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Simple Averages – Types & Uses 📘📊

A simple average is the most basic form of statistical average used to represent a group of values with a single representative figure. It helps simplify large datasets and supports comparison.

Simple averages are used extensively in:

• Business analysis
• Economics
• Costing and accounting
• Quality control
• Decision-making

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What Is a Simple Average?

A simple average is calculated by adding all values and dividing by the number of values.

It is the most fundamental tool to summarize data.

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Types of Simple Averages

Simple averages can be computed for different types of data depending on the nature of the information.

1. Average of Quantitative Data (Numerical Values)

This includes:

• Arithmetic Mean
• Geometric Mean
• Harmonic Mean

These are mathematical averages used when data is purely numerical.

2. Average of Ratios

When the data represents rates, percentages, or ratios, averages must be computed carefully.

Example ratios: marks %, profit %, return %, price per unit.

3. Average of Averages

Sometimes, we average group averages. But this must be done carefully:

• If all groups are equal in size → simple average
• If groups differ in size → weighted average (covered in next chapter)

4. Average of Time Series

Used to find:

• Average annual production
• Average monthly sales
• Average quarterly revenue

5. Average Prices / Average Costs

Common in commerce:

• Average cost of materials
• Average price per kg
• Average sales price

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Formula for Simple Average

For values X1, X2, X3, ..., Xn:

Simple Average = ΣX / n

Where:

• ΣX = sum of values
• n = number of observations

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Solved Examples

Example 1 — Average Sales

Sales of a shop for 5 days: 1200, 1500, 1100, 1700, 1300

ΣX = 1200 + 1500 + 1100 + 1700 + 1300 = 6800
n = 5
Average sales = 6800 / 5 = 1360

The average daily sales = ₹1360.

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Example 2 — Average Percentage

A student's marks % in 3 subjects are: 80%, 70%, 90%

ΣX = 80 + 70 + 90 = 240
n = 3
Average % = 240 / 3 = 80%

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Example 3 — Average of Price per Unit

A merchant bought 10 units at ₹5 each and 10 units at ₹15 each.

Simple Average Price = (5 + 15) / 2 = 10

But note: quantities are equal. If quantities were different → use weighted average (next chapter).

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Properties of Simple Averages ⭐

• Easy to calculate and interpret
• Provide a single representative figure
• Used in comparisons and summaries
• Sensitive to extreme values (for arithmetic mean)
• Not suitable for qualitative data

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Applications in Business & Economics 📌

• Average cost estimation
• Average productivity
• Average returns
• Budget analysis
• Forecasting and planning

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Summary ✨

• Simple averages summarize data using ΣX / n.
• Used for numerical, ratio-based, and time-based data.
• Foundation for understanding weighted averages.
• Important in business decision-making.

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Quiz Time 🎯