Percentile in Statistics: What is it and How to Calculate?

Statistics is the science of collecting, analyzing, interpreting, and presenting data to uncover patterns and draw meaningful conclusions. Within this field, the percentile is a fundamental measure that helps us understand the position of a value within a data distribution. When analyzing datasets, percentiles indicate the exact position of an observation relative to all other values.

Learning about percentiles gives you tools for data interpretation across many fields, from AI development to healthcare. Unlike means and standard deviations, percentiles work well with any data distribution, whether normal or skewed. This characteristic makes them particularly valuable in real-world applications, where data rarely adheres to ideal theoretical patterns. As data-driven decision-making becomes increasingly vital across industries, mastering percentiles has emerged as a significant skill for professionals and students alike.

Want to master this in-demand skill? This in-depth guide will help you learn about what is a percentile in statistics, how to calculate it, and the future trends.

1. What is a Percentile in Statistics?

Percentiles rank data points within a dataset to show their relative position. They tell us what percentage of values fall below a specific point. Further, they help us understand where any value stands compared to all others. Let us have a closer look at its definition with real-world applications:

Definition and Purpose

A percentile is a statistical measure that indicates the value below which a certain percentage of observations in a dataset fall. For instance, the 50th percentile (also known as the median) is the value at which 50% of the observations are lower and 50% are higher.

Percentiles serve several important purposes:

• Relative Standing: They provide a way to understand an individual's or an item's position relative to the rest of the dataset.
• Outlier Detection: They help identify outliers and unusual values that may warrant further investigation.
• Data Division: They create meaningful divisions within data, facilitating more nuanced analysis.
• Standardization: They allow for standardized testing and comparisons across different datasets.
• Statistical Foundation: They form the basis for many statistical methods and visualizations, enhancing data interpretation.

When calculating percentiles, we determine the value that marks the point below which x% of the data falls. This ranking method provides a clearer picture of data distribution than merely examining averages or ranges.

Also Read: What is the Difference Between Percentage and Percentile?

Real-World Examples in 2025

Percentiles are valuable tools across various professional fields, aiding experts in making informed, data-driven decisions:

• AI Model Evaluation

In AI, percentile rankings are used to compare performance metrics among competing systems. For example, a language model in the 95th percentile for reasoning tasks outperforms 95% of other models, indicating superior performance.

• Healthcare Applications

Healthcare providers utilize percentiles to create personalized treatment plans. For instance, blood pressure readings in the 80th percentile for your age group may require different actions compared to similar readings in another demographic.

• Educational Assessment

Universities employ percentiles to rank students for scholarship eligibility. A student in the 92nd percentile may qualify for financial aid programs that are unavailable to those below the 90th percentile cutoff.

• Investment Analysis

Investment firms analyze market returns through percentile rankings to assess risk profiles. Assets that perform in the top percentile during market downturns tend to attract risk-averse investors seeking stability.

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2. How to Calculate Percentiles in Statistics (2025 Updated Methods)

Calculating percentiles helps us understand where values stand within a dataset. Modern methods now account for larger datasets and varied data types. To start with the basics, you can refer to our Statistics Tutorial. Let's explore the step-by-step process to find percentiles accurately using current approaches.

Step 1: Organize and Sort Your Data

Before calculating any percentiles, we must prepare our data properly. This first step forms the foundation for all percentile calculations:

Data Cleaning

Start by checking your data for errors, missing values, and outliers. Data cleaning techniques ensure your percentile calculations reflect the true nature of your information rather than computational mistakes. Inspect your dataset for potential issues and identify and remove duplicate entries

• Handle missing values through:
  • Removal (if few in number)
  • Imputation (replacing with mean, median, or estimated values)
• Check for and address outliers that might skew your results

Data Sorting

Next, arrange all values in ascending order from smallest to largest. This sorting creates the ranked sequence necessary for percentile calculations. Sorting differs for different types of data: 

• For numerical data, sorting is straightforward
• For categorical data, establish a meaningful numerical representation
• Time-series data requires chronological arrangement before percentile analysis.

Example: Raw test scores: [87, 65, 93, 72, 81] Sorted scores: [65, 72, 81, 87, 93]

For large datasets (common in 2025), use computational tools rather than manual sorting. Statistical software packages and programming languages like Python and R offer efficient sorting algorithms that can handle millions of data points in seconds. To learn these programming languages from scratch, you can refer to our Python Tutorial and R Language Tutorial.

