Distributions

The Distributions section describes the shape of the selected values, split by category. It has three parts: a summary table, box plots per category and a distribution comparison by category on shared bins. All three use the current selection; the category filter decides which categories appear.

The summary table lists the following statistics. Exact formulas are given in Statistical Analysis.

Reading the table

• Mean vs median. A mean clearly above the median points to a long right tail; below the median, to a long left tail.
• SD vs IQR. SD reacts strongly to extreme values; IQR does not. For roughly normal data, IQR ≈ 1.35 × SD. A much larger SD than that suggests heavy tails or outliers.
• Skewness. G₁ near 0 indicates a roughly symmetric distribution. Positive values indicate a longer right tail, negative values a longer left tail.
• Coefficient of variation. Expresses spread relative to the mean, so categories with different levels can be compared. It is only meaningful for values on a ratio scale (a true zero), such as MWh, minutes or items.

Each category is drawn as a horizontal box plot on a common value axis.

Box

From Q1 to Q3; it contains the middle 50% of the values.

Line inside the box

The median.

Whiskers (Tukey)

Extend to the most extreme observation that lies within 1.5 × IQR of the box: the lower whisker to the smallest value ≥ Q1 − 1.5 · IQR, the upper whisker to the largest value ≤ Q3 + 1.5 · IQR.

The tooltip shows the category, its number of observations n, the upper whisker, Q3, the median, Q1 and the lower whisker.

The comparison chart overlays the distribution of each category. All categories use the same bin edges, computed from the values of all selected categories with the bin rules described in Frequency Analysis. Bars show relative frequency (count in the bin ÷ number of observations in that category), so categories with different numbers of observations are comparable.

Shared bins matter: if each category were binned separately, differences in bin width and alignment could look like differences in shape. With identical bins, a difference in bar height in a given class is a difference in the share of observations in that class.

The illustrative datasets were generated with known properties, which makes them useful to check how the statistics behave. Open /demo and select:

• Support Response Times: values are log-normal, so each channel shows a mean above its median, a positive skewness and a box whose upper half is longer than its lower half. Chat has the lowest level and Email the highest.
• Regional Electricity Demand: North has a higher level and a larger seasonal amplitude than South, which shows as a wider box and a larger SD.
• Items per Order: discrete values with one bin per integer. The minimum is 1 by construction (1 + Poisson). Restricting the date range to November and December shifts the distribution upward because λ is raised by 0.9 in those months.