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Showing Distributions With Histograms

Learn Showing Distributions With Histograms for free with explanations, exercises, and a quick test (for Business Analyst).

Published: December 20, 2025 | Updated: December 20, 2025

Why this matters

Business Analysts often need to summarize lots of numeric data quickly: order values, resolution times, session lengths, lead ages, or delivery delays. A histogram shows the shape of these numbers at a glance. It helps you spot typical ranges, skew, outliers, and subpopulations. Stakeholders use this to set thresholds, create SLAs, and choose realistic targets.

Concept explained simply

A histogram groups a numeric variable into consecutive intervals (bins) and shows how many observations fall into each. Bars touch because the bins are continuous ranges. The vertical axis can show counts or percentages.

  • Bar chart: categories (e.g., product lines), bars are separated.
  • Histogram: numeric ranges (e.g., delivery times), bars touch.

Mental model

Imagine pouring all your numbers into labeled boxes lined up on a shelf: 0–5, 5–10, 10–15, and so on. The more numbers a box gets, the taller that bar is.

How to create a good histogram

1) Clarify the question
Examples: What is a typical first-response time? Are most orders under $50? Are there long delays?
2) Inspect the data
Check min, max, and obvious outliers. Note if values are bounded at 0 (many time/cost variables are).
3) Choose bins
Pick start, end, and width. Aim for 8–20 bins for readability. Heuristics: about sqrt(n) bins, or adjust until the shape is stable. Use round, human-friendly edges when possible.
4) Choose vertical scale
Use counts when a single group is shown. Use percentages when comparing groups with different sample sizes.
5) Draw and label
Bars should touch. Label axes with units (e.g., minutes, dollars). Consider marking the median or a target line.
6) Iterate
If the distribution is very skewed, try a different bin width or a log-scaled x-axis. Avoid overlaying multiple histograms if they become hard to read—prefer small multiples (side-by-side panels) with identical bins and axes.

Worked examples

Example 1 — E‑commerce order values

Data: 3,200 orders; min $0, max $600; median ~$42; long right tail.

  • Bins: $0–$200 with width $10 (20 bins), plus an overflow bin $200–$600 to show the tail.
  • Scale: Percent, to compare to other weeks later.
  • Annotation: Vertical line at median ($42) and a note: “10% of orders > $90”.

Insight: Most orders cluster $20–$60; a small fraction drives high revenue in the tail.

Example 2 — Time to first response (support tickets)

Data: minutes; many tickets resolved quickly, some take hours (right-skewed).

  • Bins: 0–240 minutes, width 5 minutes (48 bins).
  • Skew handling: Try a log x-axis if long tail hides structure near zero.
  • Comparison: Two teams shown as small multiples with same bins and percent scale.

Insight: Team B has a thinner tail; fewer tickets over 120 minutes.

Example 3 — App sessions per user per day

Data: integers with many zeros.

  • Bins: 0–20 sessions, width 1 (discrete-friendly). Combine 20+ into a final bin.
  • Highlight: The 0 bin (inactive users) and 1–2 bins (light users).

Insight: A zero-inflated distribution; activation campaigns should target the 0 and 1 session groups.

Who this is for

  • Business Analysts and Data Analysts summarizing numeric metrics.
  • Product/Operations/Marketing stakeholders needing quick shape insights.

Prerequisites

  • Basic familiarity with numeric data (continuous vs. discrete).
  • Understanding of mean, median, outliers.
  • Comfort creating simple charts in a spreadsheet or BI tool.

Common mistakes and how to self-check

  • Using a bar chart for numeric data. Bars shouldn’t be separated; use a histogram with touching bars.
  • Too many/few bins. If the chart looks spiky or overly smooth, adjust until patterns are stable and readable.
  • Different bin edges across panels. For comparisons, keep the same start, end, and width.
  • Counts vs. percentages mismatch. When group sizes differ, use percent on the y-axis.
  • Unclear labels and units. Always label axes and note if using log scale or overflow bins.
  • Clipped tails without notice. If you cut off the axis, clearly state it and why.
Self-check
  • Are bins contiguous and labeled with ranges or readable ticks?
  • Are axes labeled with units (minutes, $, sessions)?
  • If comparing groups, are binning and scales identical and y-axis set to percent?
  • Does the chosen bin width reveal stable structure without noise?