The quality of your percentile calculations depends on how well you execute this sorting step. A single misplaced value can alter your results, so double-check your sorted dataset before proceeding.

Step 2: Apply the Percentile Formula

To find a specific percentile, we need a formula that identifies the exact position within our sorted data. In 2025, statisticians may use various formula variations depending on the data structure and analysis goals.

Basic Percentile Formula:

Where:

• n = number of values in your dataset
• P = the desired percentile (e.g., 21 for the 21st percentile)

Example Calculation:

For a dataset with 20 points, the position for the 40th percentile would be:

Position = [(20 + 1) × 40] ÷ 100 = 8.4

This means the 40th percentile lies between the 8th and 9th values in your sorted dataset.

Weighted Percentiles in Data Analysis

In data analysis, not all data points are created equal. Sometimes, certain observations carry more significance than others due to their inherent importance, reliability, or context. This is where weighted percentiles become important and are useful in scenarios like:

• Economic studies where population subgroups have different representative weights
• Scientific research with varying sample reliability
• Financial analysis with unequal investment contributions
• Quality control, where some measurements are more critical than others

Methodology of Weighted Percentile Calculation

Here, we modify the approach to use cumulative frequency and weight summation rather than a simple positional formula. A more precise weighted percentile calculation follows these steps:

1. Order data by value and compute cumulative weights using the formula:

Where

represents the total cumulative weight.

• _Wk​ = Individual weights associated with each data point.
• S_n = The cumulative sum of weights up to the nth observation.
• C = A constant used for adjustment (commonly 0.5 for weighted median).
• p_n​ = The position of the nth-weighted percentile within the cumulative frequency distribution

2. Determine where the desired percentile falls within the cumulative distribution.

3. When the exact percentile does not align with a data point, linear interpolation helps:

• Estimate the value between known data points
• Provide a more accurate representation of the weighted distribution.

Also Read: Basic Fundamentals of Statistics for Data Science

Step 3: Handle Ties and Interpolation

In statistical analysis, data does not always fall into perfect and predictable patterns. Consider a situation where you are trying to find the 23rd percentile in a dataset. However, the exact position does not come under any specific data point. In situations like these, interpolation plays an important role in data analysis.

Linear interpolation helps find percentile values that fall between observations. It is a mathematical method used to estimate unknown values that lie between two known data points. It employs linear polynomials to create a straight line connecting these points, allowing for the calculation of intermediate values.

The formula is given as:

Percentile value = Lower value + [(Upper value - Lower value) × decimal portion of position]

or

Where:

•  X_L= value at the lower index
• X_H = value at the higher index
• d = decimal fraction of the computed position (if the position is 8.7, then d=0.7)

Example Calculation:

If your position calculation gives 8.7, take the 8th and 9th values in your dataset and find a point that is 70% of the way between them.

Handling Ties:

Several approaches exist for managing ties in your data:

• Empirical Cumulative Distribution Function (ECDF): Determines percentile positions based on cumulative proportions.
• Average Rank Method: Assigns average positions to all tied values.
• First Occurrence Method: Uses the first appearance of tied values.
• Random Tie-Breaking: Randomly ordered tied values (useful in simulations).

For large datasets with many ties, ECDF and frequency-weighted interpolation are effective methods. Specialized algorithms can efficiently handle ties by:

• Using Timsort (Python) and Quicksort Algorithm variants (R and NumPy) for fast sorting. You can consider our Sort in Python Tutorial to learn these advanced techniques.
• Applying streaming percentile estimation algorithms like P² or TDigest to approximate percentiles without requiring full dataset storage.
• Leveraging parallel processing techniques in cloud-based tools for real-time analytics.

