Statistics • Topic 2 of 3

Mean, Median, Mode, Range

Four Measures of Central Tendency:

Measure	Definition	How to Find	Example: 2,4,6,8,10
Mean	Average	Sum ÷ Count	(2+4+6+8+10)/5 = 6
Median	Middle value	Order, find middle	2,4,6,8,10 → 6
Mode	Most frequent	Find most common	No mode (all appear once)
Range	Spread	Max - Min	10 - 2 = 8

When to Use Each:

Measure	Best Used When
Mean	Data is symmetrical, no outliers
Median	Data has outliers (very high/low values)
Mode	Data has repeating values (favorite colors)
Range	Want to know spread of data

MEAN AS "BALANCE POINT":

    Data: 2, 4, 6, 8, 10
    
    <----|----|----|----|----|---->
         2    4    6    8    10
              ↑    ↑
              ←──┼──→
         Left sum = Right sum
         (2+4=6, 8+10=18) Not equal? Actually mean=6 balances:
         Deviations: -4, -2, 0, +2, +4 → sum of deviations=0


MEDIAN VISUAL:

    Odd count (5 numbers):
    2, 4, 6, 8, 10 → median = 6 (3rd number)
    
    Even count (6 numbers):
    2, 4, 6, 8, 10, 12 → median = (6+8)/2 = 7


MODE VISUAL:

    Data: 3, 5, 5, 7, 7, 7, 9
    
    Frequency:
    9│        ■
    8│        
    7│     ■  ■  ■
    6│        
    5│  ■  ■  ■
    4│        
    3│  ■
    └──────────────
       3  5  7  9
        
    Mode = 7 (appears 3 times)


RANGE VISUAL:

    Data: 15, 22, 31, 18, 45
    
    Min = 15, Max = 45
    Range = 45 - 15 = 30
    
    <─── Range = 30 ───→
    ├─────┼─────────────┤
    15                  45

Solved Examples

Worked Example

Find mean, median, mode, and range of: 5, 8, 12, 8, 7

Solution

Mean = (5+8+12+8+7)/5 = 40/5 = 8
Order: 5,7,8,8,12 → median = 8
Mode = 8 (appears twice)
Range = 12 - 5 = 7
Answer: Mean=8, Median=8, Mode=8, Range=7

Worked Example

Find median of: 22, 15, 30, 18, 25, 20

Solution

Order: 15,18,20,22,25,30
Even count: middle two are 20 and 22
Median = (20+22)/2 = 21
Answer: 21

Worked Example

Find mode(s): 1, 2, 2, 3, 3, 4

Solution

2 appears twice, 3 appears twice
Two modes = bimodal
Answer: 2 and 3

Key Points

Mean = sum ÷ count (average)
Median = middle value (order first!)
Mode = most frequent value(s)
Range = max - min (spread)
Outliers affect mean more than median

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The mean equals:

Explanation: Sum over count.

Q2.The median is the:

Explanation: Middle value.

Q3.The mode is the value that occurs:

Explanation: Most frequent.

Q4.The range equals:

Explanation: Max minus min.

Practice more MCQs → 📝 Assignment · 35 marks