All Labs

Exploratory Data & Distribution Lab

Paste or type a dataset, and instantly see descriptive statistics, five-number summaries, outlier detection, and interactive visualizations. Compare two groups side by side with histograms, box plots, and dot plots.

Guided Experiment: Shape, Center, and Spread

How do mean, median, and standard deviation change when a dataset is symmetric versus skewed? Will the mean always be close to the median?

Write your hypothesis in the Lab Report panel, then click Next.

Histogram

0123457377.481.886.290.695ValueFrequency

Controls

Compare two datasets

Descriptive Statistics

MeasureValue
Count (n)15
Mean (x̄)84.6
Median85
ModeNone
Range22
Q181
Q388.5
IQR7.5
Std Dev (s)6.1272
Variance (s²)37.5429
Skewness-0.2402
Kurtosis (excess)-0.4249
Shaperoughly symmetric
Five-Number Summary (Data)
Min
73
Q1
81
Median
85
Q3
88.5
Max
95
Outliers (1.5 × IQR Rule)
Data: None detected
Key Formulas
xˉ=∑xin\bar{x} = \frac{\sum x_i}{n}
s2=∑(xi−xˉ)2n−1s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
s=s2s = \sqrt{s^2}
z=x−xˉsz = \frac{x - \bar{x}}{s}

Data Table

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#TrialDatasetnMeanMedianStd DevSkewnessOutliersShape
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Reference Guide

Measures of Center

The mean, median, and mode each describe the "center" of a dataset in different ways. The mean uses every value, the median splits the data in half, and the mode is the most frequent value.

xˉ=∑i=1nxin\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}

When data is symmetric, mean and median are close. When data is skewed, the mean gets pulled toward the tail.

Measures of Spread

Range, IQR, variance, and standard deviation quantify how spread out the data is. The sample standard deviation uses n-1 in the denominator (Bessel's correction).

s=∑i=1n(xi−xˉ)2n−1s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n - 1}}

IQR = Q3 - Q1 is resistant to outliers, while standard deviation is sensitive to extreme values.

Five-Number Summary and Box Plots

The five-number summary (min, Q1, median, Q3, max) is the foundation of the box-and-whisker plot. Whiskers extend to the farthest non-outlier data point.

IQR=Q3−Q1\text{IQR} = Q_3 - Q_1

Outlier fences are at Q1 - 1.5(IQR) and Q3 + 1.5(IQR). Any data point beyond these fences is flagged as a potential outlier.

Shape and Outliers

Distribution shape (symmetric, skewed, bimodal) reveals patterns that summary statistics alone may miss. Skewness measures the asymmetry of the distribution.

z=x−xˉsz = \frac{x - \bar{x}}{s}

A z-score tells how many standard deviations a value is from the mean. Values with |z| > 2 are unusual. Always pair numerical summaries with a visual display.