Popular Searches
Popular Course Categories
Popular Courses

Cleaning Data and Handling Missing or Duplicate Values

Cleaning Data and Handling Missing or Duplicate Values

Python Data Analysis and Visualization

Cleaning Data and Handling Missing or Duplicate Values in Python

Course: Python Training

Topic: Cleaning Data and Handling Missing or Duplicate Values

Course Link: Python Training Course

Demo Link: Register for a Free Course Demo

Official Website: JustAcademy


1. Introduction to Data Cleaning

Data cleaning is the process of identifying and correcting inaccurate, incomplete, inconsistent, duplicated, or incorrectly formatted data. It is an important step in data analysis, machine learning, reporting, and application development.

Real-world datasets often contain empty cells, repeated records, inconsistent text, invalid values, and unexpected data types. If these problems are not handled properly, they can lead to incorrect calculations, misleading visualizations, and unreliable machine learning models.

Python provides useful tools for cleaning data. The pandas library is particularly valuable because it offers functions for detecting missing values, removing duplicates, replacing incorrect entries, and transforming columns into appropriate data types.

Why Is Data Cleaning Important?

  • Improves the accuracy and reliability of analysis.
  • Prevents duplicate records from inflating totals and counts.
  • Helps handle incomplete datasets consistently.
  • Reduces errors during statistical analysis and machine learning.
  • Makes data easier to understand, maintain, and visualize.
  • Improves the quality of reports and business decisions.

2. Common Data Quality Problems

Problem Description Example
Missing values Required information is unavailable. A customer record has no email address.
Duplicate records The same record appears more than once. The same order is stored twice.
Inconsistent formatting Values use different formats. "Mumbai", "mumbai", and " MUMBAI ".
Incorrect data types A value is stored using an unsuitable type. A price column contains numeric strings.
Invalid values Values violate expected rules. A person's age is -5.
Inconsistent missing markers Missing information uses different representations. Empty strings, "N/A", and "unknown".
Outliers Values are unusually far from the expected range. A product price is recorded as 9999999 by mistake.

3. Introduction to pandas for Data Cleaning

Pandas is a Python library used for data manipulation and analysis. It provides two main data structures:

  • Series: A one-dimensional labeled collection of values.
  • DataFrame: A two-dimensional table with rows and columns.

Install pandas if it is not already available in your Python environment:

pip install pandas

Import pandas and create a sample DataFrame:

import pandas as pd

data = {
    "Name": ["Aarav", "Diya", "Kabir", None, "Diya"],
    "Age": [25, 30, None, 28, 30],
    "City": ["Mumbai", "Pune", "Mumbai", "Delhi", "Pune"],
    "Salary": [45000, 60000, 52000, None, 60000]
}

df = pd.DataFrame(data)

print(df)

This dataset contains missing values and repeated information. It will be used throughout the examples in these notes.

4. Inspecting a Dataset Before Cleaning

Before changing data, examine its structure and quality. Understanding the dataset helps you choose suitable cleaning operations without accidentally deleting useful information.

4.1 Display the First and Last Rows

print(df.head())
print(df.tail())

head() displays the first five rows by default, while tail() displays the last five. You can specify the number of rows, such as df.head(10).

4.2 Check the Dataset Shape

print(df.shape)

The result is a tuple containing the number of rows and columns. For example, (5, 4) represents five rows and four columns.

4.3 Inspect Column Names and Data Types

print(df.columns)
print(df.dtypes)
df.info()

Use these commands to identify incorrect data types, unexpected column names, and columns with missing values.

4.4 Generate Summary Statistics

print(df.describe())
print(df.describe(include="all"))

The first statement summarizes numeric columns by default. The second includes descriptive information for other column types where applicable.

5. Understanding Missing Values

A missing value represents information that is not available in a dataset. Pandas commonly represents missing values with NaN, None, or its dedicated pd.NA marker, depending on the column's data type.

5.1 Common Causes of Missing Values

  • A user did not provide a value in a form.
  • A sensor or system failed to record a measurement.
  • Data was lost during importing or merging files.
  • A value does not apply to a particular record.
  • A source system stores incomplete information.

5.2 Missing Values Are Not Always Errors

A missing value may indicate a genuine absence of information rather than a mistake. For example, a customer without a second phone number may be perfectly valid. Before filling or deleting missing values, understand what they mean in the context of the dataset.

