🔵Finding Mean (Average)
What is Mean (Average)?
The mean is the fair share — if you add all numbers and split equally among all items.
Formula:
Mean = Sum of all values ÷ Number of values
Steps:
- Add up all numbers (find the sum)
- Count how many numbers (n)
- Divide sum by count
Example: Find mean of 5, 7, 12, 8
- Sum = 5 + 7 + 12 + 8 = 32
- Count = 4 numbers
- Mean = 32 ÷ 4 = 8
MEAN AS "FAIR SHARE":
Data: 4, 6, 8, 10
Step 1: Stack all values:
│
│ ■ (10)
│ ■ (8)
│ ■ (6)
│ ■ (4)
└─────
Step 2: Level them out (each gets same):
│ ■ ■ ■ ■
│ ■ ■ ■ ■
│ ■ ■ ■ ■
│ ■ ■ ■ ■
└─────
Each column has 7 → Mean = 7
MEAN ON A NUMBER LINE:
Data: 2, 4, 9
Sum = 15
Count = 3
Mean = 15 ÷ 3 = 5
<---|---|---|---|---|---|---|---|---|--->
2 4 5 9
↑
Mean
Values balance around 5: (5-2)=3, (5-4)=1, (9-5)=4; 3+1=4 ✓👀 See a worked example
Find the mean of 12, 15, 18, 20, 25
- Sum = 12 + 15 + 18 + 20 + 25 = 90
- Count = 5
- Mean = 90 ÷ 5 = 18
- Answer: 18
Maria's test scores: 85, 92, 78, 95, 90. What is her average?
- Sum = 85 + 92 + 78 + 95 + 90 = 440
- Count = 5
- Mean = 440 ÷ 5 = 88
- Answer: 88
The mean of 4 numbers is 15. Three numbers are 10, 18, and 14. Find the fourth.
- Sum of all 4 = mean × count = 15 × 4 = 60
- Sum of known = 10 + 18 + 14 = 42
- Fourth = 60 - 42 = 18
- Answer: 18
🤖 Vidi's Key Points
- Mean = total ÷ number of items
- Also called "average"
- Can be a decimal (not necessarily a data value)
- Use to find missing number: total - known sum
🟢Median & Mode Introduction
Median (Middle Value)
The median is the middle number when data is arranged in order.
Steps to Find Median:
- Arrange numbers from smallest to largest
- If odd count → middle number
- 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)👀 See a worked example
Find median: 22, 15, 30, 18, 25
- Order: 15, 18, 22, 25, 30
- Middle number (3rd) = 22
- Answer: 22
Find median: 8, 12, 5, 9, 14, 7
- Order: 5, 7, 8, 9, 12, 14
- Middle two: 8 and 9
- Median = (8+9)/2 = 8.5
- Answer: 8.5
Find mode(s): 4, 7, 4, 9, 2, 7, 4, 6
- Count: 4 appears 3 times, 7 appears 2 times, others once
- Most frequent = 4
- Answer: 4
🤖 Vidi's 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
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