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3. Percentile vs. Quartile vs. Decile: Key Differences

There are three statistical divisions to help us segment data in different ways. Percentiles split data into 100 equal parts, quartiles divide it into 4 parts, and deciles separate it into 10 sections. Each measure provides a different level of detail depending on your analysis needs and data size. Here is a detailed comparison of each statistical division:

When to Use Each Measure

It is important to know when to use percentiles, quartiles, or deciles to choose the right tool for your statistical analysis. Each measure serves specific purposes and offers different benefits:

Quartiles: For Basic Distribution Analysis

Quartiles divide data into four equal parts (25% each), making them ideal for understanding the overall spread and central tendency of your data. The second quartile (Q2) equals the median, while Q1 and Q3 help establish the interquartile range (IQR).  You can refer to our measures of central tendency tutorial to learn the basics of mean, median, and mode.

Use quartiles when you need:

• A quick overview of data distribution
• To calculate box plots for visual comparison
• To identify the middle 50% of your data
• To detect outliers using the IQR rule

Deciles: For Moderate Segmentation

Deciles split data into ten equal segments (10% each), offering more detail than quartiles while remaining manageable. They work well for medium-sized datasets when you need meaningful groupings.

Use deciles when you need:

• To divide populations into distinct groups
• More granularity than quartiles provide
• Less complexity than percentiles offer
• To create tier-based systems or categories

Percentiles: For Precise Positioning

Percentiles provide the most detailed division with 100 equal segments (1% each). They excel at pinpointing exact positions within large datasets.

Use percentiles when you need:

• Maximum precision in positioning
• To work with standardized test scores
• To analyze large datasets with subtle variations
• To find specific thresholds (like the 95th percentile)

The table below compares the three measures of statistics:

Practical Scenarios in 2025

The choice between percentiles, quartiles, and deciles affects real-world decision-making across many fields. Here are some current applications:

Customer Segmentation Using Deciles

Retail companies now segment their customer base using decile analysis to allocate marketing resources efficiently. By dividing customers into ten groups based on purchase frequency or total spending, companies identify which segments drive the most profit.

A large e-commerce platform might discover that its top decile (top 10%) of customers generates 60% of total revenue. This insight leads them to create specialized loyalty programs for this group. Meanwhile, they design different engagement strategies for the 5th and 6th deciles, which represent occasional shoppers with growth potential.

Deciles work well here because they create meaningful groups without excessive fragmentation. The ten resulting segments allow for targeted strategies without overwhelming the marketing team.

Income Analysis Using Quartiles 

Government agencies and economic researchers use quartiles to analyze income distribution across populations. Quartiles provide clear divisions that highlight economic inequality while remaining easy to communicate to the public.

For example, a 2025 economic report can show:

• Q1 (bottom 25%): Annual incomes below INR 3,50,000
• Q2 (25-50%): Annual incomes between INR 3,50,000 to INR 6,80,000
• Q3 (50-75%): Annual incomes between INR 6,80,000 to INR 12,00,000
• Q4 (top 25%): Annual incomes above INR 12,00,000

Policymakers use this quartile analysis to design tax brackets and social programs. The interquartile range (IQR) (the difference between Q3 and Q1) serves as a measure of economic inequality.

Academic Performance Using Percentiles

Educational institutions track student performance using percentiles to provide detailed insights about individual achievement. A student scoring in the 87th percentile has outperformed 87% of their peers on a standardized assessment.

Percentiles offer the precision needed for:

• Identifying students who need additional support (below the 20th percentile)
• Selecting candidates for advanced programs (above the 95th percentile)
• Measuring improvement over time (movement across percentile rankings)
• Comparing performance across different subject areas

With large student populations, percentiles reveal subtle differences that quartiles or deciles might miss.

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4. Common Applications of Percentiles in Statistics

Percentiles now play a central role in numerous fields, helping professionals make sense of complex data. From healthcare to finance, education to technology, percentiles provide a standardized way to compare values within large datasets. They help make informed decisions based on relative positioning. Here are the common applications of percentiles in statistics in 2025:

AI and Machine Learning

AI systems rely on percentile measurements to evaluate and enhance their performance. Machine learning models generate vast amounts of data that require context to become meaningful, and percentiles provide this framework. Percentile in statistics performs the following role in the development of AI and Machine Learning models:

Performance Evaluation

When data scientists develop new machine learning models, they need effective ways to compare their performance against existing solutions. Percentiles in statistics in machine learning offer a clear benchmark for this comparison.

• Example: Consider a new image recognition model tested on a dataset of 10,000 images. If it correctly identifies objects in 9,500 images, it falls in the 95th percentile of accuracy compared to other models. This indicates that it outperforms 95% of the models evaluated.