6. Detecting Missing Values

6.1 Using isna() and isnull()

Both isna() and isnull() identify missing values in pandas.

print(df.isna())
print(df.isnull())

These methods return a Boolean DataFrame: True indicates a missing value, and False indicates a non-missing value.

6.2 Count Missing Values in Each Column

missing_counts = df.isna().sum()
print(missing_counts)

The sum() method counts the True values in each column, helping you identify columns that need attention.

6.3 Calculate Missing Value Percentages

missing_percentage = (df.isna().mean() * 100).round(2)
print(missing_percentage)

This calculation shows the percentage of missing values in each column. It is useful when deciding whether a column can be retained, filled, or removed.

6.4 Find Rows Containing Missing Values

rows_with_missing = df[df.isna().any(axis=1)]
print(rows_with_missing)

The expression any(axis=1) checks each row and returns True if at least one column is missing a value.

6.5 Find Rows Without Missing Values

complete_rows = df[df.notna().all(axis=1)]
print(complete_rows)

The expression all(axis=1) selects rows in which every column contains a non-missing value.

7. Removing Missing Values with dropna()

The dropna() method removes rows or columns containing missing values. It should be used carefully because removing records may discard valuable information or introduce bias.

7.1 Remove Rows with Any Missing Value

clean_df = df.dropna()
print(clean_df)

By default, dropna() removes every row that contains at least one missing value. The original DataFrame remains unchanged unless you assign the result back or use an appropriate in-place operation.

7.2 Remove Rows Only When All Values Are Missing

clean_df = df.dropna(how="all")

The how="all" option removes a row only if all its values are missing.

7.3 Remove Rows Based on Selected Columns

clean_df = df.dropna(subset=["Name", "Age"])

This removes rows where either Name or Age is missing. Missing values in other columns do not determine whether the row is removed.

7.4 Remove Columns with Missing Values

clean_df = df.dropna(axis=1)

Using axis=1 removes columns containing missing values. This can be useful for small, unreliable columns but may discard important features.

7.5 Require a Minimum Number of Non-Missing Values

clean_df = df.dropna(thresh=3)

The thresh=3 argument retains rows containing at least three non-missing values. This allows partially complete rows to remain in the dataset.

8. Filling Missing Values with fillna()

Instead of deleting incomplete records, you can replace missing values with suitable alternatives. The correct strategy depends on the meaning of the column and the reason values are missing.

8.1 Fill Missing Values with a Fixed Value

filled_df = df.fillna(0)

This replaces missing values throughout the DataFrame with zero. However, zero is not a suitable replacement for every column. For example, a missing person's age should not automatically become zero.

8.2 Fill Missing Values in a Specific Column

df["City"] = df["City"].fillna("Unknown")
print(df)

Replacing missing categorical values with a label such as "Unknown" can preserve the fact that the original information was unavailable.

8.3 Fill Numeric Values with the Mean

mean_age = df["Age"].mean()
df["Age"] = df["Age"].fillna(mean_age)

The mean is the arithmetic average. It can be appropriate for reasonably symmetric numeric distributions without extreme outliers. It is sensitive to unusually large or small values.

8.4 Fill Numeric Values with the Median

median_salary = df["Salary"].median()
df["Salary"] = df["Salary"].fillna(median_salary)

The median is the middle value when observations are sorted. It is often more robust than the mean when numeric data contains outliers or has a skewed distribution.

8.5 Fill Categorical Values with the Mode

mode_city = df["City"].mode()

if not mode_city.empty:
    df["City"] = df["City"].fillna(mode_city.iloc[0])

The mode is the most frequently occurring value. It is often used for categorical columns, but it may overrepresent the most common category. If no meaningful mode exists, consider an explicit missing category instead.

8.6 Fill Different Columns with Different Values

df = df.fillna({
    "Name": "Unknown",
    "Age": df["Age"].median(),
    "City": "Unknown",
    "Salary": df["Salary"].median()
})

This approach allows each column to use a replacement suited to its data type and meaning.

9. Forward Fill and Backward Fill

Forward fill and backward fill use neighboring values to fill missing entries. They are especially useful for ordered or time-series data when carrying nearby observations forward or backward is logically justified.

9.1 Forward Fill

df["Temperature"] = df["Temperature"].ffill()

Forward fill uses the previous non-missing value. For example, if a temperature reading is missing at 10:05, the previous available reading may be used when appropriate.

