Measures of Center
Learn mean, median, and mode - your first step into statistics
What Are Measures of Center?
When someone asks "What's your typical sale?" ā you need ONE number to represent all your data. That's what measures of center do.
Three ways to find the center:
- Mean = Average
- Median = Middle value
- Mode = Most common value
1. Mean (Average)
How: Add all numbers ā Divide by count
Example: Sales: ā¹100, ā¹150, ā¹200, ā¹250, ā¹300
Mean = (100 + 150 + 200 + 250 + 300) Ć· 5 = ā¹200
Excel: =AVERAGE(A1:A5)
Python:
sales = [100, 150, 200, 250, 300]
mean = sum(sales) / len(sales) # sum() adds, len() counts
print(mean) # Output: 200.0
2. Median (Middle Value)
How: Sort numbers ā Pick the middle one
Example (odd count): ā¹100, ā¹150, ā¹200, ā¹250, ā¹300 ā Median = ā¹200
Example (even count): ā¹100, ā¹150, ā¹250, ā¹300 ā Median = (150 + 250) Ć· 2 = ā¹200
Excel: =MEDIAN(A1:A5)
Python:
import statistics
sales = [100, 150, 200, 250, 300]
print(statistics.median(sales)) # Output: 200
3. Mode (Most Common)
How: Find the value that appears most often
Example: Ratings: 4, 5, 4, 3, 4, 5, 4 ā Mode = 4 (appears 4 times)
Excel: =MODE.SNGL(A1:A7)
Python:
import statistics
ratings = [4, 5, 4, 3, 4, 5, 4]
print(statistics.mode(ratings)) # Output: 4
When to Use Which?
| Use | When | Example |
|---|---|---|
| Mean | No extreme values | Test scores |
| Median | Has outliers | Salaries, house prices |
| Mode | Categories/popularity | Survey answers, favorite items |
Why Median Beats Mean (Sometimes)
Salaries: ā¹30k, ā¹35k, ā¹40k, ā¹45k, ā¹5,00,000 (CEO)
- Mean = ā¹1,30,000 (misleading!)
- Median = ā¹40,000 (honest)
The CEO's salary pulls mean way up. Median ignores outliers.
Quick Practice
Data: 10, 20, 30, 40, 50
- Mean = 30
- Median = 30
- Mode = None (all unique)
Data: 5, 10, 15, 20, 1000
- Mean = 210 (outlier effect!)
- Median = 15 (better representation)
Cheat Sheet
| Measure | Formula | Excel | Python |
|---|---|---|---|
| Mean | Sum Ć· Count | =AVERAGE() | statistics.mean() |
| Median | Middle value | =MEDIAN() | statistics.median() |
| Mode | Most frequent | =MODE.SNGL() | statistics.mode() |
Tip: Always check both mean AND median to spot outliers!