First, the key terms.

Unit of analysis
The entity or event represented by an observation.
Median
The middle value of an ordered sample, with a defined convention for even sizes.
Spread
How dispersed the observations are, rather than their typical level.

The idea, explained

Begin by understanding the unit represented by each row and the meaning of each field. A category such as department differs from a count or continuous measurement. Ordered ratings are not automatically equally spaced quantities. Means, medians, quantiles and measures of spread answer different questions. Exploration is useful for generating hypotheses and detecting problems, but repeatedly inspecting data and then reporting only a surprising pattern can exaggerate evidence. Keep exploratory discoveries distinct from later confirmatory tests.

STEP 1

Check types and definitions

A numerical ID is a label, not a meaningful quantity to average. Identify categorical, ordered and numerical variables, units and missing-value codes. A zero waiting time differs from an unknown waiting time. Document those distinctions before calculating summaries.

STEP 2

Compare center and spread

The mean uses all values and is sensitive to extremes. The median describes the middle rank. Standard deviation, range and interquartile range describe different aspects of variability. Show a distribution so one summary does not hide skew or distinct subgroups.

STEP 3

Explore relationships carefully

Use grouped summaries and appropriate plots to inspect trends, outliers and correlations. Check denominators, repeated observations and aggregation. An overall relationship can differ across groups. Record plausible explanations without presenting an exploratory pattern as causal proof.

Follow a worked example.

Five fictional waiting times are 2, 3, 3, 4 and 28 minutes. The mean is 40 ÷ 5 = 8 minutes; the median is 3. Both are correct calculations but communicate different features of the same small sample.

Walk it through, one step at a time

  1. Order the observations and inspect the 28-minute case. Confirm it is a real event rather than a unit or entry error.
  2. Report the long wait alongside a typical-value measure. Deleting it merely because it is inconvenient would hide part of the service experience.
  3. Compare groups or time periods only after checking whether their definitions and collection methods match. A dashboard should explain what the numbers represent.

Where people get stuck

An outlier is a reason to investigate, not automatic permission to remove an observation.

Now try it yourself.

Pause before opening each answer. Explain your reasoning in your own words.

1. Check the core idea

Why can the mean waiting time exceed the wait experienced by most people?

Reveal the answer & reasoning

A small number of very large waits can pull the mean upward. The median and a distribution plot help communicate that asymmetry.

2. Apply what you learned

Would averaging customer ID numbers describe the average customer?

Reveal the answer & reasoning

No. Those numbers identify customers; numerical arithmetic on identifiers generally has no substantive interpretation.