Comprehensive Statistics
Statistics
Calculator
Complete descriptive statistics: mean, median, mode, standard deviation, skewness, kurtosis, quartiles, z-scores, outlier detection, frequency table, and box plot.
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Mean
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Std Dev (σ)
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Count (N)
Enter Your Data
Separate values with commas, spaces, or line breaks. Up to 10,000 values supported.
Sample Datasets
Mean
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Median
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Pop SD (σ)
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Sample SD (s)
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Min
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Max
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Count (N)
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Sum
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Range
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Outliers (IQR)
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📊 Complete Descriptive Statistics
📦 Box & Whisker Plot
IQR box (Q1–Q3)
Median
Whisker
Outlier
📈 Histogram
⚠️ Outlier Detection
🔢 Frequency Distribution Table
📐 Sorted Data & Z-Scores
Comprehensive Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset. Unlike inferential statistics, they don't make predictions — they simply describe what's in the data.
Key Statistical Measures
Central tendency: Mean, Median, Mode, Geometric Mean, Harmonic Mean
Spread: SD, Variance, Range, IQR, MAD, CV
Shape: Skewness, Excess Kurtosis
Position: Q1, Q2 (Median), Q3, Percentiles, Z-scores
5-number summary: Min, Q1, Median, Q3, Max → Box plot
Outliers (IQR): Below Q1−1.5×IQR or above Q3+1.5×IQR
What is the difference between mean and median?
The mean is the arithmetic average — sum all values and divide by count. The median is the middle value when data is sorted. The mean is sensitive to outliers; the median is not. For skewed data or data with outliers (like income), median is usually more representative. If mean > median, data is right-skewed; if mean < median, it's left-skewed. When they're equal, distribution is symmetric.
What does skewness tell you?
Skewness measures asymmetry. Positive skewness (right skew) means a longer right tail — most data is on the left with a few high outliers. Examples: income, house prices. Negative skewness (left skew) means a longer left tail — most data is on the right with a few low outliers. Examples: age at retirement. A rule of thumb: |skewness| < 0.5 is fairly symmetric, 0.5–1 is moderately skewed, > 1 is highly skewed.
What is the IQR and why is it useful?
The IQR (Interquartile Range) = Q3 − Q1, the range of the middle 50% of data. It's resistant to outliers unlike the full range. The IQR is used in the box plot — whiskers extend to 1.5×IQR from the quartiles, and data beyond is marked as outliers. For example, if Q1=25 and Q3=75, IQR=50, lower fence=25−75=−50, upper fence=75+75=150. Any data outside those fences is flagged.
What is a Z-score?
A Z-score measures how many standard deviations a value is from the mean: z = (x − μ) / σ. Z=0 means exactly at the mean. Z=2 means 2 standard deviations above. Z=−1.5 means 1.5 SDs below the mean. Z-scores allow comparison across different scales — a student scoring z=1.5 on both math and English performed equally above average on both. Values with |z| > 2 or 3 are often flagged as outliers.