Contact-centre hourly calls

What it is good for

• Check whether hourly arrivals within a given hour slot behave like a Poisson process (mean ≈ variance).
• Model the daily and weekly arrival pattern.
• Describe right-skewed waiting times and their relationship with staffing.
• Relate abandonment rate to average wait (scatter plot, logistic-style curve).

Methods: Poisson distribution, dispersion index, exponential distribution, scatter plot, correlation, regression, binomial proportions.

Data quality notes

• Arrivals across all hours are over-dispersed relative to a single Poisson because λ changes by hour and weekday; within an hour-weekday slot they are close to Poisson.
• avg_wait_sec is strongly right-skewed: a few understaffed hours have very long waits.
• avg_handle_min / avg_wait_sec are null only when there were no answered / offered calls (rare, early or late hours on quiet days).

Provenance and licence

Calls offered ~ Poisson(λ) where λ follows a two-peak daily profile (late morning and late afternoon, up to ≈55 calls/hour) times a day-of-week factor (Sunday highest, Friday/Saturday lowest). Agents are scheduled from the expected (not actual) load, so busy hours are sometimes understaffed. Average handle time is gamma-distributed around 5.5 minutes. Average wait is exponential-like and grows sharply as utilisation (offered work ÷ agent capacity) approaches 1. Abandoned calls ~ Binomial(calls offered, p) with p rising with the wait.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241013). It does not describe real people or organisations; any resemblance is coincidental.