Measures of Center

What Are Measures of Center?

When someone asks "What's your typical sale?" — 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

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1. Mean (Average)

How: Add all numbers → Divide by count

Example: Sales: ₹100, ₹150, ₹200, ₹250, ₹300

Mean = (100 + 150 + 200 + 250 + 300) ÷ 5 = ₹200

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

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2. Median (Middle Value)

How: Sort numbers → Pick the middle one

Example (odd count): ₹100, ₹150, ₹200, ₹250, ₹300 → Median = ₹200

Example (even count): ₹100, ₹150, ₹250, ₹300 → Median = (150 + 250) ÷ 2 = ₹200

Excel: =MEDIAN(A1:A5)

Python:

import statistics
sales = [100, 150, 200, 250, 300]
print(statistics.median(sales))  # Output: 200

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3. Mode (Most Common)

How: Find the value that appears most often

Example: Ratings: 4, 5, 4, 3, 4, 5, 4 → 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

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When to Use Which?

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Why Median Beats Mean (Sometimes)

Salaries: ₹30k, ₹35k, ₹40k, ₹45k, ₹5,00,000 (CEO)

• Mean = ₹1,30,000 (misleading!)
• Median = ₹40,000 (honest)

The CEO's salary pulls mean way up. Median ignores outliers.

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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)

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Cheat Sheet

Tip: Always check both mean AND median to spot outliers!