Exercises

Do these hands-on tasks. Then compare with the solutions below each exercise.

Exercise 1 — Plan your bins

You have 5,000 ride-sharing trip durations (minutes), ranging from 0.5 to 120. You want a single histogram for an internal report.

  • Propose: start, end, bin width, estimated number of bins.
  • Choose counts vs. percent. Explain your choice.
  • Note any annotation you would add (e.g., service target at 15 minutes).
Show solution

Start at 0, end at 120, width 5 minutes → about 24 bins. Use percent to make later comparisons easier. Add a line at the 15-minute target and annotate the share over 30 minutes. If early bins are too tall to see shape, try width 3 minutes or a log x-axis for exploration (but keep the final chart linear for interpretability unless stakeholders are comfortable with logs).

Exercise 2 — Build one from sample data

Copy these 40 values (minutes) into your tool and create a histogram.

Data: 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 10, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 28, 30, 32, 35, 38, 40, 45, 50, 55, 60, 75, 90, 110

  • Bins: 0–120, width 5 minutes.
  • Label axes and add a vertical line at 15 minutes.
Show solution

You should see a concentration between 3 and ~20 minutes, with a sparse right tail. The 15-minute line sits near the upper part of the main cluster. Most observations fall under 30 minutes; a few extend beyond 60 with a maximum near 110.

Exercise 3 — Interpret a histogram

Imagine a histogram of delivery delays (days) from 0 to 20 with width 1 day shows a strong spike at 0–2 days, a gentle decline to 7 days, and a thin tail to 20 days. About 12% are over 7 days.

  • Where is the median likely to be (roughly)?
  • Is the distribution symmetric or skewed?
  • What operational follow-up would you suggest?
Show solution

The median is likely around 2–3 days given the strong early spike and gradual decline. The distribution is right-skewed. Suggest investigating the causes of the >7 day tail (supplier, region, product type) and set a KPI to reduce that tail share from 12% to a lower target.

Exercise checklist

  • Picked human-friendly bin edges and widths.
  • Chose count vs. percent appropriately.
  • Used the same binning when comparing groups.
  • Labeled axes and units clearly.
  • Considered skew, tails, and annotations (median/targets).

Practical projects

  • Analyze order values for last quarter. Produce a histogram, annotate the median and the 90th percentile, and write 3 insights for pricing/discount strategy.
  • Support SLA review. Build percent-scale histograms for two teams with identical binning. Recommend a realistic SLA threshold that covers at least 80% of tickets.
  • User engagement snapshot. Create small-multiple histograms of daily sessions by user segment (new vs. returning) and highlight differences in low-activity bins.

Learning path

  • Before: Basic chart types, numeric data types, summary statistics.
  • Now: Histograms for distribution shape and quick comparisons.
  • Next: Density plots, box plots, and cumulative distributions for deeper comparisons.

Next steps

  • Try different bin widths to test stability of the pattern.
  • Create small multiples for 2–3 cohorts using identical bins and percent y-axis.
  • Share one histogram with concise annotations: median line, tail percentage, and a clear takeaway sentence.

Mini challenge

You have two marketing campaigns with 1,000 and 350 orders respectively. You want to compare order value distributions. Design the comparison:

  • Choose bin edges and width.
  • Pick y-axis scale and explain why.
  • Decide: overlay or small multiples?
  • List one annotation that helps a decision-maker.
Suggested approach

Use identical bins (e.g., $0–$200, width $10, plus $200+). Use percent y-axis due to different sample sizes. Prefer small multiples over overlay for clarity. Annotate each panel with median and share of orders >$90.

Quick Test

Take the quick test below to check your understanding. Everyone can take it for free; only logged-in users will have their progress saved.

Practice Exercises

3 exercises to complete

Instructions

You have 5,000 trip durations in minutes, ranging from 0.5 to 120. Propose start, end, bin width, and number of bins. Choose counts or percent for the y-axis and explain your choice. Note any annotations (e.g., service target).
Expected Output
A clear bin plan (e.g., 0–120, width 5 min, ~24 bins), a justified y-axis choice (percent if you anticipate comparisons), and a useful annotation (target line).

Showing Distributions With Histograms — Quick Test

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