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📊 Measure of Central Tendency – Explained with Examples and Use Cases

In statistics, one of the foundational topics is the Measure of Central Tendency. These are statistical measures used to describe the center or average of a dataset. Understanding them is crucial for data analysis, research, and interpreting trends in real-world data.

There are three primary measures of central tendency:

• Mean – the arithmetic average
• Median – the middle value
• Mode – the most frequently occurring value

🔹 1. Mean (Arithmetic Average)

The mean is the sum of all data values divided by the number of values. It is commonly used in most statistical analyses but can be influenced by extreme values (outliers).

➤ Formulas:

• Population Mean (μ): μ = (∑ x_i) / N
• Sample Mean (x̄): x̄ = (∑ x_i) / n

➤ Example 1:

Dataset: 5, 7, 10, 13, 15

Mean = (5 + 7 + 10 + 13 + 15) / 5 = 50 / 5 = 10

➤ Example 2 (with Outlier):

Dataset: 5, 7, 10, 13, 90

Mean = (5 + 7 + 10 + 13 + 90) / 5 = 125 / 5 = 25

Here, the outlier (90) significantly distorts the average.

✅ Use Cases:

• Calculating average income, marks, prices, etc.
• Used in finance to determine average returns
• Helpful in quality control and performance tracking

🔹 2. Median (Middle Value)

The median is the value that lies in the middle of the dataset when arranged in ascending (or descending) order. It is not affected by outliers and is especially useful for skewed distributions.

➤ Steps to Find Median:

1. Sort the data in order
2. If count is odd → pick middle value
3. If count is even → average the two middle values

➤ Example 1 (Odd Count):

Dataset: 5, 7, 10, 13, 15

Sorted: 5, 7, 10, 13, 15

Median = 10

➤ Example 2 (Even Count):

Dataset: 5, 7, 10, 13

Median = (7 + 10) / 2 = 8.5

➤ Example 3 (With Outlier):

Dataset: 5, 7, 10, 13, 100

Median = 10 (still unaffected by the outlier)

✅ Use Cases:

• Analyzing property prices (real estate)
• Income distribution (e.g., median household income)
• Medical research: median survival times

🔹 3. Mode (Most Frequent Value)

The mode is the value that occurs most frequently in the dataset. A dataset can have one mode (unimodal), more than one mode (bimodal, multimodal), or no mode at all.

➤ Example 1:

Dataset: 4, 4, 6, 2, 4, 5, 2

Frequencies:

• 4 → 3 times
• 2 → 2 times
• 6, 5 → 1 time each

Mode = 4

➤ Example 2 (No Mode):

Dataset: 2, 3, 5, 6

All values appear once → No mode

➤ Example 3 (Multiple Modes):

Dataset: 1, 2, 2, 3, 3, 4

Mode = 2 and 3 (Bimodal)

✅ Use Cases:

• Fashion: most common shoe or clothing size
• Retail: best-selling product
• Surveys: most selected option in a poll

🧠 Summary Table

📌 Real-World Example: Housing Prices

Imagine analyzing house prices in a neighborhood:

Prices (in lakhs): 30, 32, 33, 34, 35, 36, 200

• Mean: (30 + 32 + 33 + 34 + 35 + 36 + 200) / 7 = 400 / 7 ≈ 57.1
• Median: 34
• Mode: No mode

Conclusion: Mean is skewed due to the luxury property (200L). Median gives a better idea of a “typical” house price here.

📌 When to Use Which Measure?

• Use Mean when the data is normally distributed (no outliers).
• Use Median for skewed distributions or when outliers exist.
• Use Mode for categorical data or finding the most common item.

📚 Conclusion

The measures of central tendency – mean, median, and mode – provide a way to summarize a dataset with a single value that represents the center. Each has its advantages depending on the type and shape of the data.

These concepts are not only foundational in statistics but also widely used in real-life decision-making – from economics and medicine to education and marketing.

Stay tuned! In the next part, we’ll explore Measures of Dispersion like Range, Variance, and Standard Deviation.

Thanks for reading!