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Comparison of Averages – Strengths & Weaknesses 📊⚖️

Statistics offers many types of averages, each useful in different situations. Choosing the right average is essential for accurate interpretation.

In this chapter, we compare:

• Arithmetic Mean (A.M.)
• Median
• Mode
• Geometric Mean (G.M.)
• Harmonic Mean (H.M.)
• Simple Average
• Weighted Average

This comparison helps students know which average to use and when, a popular exam question.

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1. Arithmetic Mean (A.M.)

Strengths

• Uses all observations
• Easy to calculate and understand
• Suitable for further mathematical use (variance, SD, correlation)
• Stable and reliable measure

Weaknesses

• Highly affected by extreme values
• Not suitable for skewed distributions
• Cannot be used for open-ended classes

Best Used When

• Data is continuous and symmetrical
• No extreme outliers exist

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2. Median

Strengths

• Not affected by extreme values
• Ideal for skewed distributions
• Works for open-ended and qualitative ordinal data

Weaknesses

• Ignores all values except middle position
• Does not use mathematical operations

Best Used When

• Data contains outliers (income, wealth)
• Distribution is skewed

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3. Mode

Strengths

• Easiest to understand
• Useful for qualitative data (brand preference)
• Not affected by extreme values

Weaknesses

• May not be unique (bimodal or multimodal)
• Not based on all observations

Best Used When

• Studying the "most common" value (e.g., shoe size, most sold product)

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4. Geometric Mean (G.M.)

Strengths

• Best for percentages, ratios, and growth rates
• Less affected by extreme values
• Essential for index numbers

Weaknesses

• Cannot handle zero or negative values
• Requires logarithms for large values

Best Used When

• Data is multiplicative (investment returns, growth changes)
• Index numbers require weighted G.M.

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5. Harmonic Mean (H.M.)

Strengths

• Best for averaging rates (speed, price per unit)
• Suitable when values are defined per unit

Weaknesses

• Sensitive to very small values
• Cannot handle zero values

Best Used When

• Distances or quantities are equal (average speed problems)
• Rates and ratios must be averaged correctly

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6. Simple Average

Strengths

• Very easy to compute
• Good for quick summaries

Weaknesses

• Assumes all values are equally important
• Misleading when quantities differ

Best Used When

• All items carry equal weight

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7. Weighted Average

Strengths

• Most accurate average when weights differ
• Used in finance (WACC), index numbers, costing, GPA

Weaknesses

• Requires correct weighting
• Sensitive to incorrect assignment of weights

Best Used When

• Quantities or importance levels vary
• Economic and financial calculations

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Summary Comparison Table 📘

Average	Uses All Data	Affected by Extremes	Suitable For	Not Good For
Mean (A.M.)	Yes	Yes	Symmetrical data	Skewed data
Median	No	No	Skewed data, open-ended classes	Mathematical analysis
Mode	No	No	Qualitative data	Continuous unique data
G.M.	Yes	Less	Growth rates, ratios	Zero/negative values
H.M.	Yes	Yes (small values)	Rates, speed	Zero values
Simple Avg.	No	Yes	Equal-sized groups	Different quantities
Weighted Avg.	Yes	Depends on data	Index numbers, costing	Wrong weights

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How to Choose the Right Average (Decision Guide)

Follow this simple flow:

Is data qualitative? → Use Mode

Is distribution skewed or has outliers? → Use Median

Are values rates or ratios? → Use Harmonic Mean

Are values growth rates or multiplicative? → Use Geometric Mean

Do groups have different weights? → Use Weighted Average

Otherwise → Use Arithmetic Mean

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Practical Applications in Business & Economics 📌

• Income analysis → Median
• Most demanded product → Mode
• Price index calculation → G.M.
• Cost per unit when quantities differ → Weighted average
• Investment growth → G.M.
• Transport problems → H.M.
• Employee performance score (credit-based) → Weighted average

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Summary ✨

• No single average is universally best.
• Each average serves different purposes based on data characteristics.
• Choosing the correct measure improves accuracy and interpretation.
• A common exam question is: "Compare Mean, Median, and Mode"—this chapter fully prepares you.

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Quiz Time 🎯