9.2 Backward Fill

df["Temperature"] = df["Temperature"].bfill()

Backward fill uses the next non-missing value. This can be useful for some historical records, but it can introduce future information into predictive datasets if applied carelessly.

9.3 Limit the Number of Consecutive Values Filled

df["Temperature"] = df["Temperature"].ffill(limit=2)

The limit restricts forward filling to at most two consecutive missing entries per uninterrupted run. Always sort time-series data by its time column before using these methods.

10. Interpolation for Numeric Data

Interpolation estimates missing numeric values from surrounding observations. It can be useful for continuous measurements that change gradually, such as temperature or sensor readings.

df["Temperature"] = df["Temperature"].interpolate(method="linear")

Linear interpolation estimates a missing value based on the values before and after it. The method should only be used when the data structure and assumptions justify it.

For time-series data, interpolation can also use time information when the index is a suitable datetime index:

df = df.sort_index()
df["Temperature"] = df["Temperature"].interpolate(method="time")

Interpolation does not automatically make a dataset correct. Check whether the estimated values are realistic and whether the method is suitable for the domain.

11. Handling Special Missing-Value Markers

Some datasets represent missing information using strings such as "N/A", "NA", "null", "None", or empty text. These may not automatically be recognized as missing values in every import or data-processing workflow.

11.1 Replace Known Markers with Missing Values

import pandas as pd

df = df.replace(
    ["N/A", "NA", "null", "None", ""],
    pd.NA
)

Only replace strings that genuinely represent missing information in your dataset. For example, the text "None" may be a legitimate category in a particular application.

11.2 Remove Leading and Trailing Whitespace

df["City"] = df["City"].str.strip()

Whitespace can cause values that appear identical to be treated as different strings. For example, "Mumbai" and " Mumbai " are different before cleaning.

11.3 Normalize Text Case

df["City"] = df["City"].str.strip().str.title()

This produces consistent title casing for many city names. Be careful with abbreviations, brand names, and languages where title casing may not be appropriate.

12. Detecting Duplicate Records

A duplicate occurs when a row or a selected set of column values repeats. Duplicates can result from repeated imports, data-entry mistakes, merging files, or systems that submit the same record multiple times.

Not every repeated value is a duplicate. Two customers may share the same city, and two products may have the same price. Duplicate detection should reflect the business meaning of the record.

12.1 Identify Duplicate Rows

duplicate_rows = df.duplicated()
print(duplicate_rows)

The duplicated() method returns a Boolean Series. By default, the first occurrence of a row is marked False, while later identical occurrences are marked True.

12.2 Count Duplicate Rows

duplicate_count = df.duplicated().sum()
print("Duplicate rows:", duplicate_count)

12.3 Display Duplicate Rows

duplicates = df[df.duplicated(keep=False)]
print(duplicates)

The keep=False option marks every member of a duplicated group as a duplicate, including its first occurrence. This is useful when investigating all records involved.

12.4 Find Duplicates Based on Specific Columns

duplicate_emails = df[df.duplicated(subset=["Email"], keep=False)]
print(duplicate_emails)

Here, records are considered duplicates when their email values match, even if other columns differ. Choose the subset according to a reliable identifier or a business rule.

13. Removing Duplicate Records with drop_duplicates()

The drop_duplicates() method removes repeated rows or repeated combinations of selected column values.

13.1 Remove Entirely Identical Rows

clean_df = df.drop_duplicates()
print(clean_df)

By default, pandas retains the first occurrence of an identical row and removes later occurrences.

13.2 Keep the Last Occurrence

clean_df = df.drop_duplicates(keep="last")

This retains the last occurrence of each duplicated record. It can be useful when the latest row is the preferred version, provided the row order has a meaningful interpretation.

13.3 Remove All Members of Duplicate Groups

clean_df = df.drop_duplicates(keep=False)

This removes every row belonging to a duplicated group. Use it only when all such groups should be excluded rather than reduced to a single record.

13.4 Remove Duplicates Based on Selected Columns

clean_df = df.drop_duplicates(subset=["Email"])

Only the selected columns are used to determine duplication. If email addresses should be unique, this can retain one record per email address, but you should decide which record to retain when the associated information differs.

