3, 5, 8, 8, 11, 13, 15

STEP 2.

Pick out the middle number

Middle number:

3, 5, 8, (8), 11, 13, 15

Final answer

The median of the following numbers:

15, 11, 8, 3, 13, 8, 5

= 8

Finding the median of uneven distribution

In a case where the total numbers in the distribution is uneven, there will be two middle numbers.

Formula for finding the median of uneven distribution

The formula for finding the median of uneven distribution is to arrange the numbers according to their size, pick out the two middle numbers and find their mean.

Question on finding the median of uneven distribution

Find the median of the following numbers:

15, 11, 8, 3, 13, 8, 5, 21

STEP 1.

Arrange the numbers according to their size

3, 5, 8, 8, 11, 13, 15, 21

STEP 2.

Pick out the two middle numbers

Middle numbers:

3, 5, 8, (8, 11), 13, 15, 21

STEP 3.

Find the mean of the two middle numbers

\frac{8+11}{2}
  • Add the two middle numbers
\frac{19}{2}
  • Divide by their total
\frac{19}{2}=9.5

Final answer

The median of the following numbers:

15, 11, 8, 3, 13, 8, 5, 21

= 9.5

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