Data & Probability · Measures of center · 1.2

Median (middle).

The median is the middle value once the data is in order. With an odd count it’s the single middle one; with an even count, average the two middle values. Ordered 2, 4, 5, 7, 9 → median 5.

01 / THE IDEA

See it work.

The data

See the values.

7122934455

Watch the method

Median (middle)

Median = the middle value of the ordered list.

1 / 2
Find the median of: 7, 2, 9, 4, 5.
1

Order the values

Sort from least to greatest.

2,4,5,7,92, 4, 5, 7, 9
2

Find the middle

The median is the middle value.

55
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type the answer — a fraction or decimal is fine.

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

The middle of the line

Half the values fall below the median and half above.

Why it works

Line them up; point to the center.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the median of: 3, 3, 4, 8, 1, 10.

1

Order the values

Sort from least to greatest. 1, 3, 3, 4, 8, 10

2

Find the middle

With an even count, average the two middle values. 3.5

EX 2medium

Find the median of: 7, 10, 18, 17, 6.

1

Order the values

Sort from least to greatest. 6, 7, 10, 17, 18

2

Find the middle

The median is the middle value. 10

EX 3hard

Find the median of: 7, 18, 18, 14, 3.

1

Order the values

Sort from least to greatest. 3, 7, 14, 18, 18

2

Find the middle

The median is the middle value. 14

04 / COMMON TRAPS

Where students slip.

Trap

Forgetting to order first.

Fix

Sort the values before finding the middle.

Trap

Mishandling an even count.

Fix

Average the two middle values.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Find the median of: 20, 6, 14, 15, 6, 20.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
C2

Find the median of: 9, 5, 17, 10, 2.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
C3

Find the median of: 8, 1, 14, 18, 16.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
C4

Find the median of: 8, 10, 15, 14, 13.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
Apply

Apply (4)

A1

Find the median of: 14, 4, 19, 14, 14.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
A2

Find the median of: 10, 5, 5, 14, 8.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
A3

Find the median of: 10, 1, 12, 4, 20.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
A4

Find the median of: 9, 14, 7, 18, 7.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
Extension

Extension (4)

E1

Find the median of: 6, 20, 18, 17, 7.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
E2

Find the median of: 2, 11, 12, 9, 11.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
E3

Find the median of: 17, 17, 14, 16, 2, 10.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).
E4

Find the median of: 8, 10, 15, 20, 18.

Need a hint?
  • Put the values in order.
  • Find the middle (average two if even).