13.5 Remove Duplicates After Sorting

df = df.sort_values("UpdatedAt")
df = df.drop_duplicates(subset=["CustomerID"], keep="last")

This pattern retains the last record for each customer after sorting by an update timestamp. Confirm that timestamps are valid and sorted in the intended order before applying the operation.

14. Cleaning Data Before Duplicate Detection

Records may appear different because of whitespace, letter case, or inconsistent formatting. Normalizing these values before checking duplicates can reveal repeated records that would otherwise be missed.

df["Email"] = df["Email"].str.strip().str.lower()
df["Name"] = df["Name"].str.strip()

df = df.drop_duplicates(subset=["Email"])

Lowercasing email addresses is commonly used for matching in data-cleaning workflows, but identity and uniqueness rules should follow the requirements of the source system. Avoid removing records solely because names are similar.

15. Converting Columns to Appropriate Data Types

Correct data types make calculations and comparisons more reliable. For example, a salary stored as text cannot always be used directly for numeric calculations.

15.1 Convert a Column to Numeric

df["Salary"] = pd.to_numeric(df["Salary"], errors="coerce")

The errors="coerce" argument converts values that cannot be interpreted as numbers into missing values. Inspect those newly missing values to determine whether they indicate invalid input or a different data format.

15.2 Convert a Column to a String Type

df["CustomerID"] = df["CustomerID"].astype("string")

Identifiers such as customer IDs and postal codes may be better represented as strings, especially when leading zeros are significant.

15.3 Convert Dates

df["OrderDate"] = pd.to_datetime(
    df["OrderDate"],
    errors="coerce"
)

Invalid date strings become missing datetime values. Check these rows before deciding whether to correct, replace, or remove them.

16. Validating Data After Cleaning

Data cleaning should include validation. After modifying a dataset, verify that the intended changes occurred and that important information has not been accidentally lost.

16.1 Check Remaining Missing Values

print(df.isna().sum())

16.2 Check Remaining Duplicates

print("Duplicate rows:", df.duplicated().sum())

16.3 Check Unique Values

print(df["City"].value_counts(dropna=False))
print(df["City"].unique())

value_counts() shows how frequently values occur, while unique() displays distinct values. These methods help identify unexpected categories and inconsistent labels.

16.4 Validate Numeric Ranges

invalid_ages = df[(df["Age"] < 0) | (df["Age"] > 120)]
print(invalid_ages)

Range rules must be appropriate for the application. An unusual value should be investigated before being removed or changed.

16.5 Compare Row Counts Before and After Cleaning

original_rows = len(original_df)
cleaned_rows = len(df)

print("Original rows:", original_rows)
print("Cleaned rows:", cleaned_rows)
print("Rows removed:", original_rows - cleaned_rows)

Keeping an original copy allows you to measure how much the cleaning process changed the dataset.

17. Complete Example: Cleaning a Customer Dataset

The following example demonstrates a repeatable workflow for identifying missing information, standardizing text, removing exact duplicate rows, and validating the cleaned dataset.

import pandas as pd

data = {
    "CustomerID": [101, 102, 103, 103, 104, 105],
    "Name": ["Aarav", "Diya", " Kabir ", " Kabir ", None, "Meera"],
    "Age": [25, 30, None, None, 42, 29],
    "City": ["Mumbai", "Pune", "Mumbai", "Mumbai", None, "Delhi"],
    "Email": [
        "[email protected]",
        "[email protected]",
        "[email protected]",
        "[email protected]",
        None,
        "[email protected]"
    ]
}

original_df = pd.DataFrame(data)
df = original_df.copy()

# Step 1: Inspect the original data
print("Original data:")
print(df)
print("\\nMissing values:")
print(df.isna().sum())

# Step 2: Standardize text columns
df["Name"] = df["Name"].str.strip()
df["City"] = df["City"].str.strip().str.title()
df["Email"] = df["Email"].str.strip().str.lower()

# Step 3: Remove exact duplicate rows
df = df.drop_duplicates()

# Step 4: Fill missing numeric values using the median
df["Age"] = df["Age"].fillna(df["Age"].median())

# Step 5: Preserve unknown information explicitly
df["Name"] = df["Name"].fillna("Unknown")
df["City"] = df["City"].fillna("Unknown")

# Step 6: Check the results
print("\\nCleaned data:")
print(df)

print("\\nRemaining missing values:")
print(df.isna().sum())

print("\\nRemaining exact duplicate rows:")
print(df.duplicated().sum())

Important: The example removes exact duplicate rows, but it does not automatically remove records sharing a CustomerID or email. Those records may require investigation to determine whether they represent duplicate customers, updated records, or legitimate transactions.

