Line Plots & Mean • Topic 2 of 2

Median & Mode Introduction

Median (Middle Value)

The median is the middle number when data is arranged in order.

Steps to Find Median:

  1. Arrange numbers from smallest to largest
  2. If odd count → middle number
  3. If even count → average of two middle numbers

Example (Odd): 3, 7, 9, 11, 15 → median = 9

Example (Even): 3, 7, 9, 11 → median = (7+9)/2 = 8

Mode (Most Frequent)

The mode is the value that appears most often.

  • One mode: 2, 2, 3, 4, 5 → mode = 2
  • Two modes (bimodal): 1, 1, 2, 2, 3 → modes = 1 and 2
  • No mode: 1, 2, 3, 4, 5 → no mode
FINDING MEDIAN:

    Data: 5, 2, 8, 1, 9
    
    Step 1: Order: 1, 2, 5, 8, 9
                 ↑
    Median = 5 (3rd number)


FINDING MEDIAN (EVEN COUNT):

    Data: 3, 6, 4, 9, 2, 7
    
    Step 1: Order: 2, 3, 4, 6, 7, 9
                     ↑  ↑
                  Middle two: 4 and 6
    
    Median = (4 + 6) ÷ 2 = 5


MODE VISUAL (Bar Chart):

    Frequency
        │
      4│    ■
      3│    ■   ■
      2│    ■   ■   ■
      1│    ■   ■   ■   ■
        └───┬───┬───┬───┬───
            2   3   4   5   6
    
    Mode = 4 (appears 3 times, most frequent)
Solved Examples
1
Worked Example

Find median: 22, 15, 30, 18, 25

Solution
  • Order: 15, 18, 22, 25, 30
  • Middle number (3rd) = 22
  • Answer: 22
2
Worked Example

Find median: 8, 12, 5, 9, 14, 7

Solution
  • Order: 5, 7, 8, 9, 12, 14
  • Middle two: 8 and 9
  • Median = (8+9)/2 = 8.5
  • Answer: 8.5
3
Worked Example

Find mode(s): 4, 7, 4, 9, 2, 7, 4, 6

Solution
  • Count: 4 appears 3 times, 7 appears 2 times, others once
  • Most frequent = 4
  • Answer: 4

Key Points

  • Median = middle value (order first!)
  • Even count → average of two middle numbers
  • Mode = most frequent value
  • Data can have 1 mode, 2+ modes, or no mode
  • Mean, median, mode all describe "center" differently
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The median is the ___ value when data is ordered.
Explanation: Middle value.
Q2.The mode is the value that occurs:
Explanation: Most frequent.
Q3.The median of $3, 5, 7$ is:
Explanation: Middle value $5$.
Q4.The mode of $2, 2, 3$ is:
Explanation: $2$ occurs most.
Practice more MCQs → 📝 Assignment · 35 marks