Univariate Statistics Analyzer

Descriptive Statistics Data Quality

Your first step in any data analysis: understand each variable individually before exploring relationships. Upload marketing data and instantly assess distributions, detect outliers, test for normality, and generate publication-ready summaries.

QUICK START: Choose Your Path

OVERVIEW & OBJECTIVE

What is univariate analysis? Univariate analysis examines one variable at a time to understand its distribution, central tendency (typical values), spread (variability), and shape. This is often your first step in any data analysis project—before looking at relationships between variables, you need to understand each variable individually.

Why start here? This tool helps you spot data quality issues (missing values, outliers), understand your customer base (what's typical vs. unusual), and make informed decisions about which variables matter for deeper analysis.

💡 When to use univariate analysis:

Data cleaning: Identify missing values, outliers, and data entry errors before any analysis
Assumption checking: Test if continuous variables are normally distributed (required for many statistical tests)
Variable selection: Understand which variables have enough variation to be useful predictors
Baseline profiling: Describe your customer base, transactions, or survey responses

Understanding Variable Types

Continuous Variables (Quantitative)

What they are: Numbers that can take any value within a range. Examples: age, revenue, website visit duration, number of clicks, satisfaction score (1-10).

What we measure:

Mean — The average. Tells you the "typical" value but can be skewed by outliers.
Median — The middle value when sorted. More resistant to outliers than the mean.
Mode — The most frequently occurring value.
Standard Deviation (SD) — How spread out the data is from the mean. Smaller = more consistent, larger = more variable.
Range & IQR — Range shows min to max. IQR (interquartile range) shows the middle 50% of data, filtering out extreme values.
Skewness — Measures if data leans left or right. Positive skew = long tail on right (most values are low). Negative skew = long tail on left (most values are high).
Kurtosis — Measures if data has heavy tails (extreme values) or is peaked. High kurtosis = more outliers.

Visualizations: Box plots show quartiles and outliers. Histograms show distribution shape. Violin plots combine both. Density plots smooth out histograms.

Categorical Variables (Qualitative)

What they are: Labels or categories. Examples: customer segment (A/B/C), product type, region, yes/no responses, gender, campaign name.

What we measure:

Frequency — How many times each category appears.
Percentage — What proportion of the total each category represents.
Mode — The most common category.
Unique values — How many distinct categories exist.

Visualizations: Bar charts show counts per category. Pie charts show proportions. Horizontal bars work better when you have many categories.

What this tool does for you

Auto-detection: Automatically identifies if each variable is continuous (numeric) or categorical (labels), so you don't have to decide.
Data quality dashboard: See missing data percentages, outlier counts, and distribution health at a glance.
Normality testing: Shapiro-Wilk test and Q-Q plots help you check if data is normally distributed (important for subsequent analyses).
Multiple visualizations: Choose from box plots, histograms, violin plots, and density plots for continuous variables; bar charts, pie charts, and horizontal bars for categorical variables.
Comprehensive statistics: Every relevant statistic calculated automatically—mean, median, SD, range, IQR, skewness, kurtosis for continuous; frequencies, percentages, mode for categorical.
Plain language explanations: Every statistic includes both technical definitions and practical interpretations ("what does this mean for my business?").
Export capabilities: Download summary tables as CSV for presentations or further analysis in Excel.
Manual override: If the tool misclassifies a variable, you can manually switch between continuous and categorical analysis.

Understanding Normality (Why It Matters)

Many statistical tests (t-tests, ANOVA, regression) assume your data follows a normal (bell-shaped) distribution. If your data is heavily skewed or has extreme outliers, these tests may give misleading results.

How to check for normality:

Visual inspection: Does the histogram look roughly bell-shaped?
Q-Q plot: Do points fall close to the diagonal line?
Shapiro-Wilk test: p > 0.05 suggests data could be normal; p < 0.05 suggests non-normality
Skewness & Kurtosis: Values near 0 suggest normality; |skew| > 1 or |kurtosis| > 2 suggest departures

⚠️ What if my data isn't normal?