18. A More Careful Workflow for Duplicate Customer Records

When the business rule states that each customer should have one record, inspect repeated identifiers and decide which record is authoritative instead of blindly deleting rows.

# Inspect repeated customer IDs
repeated_ids = df[
    df.duplicated(subset=["CustomerID"], keep=False)
].sort_values("CustomerID")

print(repeated_ids)

# If the latest record should be retained, sort using a reliable
# timestamp column first:
#
# df["UpdatedAt"] = pd.to_datetime(df["UpdatedAt"], errors="coerce")
# df = df.sort_values("UpdatedAt")
# df = df.drop_duplicates(subset=["CustomerID"], keep="last")

Do not use this rule unless the identifier is reliable and the business requirements confirm that only one row per identifier should remain.

19. Best Practices for Data Cleaning

  • Keep the original data: Create a copy before applying destructive changes.
  • Understand the source: Investigate why values are missing or repeated.
  • Choose replacements carefully: Mean, median, mode, and fixed labels are not interchangeable.
  • Do not fill everything with zero: Zero may be a meaningful measurement rather than a missing-value marker.
  • Define duplicate rules: Decide whether duplicates mean identical rows, repeated identifiers, or repeated business events.
  • Standardize before matching: Normalize whitespace and case where appropriate.
  • Validate data types: Convert dates, numeric values, and identifiers deliberately.
  • Track changes: Record how many values were filled, rows removed, and records changed.
  • Check for bias: Removing incomplete records may disproportionately affect certain groups.
  • Avoid data leakage: In machine-learning workflows, calculate imputation values from training data only, then apply the same transformation to validation and test data.
  • Make cleaning reproducible: Use documented Python code instead of relying only on manual spreadsheet edits.
  • Recheck the results: Confirm that cleaning rules have not introduced new inconsistencies.

20. Common Mistakes and Troubleshooting

Problem Possible Cause Solution
Missing values are not detected Missing information is stored as text. Inspect unique values and replace known missing markers with pd.NA.
Too many rows disappear dropna() removes rows containing any missing value. Use subset, thresh, or a justified imputation strategy.
Duplicate rows remain Rows differ in one or more columns. Inspect duplicates using a suitable subset.
Legitimate records are deleted Repeated values were assumed to be duplicates. Use reliable identifiers and domain-specific rules.
Numeric conversion produces missing values Text contains symbols or invalid numbers. Inspect failed conversions and clean formats before conversion.
Imputed values look unrealistic The replacement method does not suit the data distribution. Review distributions, outliers, and domain constraints.
Changes do not appear in the original DataFrame A cleaned result was assigned to a different variable. Use the returned DataFrame or explicitly assign it back.

21. Practical Exercises

Exercise 1: Identify Missing Values

Create a DataFrame containing customer names, ages, and email addresses. Count the missing values in each column and calculate their percentages.

Exercise 2: Fill Missing Numeric Values

Create a dataset of product prices with missing entries. Compare filling the missing prices with the mean and median. Explain which method is more appropriate when the data contains extreme prices.

Exercise 3: Remove Duplicate Records

Create a dataset containing repeated employee records. Use duplicated() to identify duplicates and drop_duplicates() to remove exact repeats.

Exercise 4: Normalize Text

Use values such as "mumbai", "Mumbai", and " Mumbai ". Standardize them and count the distinct city names before and after cleaning.

Exercise 5: Build a Data Quality Report

Write a Python program that reports the number of rows, number of columns, missing values per column, missing-value percentages, duplicate row count, and data types. Save the cleaned dataset to a CSV file.

22. Mini Project: Customer Data Cleaning

Project objective: Clean a customer dataset before preparing it for analysis or reporting.

Requirements

  1. Load customer records from a CSV file using pandas.
  2. Inspect column names, data types, and sample records.
  3. Identify missing values and calculate their percentages.
  4. Standardize text fields such as names, cities, and email addresses.
  5. Convert numeric and date columns to suitable types.
  6. Remove exact duplicate rows.
  7. Investigate duplicate customer identifiers separately.
  8. Choose appropriate strategies for remaining missing values.
  9. Validate required columns and business rules.
  10. Export the cleaned dataset to a new CSV file.