Model Training

Model training also benefits from percentile analysis. During the training process, AI systems track their accuracy improvements over time. A common approach involves monitoring the 50th percentile (median) performance as a baseline while tracking the 95th percentile as a stretch goal. This dual-percentile approach helps teams understand both typical and best-case performance scenarios.

Outlier Detection

In AI, percentiles are important for identifying unusual patterns through outlier detection. Many anomaly detection algorithms flag data points that fall beyond the 99th percentile as potential issues requiring human review. This application is particularly valuable in fraud detection, where unusual transactions demand immediate attention.

Fairness Metrics

Fairness metrics in AI and evaluation metrics in machine learning rely on percentiles to ensure models treat all demographic groups equally. Researchers compare the 10th, 50th, and 90th percentiles of prediction accuracy across different demographic groups to identify potential bias. If one group consistently shows lower percentile scores, adjustments may be necessary to improve fairness and ensure equitable treatment across populations.

Natural Language Processing

In natural language processing (NLP), percentiles help measure response quality. When AI systems generate text, evaluators might rank responses based on relevance, accuracy, and coherence. Responses in the top percentiles can serve as templates for future improvements, while those in lower percentiles highlight areas needing refinement.

Healthcare Analytics

Healthcare providers use percentiles as important tools in patient assessment and medical decision-making. Growth charts represent one of the most widespread applications, where doctors plot children's measurements against percentile curves to monitor development. Percentile in statistics enhances healthcare analytics with:

Pediatric Development Tracking

When a pediatrician measures a child's height, weight, and head circumference, they compare these values to percentile charts based on thousands of children. 

• Example: A child at the 75th percentile for weight weighs more than 75% of children of the same age and gender. This comparison helps doctors identify growth patterns that may require attention. A child whose weight drops from the 50th to the 5th percentile between visits signals potential health concerns.

Cardiovascular Risk Assessment

Percentiles guide risk assessment across medical specialties. Cardiologists evaluate heart disease risk by comparing patients' cholesterol levels to age-matched percentile ranges.

• Example: A patient with LDL cholesterol in the 90th percentile faces higher cardiovascular risk than those in lower percentiles, which may influence treatment decisions.

Hospital Performance Optimization

Hospital systems now use percentile analysis to improve care quality. By tracking patient outcomes like recovery time and complication rates, hospitals identify which units perform in top percentiles. These high-performing units then share their practices with others to raise overall care standards.

Medical Research

Medical researchers rely on percentiles when analyzing clinical trial results. Instead of focusing only on average responses to treatments, they examine how drugs affect patients across different percentile ranges. 

• Example: A medication can show strong benefits for patients in the 75th–90th percentile of disease severity but minimal effect for those in lower percentiles. This leads to more targeted prescribing guidelines.

Financial Risk Analysis

Financial institutions depend on percentiles to manage risk and make investment decisions. In this field, percentiles provide a structured way to understand uncertainty and prepare for various market conditions. Percentile in statistics helps with financial risk analysis in the following ways:

Value at Risk (VaR) Calculations

Value at Risk (VaR), a fundamental risk metric, uses percentiles to express potential losses. Regulators require financial institutions to maintain capital reserves based on these percentile calculations to ensure stability during market downturns.

• Example: A 95% VaR of ₹83 crore means there is only a 5% chance of losing more than this amount in a given timeframe. Banks calculate this by ranking possible loss scenarios and identifying the 95th percentile value.

Stress Testing 

Stress testing, now mandatory for major banks, relies on percentile analysis. Institutions model how their portfolios would perform under extreme market conditions, defined as events beyond the 99th percentile of historical market moves.

Credit Scoring Models

Credit scoring models incorporate percentile rank to assess borrower risk. Lenders compare applicants to percentile distributions of similar borrowers, with those scoring above the 80th percentile receiving the best interest rates. This approach allows for more nuanced risk assessment than simple approval/denial decisions.

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5. Challenges and Misconceptions in Understanding Percentiles

People often misunderstand percentiles, which leads to incorrect data interpretation and flawed decisions. These misunderstandings stem from confusion about what percentiles truly measure and how they relate to the underlying data distribution.