Don't panic! You have options: (1) Use non-parametric tests that don't assume normality, (2) Transform your data (log, square root), or (3) With large samples (n > 30), many tests are robust to non-normality.

MARKETING SCENARIOS

Load a marketing use case:

📊 Real Marketing Data Scenarios

Select a preset scenario to explore real-world datasets with mixed variable types. Each scenario includes continuous metrics (revenue, engagement scores, visit duration) and categorical dimensions (segments, channels, regions) so you can practice interpreting both types.

INPUTS & SETTINGS

Upload Data or Select Variables

Drag & Drop data file (.csv, .tsv, .txt)

Provide a CSV or TSV with column headers. Up to 5,000 rows per file.

Variables in Dataset

ℹ️ About Data Types & How to Change Them

We automatically detect whether each variable is Continuous (numeric) or Categorical (labels/groups). Sometimes you may want to override this:

📊 Treat as Continuous when...

Values represent measurements (revenue, age, scores)
Mathematical operations make sense (averages, sums)
You want histograms, box plots, mean/median statistics

🏷️ Treat as Categorical when...

Numbers represent groups or codes (1=Low, 2=Med, 3=High)
There are few unique values that represent categories
You want frequencies, percentages, bar charts

Example: A "Satisfaction" variable with values 1-5 could be treated as continuous (mean = 3.7) or categorical (40% rated it "5"). Click the ✏️ button next to any variable to change its type.

DATA QUALITY DASHBOARD

📋

Total Records —

📊

Variables —

⚠️

Missing Values —

🎯

Potential Outliers —

📋 Variable-by-Variable Data Quality

💡 Data Quality Tips

Missing values: Consider if they're random or systematic. High missing % may indicate a data collection issue.
Outliers: Check if extreme values are real or data entry errors. The IQR method flags values beyond 1.5×IQR from quartiles.
Variable types: Verify the auto-detected types are correct. Use the override buttons if needed.

🎓 Understanding Data "Problems" vs. Data Characteristics

New analysts often panic when they see outliers or non-normal data. But not every statistical "flag" is a problem to fix—some are just characteristics of your data that inform how you analyze it. Learning to tell the difference is a crucial analytical skill.

🟢 EXPECTED PATTERN

Not a problem—just how this type of data behaves

Right-skewed money data: Income, revenue, and purchase amounts are almost always right-skewed. Most customers spend modest amounts; a few big spenders pull the tail right. This is normal for this data type.
Non-normal bounded scales: Rating scales (1-5 stars, 1-10 NPS) can't be perfectly normal because they have floors and ceilings. Pile-ups at extremes are expected.
Legitimate high-value outliers: Your top 1% of customers really do spend 10× more. Enterprise clients really do have 50× more employees. These aren't errors—they're valuable insights.
Bimodal distributions: Seeing two peaks often means you have two distinct customer segments—that's a finding, not a flaw!

What to do: Document the pattern, consider using median instead of mean for central tendency, and choose appropriate statistical tests (non-parametric if needed).

🟡 NEEDS INVESTIGATION

Could be real, could be a problem—dig deeper

Unusually high outlier rate (>5%): If many values are flagged as outliers, either your data has unusual spread or something went wrong during collection.
Unexpected missing patterns: If one variable has 40% missing while others have 2%, investigate why. Was that question optional? Did the form break?
Strange distribution shapes: A sharp cliff at a round number (like many $99.99 values) might indicate data truncation or intentional pricing effects.
Extreme value gaps: If you have values 1-100 and then suddenly a 10,000, investigate that jump before assuming it's valid.

What to do: Look at the raw data. Ask: "Is there a business reason this value exists?" Check with whoever collected the data before making changes.

