📊 Descriptive Statistics Explained Simply | Mean, Median & Std Dev

Part 3: Statistics for Data Science Series

Goal: Learn how to summarize data effectively before analysis

When working with data, the first and most important question is:

👉 “What does this data look like?”

This is where Descriptive Statistics comes in.

Descriptive statistics help us summarize, understand, and interpret data using simple numerical measures. Before any machine learning, prediction, or dashboarding — descriptive stats are your foundation.

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📌 What is Descriptive Statistics?

Descriptive statistics are techniques used to summarize and describe the main features of a dataset.

They help answer questions like:

• What is the average value?
• How spread out is the data?
• Are there extreme values?
• Where does most of the data lie?

👉 Unlike inferential statistics, descriptive statistics do not make predictions — they explain what already exists.

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📈 Measures of Central Tendency (Finding the “Center”)

1️⃣ Mean (Average)

Definition:
The sum of all values divided by the total number of values.

Formula:
Mean = (Sum of values) / (Number of values)

📌 Real-Life Example:
Average daily sales of an e-commerce store over 5 days:
₹10k, ₹12k, ₹11k, ₹13k, ₹14k

Mean = ₹12k

🟢 Best used when data has no extreme outliers

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2️⃣ Median (Middle Value)

Definition:
The middle value when data is sorted.

📌 Example:
Monthly salaries in a startup:
₹25k, ₹30k, ₹35k, ₹40k, ₹5,00,000

Median = ₹35k

🟢 Best used when data contains outliers

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3️⃣ Mode (Most Frequent Value)

Definition:
The value that appears most often.

📌 Example:
Most sold product sizes:
M, M, L, S, M, L

Mode = M

🟢 Useful for categorical data

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📊 Measures of Dispersion (Understanding Spread)

4️⃣ Range

Definition:
Difference between the maximum and minimum values.

📌 Example:
City temperature range:
Min = 20°C, Max = 45°C

Range = 25°C

⚠️ Highly sensitive to outliers

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5️⃣ Variance

Definition:
Average of squared differences from the mean.

• Low variance → values are close together
• High variance → values are spread out

🟢 Widely used in finance and risk analysis

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6️⃣ Standard Deviation

Definition:
Square root of variance.

📌 Example:
Stocks with high standard deviation are more volatile.

🟢 Most important dispersion metric
🟢 Same unit as original data

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📐 Percentiles & Interquartile Range (IQR)

7️⃣ Percentiles

Definition:
A percentile shows the value below which a certain percentage of data falls.

📌 Example:
90th percentile salary = ₹20 LPA
You earn more than 90% of employees.

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8️⃣ Interquartile Range (IQR)

Formula:
IQR = Q3 − Q1

Why it matters:

• Identifies outliers
• Used in box plots
• Robust against extreme values

📌 Real Scenario:
Detecting abnormal insurance claims or fraud transactions.

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🧠 Summary Statistics in Python (Hands-On)

Pandas is the most widely used Python library for descriptive statistics.

🔹 Sample Dataset

import pandas as pd

data = {
    "Sales": [12000, 15000, 10000, 18000, 16000],
    "Profit": [2000, 3000, 1500, 4000, 3500]
}

df = pd.DataFrame(data)

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🔹 Using Pandas .describe()

df.describe()

.describe() instantly provides:

• Count
• Mean
• Standard Deviation
• Minimum & Maximum
• 25%, 50% (Median), 75% percentiles

🟢 Used in almost every real-world data analysis project

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🔹 Individual Statistics in Pandas

df.mean()
df.median()
df.std()
df.var()
df.quantile(0.75)

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🏢 Real-World Applications

📌 Business

• Average revenue per customer
• Monthly sales analysis
• Customer behavior tracking

📌 Finance

• Stock volatility measurement
• Risk evaluation
• Portfolio performance

📌 Healthcare

• Patient recovery analysis
• Hospital stay durations
• Disease statistics

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🚀 Key Takeaways

• Descriptive statistics summarize data
• Mean, median, mode explain central tendency
• Standard deviation explains variability
• Percentiles & IQR handle outliers
• Pandas .describe() is essential for EDA

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🔜 What’s Next?

Part 4: Data Visualization for Statistics

• Histograms
• Box plots
• Bar charts
• Python visualizations

Statistics isn’t hard — it’s just misunderstood. Keep learning! 🚀

❓ Frequently Asked Questions (FAQ)

What is descriptive statistics?

Descriptive statistics is a branch of statistics that summarizes and describes the main characteristics of a dataset using measures like mean, median, mode, variance, and standard deviation.

Why is descriptive statistics important in data science?

Descriptive statistics helps data scientists understand data distribution, identify patterns, detect outliers, and prepare datasets for further analysis and machine learning models.

What is the difference between mean and median?

