Measures of Central Tendency – Introduction 🎯📊

Every dataset has many values.
But decision-makers need one value that represents the entire dataset.

This value is called a measure of central tendency or average.

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What Is Central Tendency?

Definition:

A measure of central tendency is a single value that represents the entire dataset and indicates the central or typical value of distribution.

Examples:

• Average income
• Average marks
• Average price

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Why Do We Need Averages? 🎯

1. Simplifies Data

Converts bulky data into a single meaningful figure.

2. Helps in Comparison

Compare:

• Year to year
• Region to region
• Product to product

3. Useful in Decision-Making

Businesses use averages for:

• Pricing
• Budgeting
• Sales forecasting

4. Foundation for Further Analysis

Standard deviation, correlation, index numbers → all require averages.

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Characteristics of a Good Average ✔️

A good average must be:

1. Easy to Understand & Calculate

Should be simple and intuitive.

2. Rigidly Defined

Same value must be obtained by all people applying the formula.

3. Based on All Observations

Should consider the entire dataset (but mode sometimes doesn’t).

4. Not Affected by Extreme Values

Some averages like median withstand outliers.

5. Capable of Further Mathematical Treatment

Mean is excellent for advanced analysis.

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Types of Averages 📚

Measures of central tendency include:

• Arithmetic Mean
• Median
• Mode
• Geometric Mean
• Harmonic Mean
• Quartiles / Percentiles (often supporting measures)

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Difference Between Average & Actual Values

Example:
Marks = 20, 40, 60, 80
Average = 50

But no student scored exactly 50.
Still, 50 represents the group.

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When Averages Fail ❌

• Extreme values distort mean
• Skewed distributions misrepresent data
• Not applicable for qualitative data

Example:
A family with incomes 10,000; 12,000; 15,000; 1,00,000
Mean income → high due to the outlier.

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Flow of Selecting an Average

Nature of Data
↓
Need for Mathematical Use?
↓
Presence of Outliers?
↓
Choose Mean / Median / Mode

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Summary ✨

• Averages summarize complex data.
• A good average is simple, clear, stable, and mathematically useful.
• Types include mean, median, mode, GM, and HM.

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Quiz Time! 🎯