Example CSV Loading and Saving

import pandas as pd

df = pd.read_csv("customers.csv")
original_df = df.copy()

# Standardize text fields when present
if "Name" in df.columns:
    df["Name"] = df["Name"].str.strip()

if "Email" in df.columns:
    df["Email"] = df["Email"].str.strip().str.lower()

# Remove exact duplicate rows
df = df.drop_duplicates()

# Generate a basic quality report
report = pd.DataFrame({
    "Missing Count": df.isna().sum(),
    "Missing Percentage": (df.isna().mean() * 100).round(2),
    "Data Type": df.dtypes.astype(str)
})

print(report)
print("Rows before cleaning:", len(original_df))
print("Rows after cleaning:", len(df))

df.to_csv("customers_cleaned.csv", index=False)
report.to_csv("customer_quality_report.csv")

print("Cleaning and export completed.")

This is a starting point, not a universal cleaning policy. Add column-specific imputation, validation, and duplicate handling based on the real dataset's requirements.

23. Interview Questions and Answers

Q1. What is data cleaning?

Answer: Data cleaning is the process of detecting and correcting incomplete, inaccurate, inconsistent, duplicated, or incorrectly formatted data to improve data quality.

Q2. Which pandas methods are used to detect missing values?

Answer: isna() and isnull() identify missing values. Methods such as sum() and mean() can then summarize their counts or percentages.

Q3. What is the difference between dropna() and fillna()?

Answer: dropna() removes rows or columns based on missing-value conditions, while fillna() replaces missing values with specified values or strategies.

Q4. What is the difference between duplicated() and drop_duplicates()?

Answer: duplicated() identifies duplicate rows or values according to selected columns. drop_duplicates() returns a DataFrame with the selected duplicate records removed.

Q5. When should the mean or median be used for imputation?

Answer: The mean is often appropriate for relatively symmetric numeric data without extreme outliers. The median is more robust to outliers and is often preferred for skewed distributions.

Q6. What does keep="first" mean in drop_duplicates()?

Answer: It retains the first occurrence of a duplicate group and removes later occurrences. This is the default behavior.

Q7. What does subset do in duplicated() and drop_duplicates()?

Answer: The subset parameter specifies the columns used to determine whether records are duplicates.

Q8. Why should duplicate records be investigated before deletion?

Answer: Repeated values may represent legitimate transactions or separate people. Deleting them without understanding the business rules can remove valid data.

Q9. What is forward filling?

Answer: Forward filling replaces a missing value with the preceding available value. It is commonly used for ordered or time-series data when appropriate.

Q10. How can inconsistent text values be standardized?

Answer: String operations such as str.strip(), str.lower(), and str.title() can standardize whitespace and letter case where suitable.

Q11. What is the purpose of pd.to_numeric()?

Answer: It converts values into numeric types. With errors="coerce", values that cannot be converted become missing values.

Q12. Why is validation important after data cleaning?

Answer: Validation confirms that cleaning rules worked as expected and checks that missing values, duplicates, invalid types, or inconsistent records have been handled appropriately.

24. Quick Revision Checklist

  • Understand the dataset before making changes.
  • Inspect rows, columns, data types, and summary statistics.
  • Use isna() and isnull() to detect missing values.
  • Use dropna() to remove incomplete records when justified.
  • Use fillna() for appropriate imputation strategies.
  • Use ffill(), bfill(), or interpolation only when suitable.
  • Normalize text before checking for duplicates.
  • Use duplicated() to detect repeated records.
  • Use drop_duplicates() with deliberate duplicate rules.
  • Convert columns to correct data types and validate value ranges.
  • Compare the original and cleaned datasets.
  • Save the cleaned output and document important transformations.

25. Conclusion

Cleaning data and handling missing or duplicate values are essential skills for Python developers, data analysts, and machine learning practitioners. Pandas makes these tasks manageable through methods such as isna(), fillna(), dropna(), duplicated(), and drop_duplicates().

The most important principle is to clean data according to its meaning, not simply to remove every unusual value. A reliable workflow includes inspecting the data, applying justified transformations, validating the results, and preserving the original information so that the process remains transparent and reproducible.

Additional Learning Resources

whatsapp