Misinterpreting Percentile Ranks

One common mistake involves confusing percentile ranks with percentage scores. A student in the 90th percentile did not answer 90% of questions correctly. Instead, this student performed better than 90% of all test-takers, regardless of their score.

Consider a difficult exam where the highest score was 75%. A student who scored 70% might still rank in the 95th percentile because they performed better than 95% of their peers. Their percentile rank reflects their relative position, not their absolute achievement.

Another misconception appears when people assume percentiles represent equal intervals. The difference between the 10th and 20th percentiles may represent a smaller absolute change than the difference between the 80th and 90th percentiles. This happens because data often clusters around the middle and spreads out at the extremes.

Handling Skewed Data Distributions

A skewed data distribution occurs when the data points are not evenly distributed around the center. Instead, most values cluster at one end of the range, while fewer values stretch out in the opposite direction, creating what statisticians call a "tail." You can refer to our Range in Statistics tutorial to learn more about data distribution. 

In these cases, standard percentile calculations can mislead. The 50th percentile (median) provides a more accurate measure of central tendency than the mean in skewed distributions, as it resists the pull of extreme values.

Outliers in data mining (values far from most observations) can affect percentile interpretations. A single billionaire in a dataset of wage earners pushes all high percentiles upward. Statisticians address this by using trimmed percentiles, which exclude the most extreme values before calculation.

Winsorization is a method used to handle skewed data by capping extreme values. Instead of removing outliers, it limits them to a set threshold. This keeps the overall structure intact while preventing extreme points from distorting analysis. By doing so, the data remains more balanced, and meaningful patterns stay visible.

Log transformations offer another approach for highly skewed data. By converting values to a logarithmic scale before calculating percentiles, analysts can compress the range of large values while stretching the range of small values. This creates a more balanced distribution for percentile analysis.

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6. Future Trends in Percentile Analysis (2025 and Beyond)

Percentile use in statistics continues to advance as data volumes grow and computational methods improve. New approaches now make percentiles more accessible and meaningful across diverse fields. The integration of automated tools, ethical frameworks, and advanced visualization techniques reshapes how we understand and use percentiles in decision-making.

Automation in Percentile Calculations

Automated systems now handle percentile calculations with unprecedented speed and accuracy. These tools process massive datasets in real-time, turning raw numbers into information without human intervention. Percentile in statistics uses automation in the following ways:

Smart Analytics and Market Responsiveness

Smart analytics platforms now monitor percentile shifts automatically. This automation helps businesses respond quickly to changing market conditions without constant manual analysis

• Example: An e-commerce system tracks product performance by percentile rank, sending alerts when items drop below the 25th percentile in sales.

Multi-Dimensional Performance Insights

AI-powered dashboards calculate percentiles across multiple dimensions simultaneously. A marketing team can view customer engagement metrics by age group, location, and purchase history all at once. These percentile rankings are updated as new data arrives. This multi-dimensional view helps identify patterns that remain hidden in simpler analyses.

Edge Computing and IoT Integration

Edge computing brings percentile calculations closer to data sources. IoT devices now perform basic percentile calculations before sending data to central servers, reducing bandwidth needs and enabling faster response times. A manufacturing plant can use this approach to monitor equipment performance, with sensors calculating real-time percentile rankings for temperature, vibration, and pressure.

Anomaly Detection

Automated anomaly detection depends on percentile thresholds. Systems continuously monitor data streams, flagging values that fall outside established percentile ranges for review. This approach helps organizations identify potential issues before they become serious problems, from network security threats to quality control failures.

Ethical Implications in Data Ranking

As percentiles gain prominence in decision-making, their ethical implications receive increasing attention. Organizations must consider how percentile rankings affect individuals and whether these rankings introduce or reinforce biases. The ethical challenges due to data ranking with percentile are:

Fairness in Hiring Practices

Hiring processes come under scrutiny when they rely on percentile cutoffs. Consider if companies reject candidates below the 80th percentile on standardized assessments. They may exclude qualified individuals who possess skills that do not align with testing formats. This raises questions about fairness and diversity in the workplace, as certain demographic groups may perform differently on these tests due to cultural or educational factors.