🔴 LIKELY DATA ERROR

Strong evidence something went wrong—fix before analysis

Impossible negative values: Negative age, negative revenue (unless tracking refunds), negative item counts.
Values outside theoretical bounds: Percentages over 100%, ratings of 6 on a 1-5 scale, ages over 120, probabilities below 0.
Suspicious repetition: Same extreme value repeated many times (copy-paste error?), or values that look like dates in a numeric field (e.g., "20260208").
Unit mismatches: One value in thousands while others are in millions (e.g., $50 vs. $50,000,000 for similar transactions).

What to do: Flag for review. Don't delete automatically—document what you found and how you handled it. Consider if these rows should be excluded or corrected.

STATISTICS & VISUALIZATIONS

Summary Statistics

Visualization type:

📊 How to Read This Chart

🧪 What-If Sandbox

Experiment

What is this? A safe space to experiment with your data and see how statistics change under different conditions.

Why use it? Build intuition about how outliers affect averages, how sample size impacts precision, and whether your findings are robust.

Try these experiments:

Remove outliers — See how much extreme values affect your mean and standard deviation
Change sample size — Watch how statistics "wobble" with fewer data points

🔬 Open Sandbox Controls

📈 Normality Assessment

Many statistical tests assume your data is normally distributed. Use these diagnostics to check.

Shapiro-Wilk Test

Test Statistic (W) —

p-value —

Q-Q Plot (Quantile-Quantile)

💡 How to Interpret Normality Results

Reading the Shapiro-Wilk test:

p ≥ 0.05: No strong evidence against normality. You can reasonably assume the data is normally distributed.
p < 0.05: Evidence that data departs from normality. Consider non-parametric tests or transformations.
W close to 1: Data closely follows a normal distribution.
Note: With large samples (n > 50), even tiny departures from normality become "significant." Use visual inspection alongside the test.

Reading the Q-Q plot:

Points on the line: Perfect normality—your data matches the theoretical normal distribution.
S-shaped curve: Heavy tails—more extreme values than expected (leptokurtic).
Points curve away at ends: Light tails—fewer extreme values than expected (platykurtic).
Points above line at right: Right-skewed distribution.
Points below line at right: Left-skewed distribution.

💡 How to Interpret These Statistics

Central Tendency (Where's the middle?)

Mean ≈ Median: Data is roughly symmetric—mean is a good summary.
Mean > Median: Right-skewed—outliers on high end pull mean up. Median may be more representative.
Mean < Median: Left-skewed—outliers on low end pull mean down.

Spread (How variable is the data?)

Coefficient of Variation (CV = SD/Mean): CV < 0.5 is low variability, > 1 is high variability.
IQR vs Range: If Range >> 4×IQR, you likely have extreme outliers.
SD interpretation: In a normal distribution, ~68% of values fall within ±1 SD of mean, ~95% within ±2 SD.

Shape (Distribution patterns)

|Skewness| < 0.5: Approximately symmetric.
|Skewness| 0.5–1: Moderately skewed.
|Skewness| > 1: Highly skewed—consider transformations or non-parametric methods.
|Kurtosis| > 2: Heavy tails with more outliers than normal distribution.

Univariate Statistics Analyzer

👨‍🏫 Professor Mode: Guided Learning Experience

QUICK START: Choose Your Path

Try an Example

Upload My Data

Learn the Basics

OVERVIEW & OBJECTIVE

Continuous Variables (Quantitative)

Categorical Variables (Qualitative)

MARKETING SCENARIOS

📊 Real Marketing Data Scenarios

INPUTS & SETTINGS

Upload Data or Select Variables

Variables in Dataset

📊 Treat as Continuous when...

🏷️ Treat as Categorical when...

DATA QUALITY DASHBOARD

🔎 Issues Detected in Your Data

STATISTICS & VISUALIZATIONS

Summary Statistics

🧪 What-If Sandbox

📈 Normality Assessment

Shapiro-Wilk Test

Q-Q Plot (Quantile-Quantile)

Summary Tables

APA-Style Statistical Reporting

Managerial Interpretation

🔮 WHAT'S NEXT? — From Univariate to Deeper Analysis

🏆 CHALLENGE MODE — Test Your Understanding

Analysis Checklist

My Findings

🏆 Challenge Mode