MathBatchSign in
Free worksheet generator

Median Worksheet Generator

Generate free median worksheets using positive-only, negative-only, and mixed-sign integer data sets with verified answers.

Verified answersGenerated with deterministic math
Free step-by-step lesson

Learn median

The median is the middle value of an ordered data set. When a set has an even number of values, the median is the mean of the two middle values.

By the end of this lesson

You will find the middle of ordered data, including sets with an even number of values.

Review first if you need it: Mean
01

The idea in plain English

The median is the middle value after the data is put in order.

It is often useful when extreme values would pull the mean too far.

02

How to recognise this kind of question

  • The question says median or middle value.
  • A list of numerical data is given.
  • The number of values may be odd or even.

Quick decision: Order first. One middle value is the median; two middle values must be averaged.

03

The method

  1. Rewrite the values in order from least to greatest, keeping every negative sign.
  2. If the set has an odd number of values, select the single middle value.
  3. If the set has an even number of values, add the two middle values and divide by two.
  4. Check that the same number of data values appear on each side of the median position.
04

Worked examples

Start here

Find the median: −8, 5, −2, 9, 1, −4

  1. Order the values: −8, −4, −2, 1, 5, 9.
  2. The two middle values are −2 and 1.
  3. Average them: (−2 + 1) ÷ 2 = −0.5.

Answer: −0.5

A little harder

Find the median of 9, 2, 5, 12.

  1. Order: 2, 5, 9, 12.
  2. There are two middle values: 5 and 9.
  3. Average them: (5 + 9) ÷ 2.

Answer: 7

05

Your turn—with help

Try it

Find the median of 8, 1, 6, 3, 10.

Need a hint?

Put the values in order before choosing the middle.

Show the answer and steps
  1. Order: 1, 3, 6, 8, 10.
  2. The third value is in the middle.

Answer: 6

06

Watch out for this mistake

Incorrect: Median of 9, 2, 5 is 2

Why it fails: The middle position was chosen before ordering the data.

Do this instead: Order 2, 5, 9; the median is 5.

07

Quick check

Try these without looking. Then open each answer to check your thinking.

Question 1

Median of 7, 2, 4

Need a hint?

Order first.

Show the answer and steps
  1. 2, 4, 7 has 4 in the middle.

Answer: 4

Question 2

Median of 1, 3, 9, 11

Need a hint?

Average the two middle values.

Show the answer and steps
  1. Middle values are 3 and 9.
  2. (3 + 9) ÷ 2 = 6.

Answer: 6

Question 3

Median of 5, 5, 8, 20, 30

Need a hint?

Repeated values still count.

Show the answer and steps
  1. The ordered list is already shown.
  2. The third value is 8.

Answer: 8

Remember thisOrder first, then find the middle.

Common mistakes

  • Choosing the value in the middle of the original unsorted list.
  • Putting negative numbers in the wrong order.
  • Selecting both middle values without averaging them for an even-sized set.
  • Dividing the sum of the middle values by the total number of values instead of two.

Practice tips

  • Cross off one value from each end of the ordered list until reaching the center.
  • Remember that a negative number with a larger absolute value is farther left on the number line.
  • Use the number of values—not their size—to locate the middle position.
Free printable practice

Now practise what you learned.

Create a fresh set with verified answers. No signup required.

20 verified problemsSeed 482731
MMathBatch
Worksheet #482731
Statistics practice

Median

Name Date

Find the median of each data set.

  1. −7, −18, −25, −23, −1
  2. −24, −30, −26, 30, 23, 26
  3. 13, 7, 29, 28, 14, 4, 23
  4. −1, −9, −16, −15, −12, −19
  5. 15, −1, 23, 28, −14, 26
  6. 25, 27, 10, 15, 28
  7. −24, −7, −23, −9, −27
  8. −14, 6, −13, 13, −12, −23, −15
  9. 14, 1, 10, 22, 16
  10. −30, −5, −8, −28, −3, −6
  11. 11, −25, −23, −3, 24, 17
  12. 5, 29, 22, 10, 8, 30, 18
  13. −18, −7, −9, −23, −2
  14. −19, −17, 16, 4, −4, −29
  15. 21, 28, 7, 22, 4, 13, 11
  16. −17, −21, −20, −3, −29, −4
  17. −29, 11, 4, 25, −27
  18. 2, 4, 16, 21, 25, 17, 19
  19. −10, −29, −9, −4, −25
  20. −20, −17, −28, 19, −14, 11, −22
Fresh math practice. Every time.mathbatch.com