Descriptive Statistics:
The Starting Point for Machine Learning—Mean, Median & Mode

What Are Descriptive Statistics?

Descriptive statistics are like a summary of a book. Imagine you have a giant dataset filled with numbers. Instead of analyzing every single number individually, descriptive statistics let you condense all that information into a few key takeaways.

Think of descriptive statistics as the answers to these questions:

• What is the typical value in the data?
• How spread out are the numbers?
• Are there any unusual numbers (outliers) in the dataset?

These tools don’t just organize data; they help us make decisions. For example, a sports coach might use descriptive statistics to figure out an average player’s performance, or a teacher might use it to understand how a class performed on a test.

Key Terms

• Mean (Average): Represents the typical value of your dataset.
• Median (Middle Value): The middle number in a sorted dataset.
• Mode (Most Frequent Value): The value that appears most often.

These concepts sound simple, but their real-world applications are profound. Let’s dive deeper into each one.

Mean: The Average Value

The mean is the first thing people think of when summarizing data. It’s the average—a single number that represents the entire dataset.

How to Calculate the Mean

To find the mean:

• Add up all the numbers in the dataset.
• Divide by the total number of values.

Real-World Example

Imagine your test scores over five exams are: 80, 85, 90, 75, and 95. To calculate the mean:

• Add : 80 + 85 + 90 + 75 + 95 = 425
• Divide : 425 ÷ 5 = 85

The mean score is 85. This tells you that, on average, you scored 85 on your tests.

Why the Mean Is Useful

The mean helps you understand the “typical” value of a dataset. If you’re a teacher, the mean class score can tell you how well students performed overall. If you’re a business owner, the mean monthly sales can help you track growth.

Limitations of the Mean

The mean can be misleading when there are outliers. Outliers are values that are much higher or lower than the rest of the data.

Example of Outliers: Imagine your test scores are: 80, 85, 90, 75, and 300. The mean becomes:

• Add : 80 + 85 + 90 + 75 + 300 = 630
• Divide : 630 ÷ 5 = 126

Does 126 represent your performance? Not really! That one outlier (300) skews the mean, making it higher than most of your scores.

Median: The Middle Value

The median is the middle number in a dataset when it’s sorted in order. Unlike the mean, the median isn’t affected by outliers, making it a more accurate representation of data in certain cases.

How to Calculate the Median

• Arrange the data in ascending order.
• Find the middle value.
  • If there’s an odd number of values, the median is the middle one.
  • If there’s an even number of values, the median is the average of the two middle numbers.

Real-World Example

Your daily spending over a week: 30, 40, 45, 50, 100.

• Arrange: 30, 40, 45, 50, 100
• Median = 45 (middle value)

If an outlier changes your spending to 30, 40, 45, 50, 1000, the median stays at 45. This stability makes the median useful when dealing with skewed data.

Why the Median Is Useful

The median is great for datasets with extreme values or skewed distributions, such as house prices. For example, if most houses in a neighbourhood cost $200,000 but one mansion costs $10 million, the median price gives a clearer picture of the typical home instead of the anomalies. If a family is planning to buy a house and they look at the mean, and it is very high they probably would not want to buy the house that’s where median comes into play. Median gives a clearer picture of the normal prices instead of the outliers.

Mode: The Most Frequent Value

The mode is the value that appears most often in a dataset. It’s especially useful for categorical data or finding trends.

How to Find the Mode

• Count how many times each value appears.
• The value with the highest count is the mode.

Real-World Example

Survey responses about favourite ice cream flavours: Vanilla, Chocolate, Chocolate, Strawberry, Vanilla, Chocolate.

Mode = Chocolate (appears 3 times).

Why the Mode Is Useful

The mode helps identify popularity or commonality. For instance, in marketing, knowing the most purchased product can guide inventory decisions, like which product do we stock up on.

Summary Each Concept

• Mean: Calculate by adding all numbers and dividing by the count. Useful for getting the "average" but can be skewed by outliers.
• Median: Found by arranging data and picking the middle value. Excellent for skewed data because it's not influenced by outliers.
• Mode: Identified by finding the most frequent data point. Great for understanding commonality or popularity in categorical data.

Conclusion

Descriptive statistics aren’t just numbers; they’re tools that help us make sense of data and the world around us. By understanding mean, median, mode, variance, and standard deviation, you can:

• Summarize data quickly.
• Identify patterns and outliers.
• Prepare data for deeper analysis in machine learning.

So, the next time you see a dataset, don’t just glance over it—ask yourself: What story is this data telling? With descriptive statistics, you have the power to find out.

Insights with Descriptive Statistics

Through mean, median, and mode, descriptive statistics allow us to quickly summarize data, identify patterns, and prepare for more complex analyses. These concepts aren't just tools for calculation; they offer us ways to view and interpret the vast amounts of data that inform decisions in fields ranging from education to economics.

You might be wondering why I've mentioned Variance and Standard Deviation towards the end. This is because these concepts are fundamental in descriptive statistics and are vital for machine learning and data analysis. Variance and Standard Deviation provide us with insights into the spread and variability of data, aspects that mean, median, and mode cannot capture alone.

If you feel you're falling behind in any of these areas or have a keen interest in learning machine learning, now is the time to act. Pydun Technology’s specialized training programs are designed to equip you with the skills and confidence to overcome obstacles and master complex concepts.

At Pydun, we believe the journey isn’t just about hard work—it’s about simplifying complexity, understanding the core principles, and connecting these concepts to real-world applications.

Stay tuned for the next blog where we will delve deeper into how Variance and Standard Deviation play a crucial role in understanding data spread and variability. This knowledge not only enhances our ability to summarize data but also helps in predicting and controlling future outcomes in complex data environments.