The mean is the average of all values, while the median is the middle value when data is sorted. Median is more reliable when the dataset contains outliers.

When should I use standard deviation?

Standard deviation is used to measure how spread out values are from the mean. It is commonly used in finance, business analytics, and risk assessment.

What is Pandas describe() used for?

The describe() function in Pandas provides a quick summary of key descriptive statistics including count, mean, standard deviation, minimum, maximum, and percentiles.

Is descriptive statistics enough for data analysis?

Descriptive statistics is the first step in data analysis. For predictions and conclusions about future data, inferential statistics and machine learning techniques are required.

📊 Types of Data & Data Collection Methods in Data Science (Part 2)

Understanding data is the first and most important step in data science.

Before analysis, modeling, or machine learning, a data scientist must know what type of data they are working with and how it was collected.

In Part 2 of our Statistics for Data Science series, you’ll learn:

• Different types of data used in data science
• How data is collected in real-world projects
• Sampling methods and their importance
• Hands-on examples to classify datasets

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🎯 Goal of This Post

Understand your data before analyzing it.

Incorrect data understanding leads to:

• Wrong statistical methods
• Poor model performance
• Misleading insights

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📌 Types of Data in Data Science

Data can be classified in multiple ways depending on its nature and usage.

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🔹 Qualitative vs Quantitative Data

📘 Qualitative Data (Categorical Data)

Qualitative data describes qualities or characteristics and is non-numeric.

Examples:

• Gender (Male/Female)
• Product category
• Customer feedback (Good, Bad, Average)
• City names

📌 Used for:

• Classification
• Sentiment analysis
• Grouping and segmentation

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📗 Quantitative Data (Numerical Data)

Quantitative data represents numbers and measurable values.

Examples:

• Age
• Salary
• Temperature
• Number of purchases

📌 Used for:

• Statistical calculations
• Regression models
• Forecasting

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🔹 Discrete vs Continuous Data

📘 Discrete Data

Discrete data consists of countable values.

Examples:

• Number of customers
• Number of defects
• Number of website visits

📌 Values are whole numbers.

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📗 Continuous Data

Continuous data can take any value within a range.

Examples:

• Height
• Weight
• Time
• Temperature

📌 Can have decimal values.

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🔹 Structured vs Unstructured Data

📘 Structured Data

Structured data is organized in rows and columns.

Examples:

• Excel files
• SQL tables
• CSV datasets

📌 Easy to analyze using SQL, Excel, Python, or BI tools.

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📗 Unstructured Data

Unstructured data has no predefined format.

Examples:

• Text documents
• Emails
• Images
• Videos

• Social media posts

📌 Requires advanced processing (NLP, Computer Vision).

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📌 Data Collection Methods in Data Science

Understanding how data is collected helps assess data quality and bias.

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🔹 Common Data Collection Techniques

1️⃣ Surveys & Questionnaires

• Online forms
• Feedback surveys
• Market research

📌 Risk: Response bias

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2️⃣ Observational Data

• Website click tracking
• User behavior logs
• Sensor data

📌 Real-time and unbiased

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3️⃣ Experiments (A/B Testing)

• Marketing experiments
• Product feature testing

📌 Controlled and reliable

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4️⃣ Transactional Data

• Sales records
• Banking transactions
• E-commerce logs

📌 Highly structured and reliable

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5️⃣ Third-Party Data

• Government datasets
• APIs
• External vendors

📌 Verify credibility and freshness

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📌 Sampling Methods in Statistics

Sampling allows us to study a subset of data instead of the entire population.

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🔹 Types of Sampling Methods

📘 Random Sampling

• Every unit has equal chance
• Reduces bias

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📘 Stratified Sampling

• Population divided into groups (strata)
• Sample taken from each group

📌 Used in surveys and finance

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📘 Systematic Sampling

• Every nth observation selected

📌 Simple and efficient

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📘 Convenience Sampling

• Easily available data

📌 Risk: High bias

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📌 Why Sampling Matters in Data Science

• Saves time and cost
• Makes large datasets manageable
• Enables faster experimentation
• Supports inferential statistics

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🧪 Hands-On: Classify Sample Datasets

Let’s classify real-world datasets.

Dataset	Qualitative / Quantitative	Discrete / Continuous	Structured / Unstructured
Customer Gender	Qualitative	Discrete	Structured
Monthly Salary	Quantitative	Continuous	Structured
Product Reviews	Qualitative	N/A	Unstructured
Number of Orders	Quantitative	Discrete	Structured
Website Session Time	Quantitative	Continuous	Structured

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🧠 Key Takeaways

✔ Always identify data type before analysis
✔ Choose statistical methods based on data nature
✔ Understand data collection to avoid bias
✔ Sampling impacts accuracy and conclusions

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🔗 What’s Next in This Series?

👉 Part 3: Descriptive Statistics – Mean, Median, Mode & Variability