Economic Inclusion and Lending

Lending decisions based on percentile rankings can perpetuate economic disparities. Consider if loan approvals go only to applicants above the 70th percentile for credit scores. This practice forces individuals from communities with limited access to banking services to face continued exclusion. Some financial institutions supplement percentile-based credit assessments with alternative data sources to create more inclusive lending practices.

Equity Challenge in Education

Education systems struggle with equity issues in percentile-based advancement. When program admission or grade promotion relies on percentile rankings, students with fewer educational resources may face systematic disadvantages. Some schools now use growth percentiles that measure individual improvement rather than absolute standing to address these concerns.

Privacy and Data Protection

Privacy concerns emerge as percentile analyses become more granular. When companies rank customers by multiple behavioral metrics, the resulting profiles can reveal sensitive personal information. Data protection frameworks now limit how organizations can use percentile rankings, especially in contexts where rankings might lead to discrimination or exploitation.

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7. How upGrad Can Help You Learn Statistics

upGrad offers structured statistics education programs designed for working professionals and students alike. These programs combine theoretical knowledge with practical applications, helping you master statistical concepts, including percentiles and their calculations. The courses adapt to your learning pace while providing rigorous training that meets industry standards.

Industry-Aligned Certification Programs

upGrad's data science certification programs address the growing demand for statistical analysis-driven decision-makers across industries. These programs focus on practical skills that employers value. upGrad’s certification programs feature:

• A curriculum designed in partnership with industry experts from companies like Microsoft and Amazon
• Regular updates to reflect current industry practices and emerging statistical methods
• Assignments and Data Analytics projects that mirror real workplace challenges
• Industry-recognized credentials that demonstrate your statistical proficiency to employers
• Dedicated modules on ethical considerations in statistical analysis

The table below lists the top data science courses by upGrad:

Mentorship and Networking Opportunities

upGrad pairs you with experienced statistics and data professionals who provide personalized guidance throughout your learning journey. These mentors help you navigate complex statistical concepts and apply them to your specific field of interest.

Your mentor will schedule regular one-on-one sessions to review your progress. They answer questions about challenging topics like percentile calculations for skewed distributions and provide feedback on your project work. The mentorship program also includes salary negotiation coaching, helping you leverage your new statistical skills for career advancement.

The upGrad alumni network connects you with professionals across countries. This global community offers invaluable networking opportunities through virtual events, discussion forums, and local meetups.

Industry expert webinars feature statisticians from leading organizations who share insights about applying statistical methods in their work. These sessions often include Q&A opportunities where you can ask about applications of percentiles and other statistical tools in business contexts.

Career Transition Support

upGrad's placement support helps you translate your statistical knowledge into career success. It guides you through every step of your professional development. Resume-building workshops teach you how to highlight your statistical skills effectively. Career counselors help you showcase your project work with percentiles and other statistical analyses, demonstrating your ability to derive insights from complex data. These sessions include one-on-one resume reviews and personalized feedback to ensure your application materials stand out.

Interview preparation services include mock interviews with industry professionals who ask statistical questions encountered in data-related job interviews. You will practice concepts like percentiles, outlier detection, and hypothesis testing in clear, accessible language that shows your deep understanding.

upGrad maintains placement partnerships with over 1,400+ companies across various industries. These partner companies recruit from upGrad's talent pool, giving you access to exclusive job opportunities.

Wrapping Up

Percentile in statistics is one of the most practical and accessible tools for understanding data distributions. Its application spans numerous fields, from healthcare monitoring to educational assessment and financial analysis to quality control. The strength of percentiles lies in their flexibility. They work effectively with normal distributions, skewed datasets, and even multimodal information. This makes them reliable tools regardless of your data's structure.

When communicating statistical findings to non-specialists, percentiles provide intuitive frameworks that bridge technical analysis and practical understanding. As data volumes grow and analytics become more integrated into daily operations, the importance of percentiles will only increase. By mastering percentiles in statistics, you gain valuable skills that enhance your ability to extract meaningful insights from data.

Confused about how to start your career in data analytics? Talk to upGrad’s team of experts and career counselors for a one-on-one session for the best guidance.

Explore our free certification courses in data science:

• Introduction to Database Design with MySQL course
• Advanced SQL: Functions and Formulas Course
• Analyzing Patterns in Data and Storytelling Course
• Linear Algebra for Analysis Course

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