Amogh N P
✦ In loving memory of Amogh N P — Architect · Designer · Visionary ✦
An architect reading data and charts — design informed by evidence.
Unit II25ART102 · Mathematics in Architecture

Basic Statistics

Reading the numbers — averages, spread, and the data behind design.

≈ 30 min · live calculator

Good design increasingly rests on evidence — surveys, sensor data, footfall, energy bills. Statistics is how you turn a pile of numbers into a clear story: a typical value, how much things vary, and how confident you can be. Here are the essentials, with a calculator to play with.

Learning objectives

By the end of this lesson, you will be able to — mapped to the course outcomes for Building Materials & Construction I:

1
CO2 · Understand

Describe data and choose the right chart (bar, pie, histogram).

2
CO2 · Apply

Calculate mean, median and mode and know when each is appropriate.

3
CO2 · Apply

Measure spread with range, variance and standard deviation; read the normal curve.

4
CO2 · Analyse

Identify where statistics is used in architecture and planning.

Central tendency

The three averages

Mean, median and mode each answer “what's typical?” differently. Enter your own data below and watch all four summary numbers update.[1]

Mean, median & mode Data set: 2, 3, 3, 5, 7 23357 Mean = (2+3+3+5+7)/5 = 4 Median = middle value = 3 Mode = most frequent = 3 Use the median when data are skewed or have outliers; the mode is the only average for categories.
DiagramMean, median and mode worked out for a small dataset
Try it

Mean, median, mode & standard deviation

Mean
0.00
Median
0.00
Mode
none
Std dev (σ)
0.00

6 values · σ uses the population formula √(Σ(x−x̄)²/n).

Dispersion

Spread & the normal curve

An average alone hides how much the data scatter. Standard deviation measures that spread; for data that follow the normal bell curve, the 68–95–99.7 rule tells you how much falls near the mean.[2]

The normal curve — the 68–95–99.7 rule μ −1σ+1σ −2σ+2σ 68% 95% 99.7% ~68% of values fall within ±1σ of the mean, ~95% within ±2σ, ~99.7% within ±3σ — when data are normal.
DiagramThe normal distribution bell curve with the 68-95-99.7 percent bands
Why it matters

Statistics at work in architecture

From the comfort of occupants to the safety of structures, statistics quietly underpins good practice. Select an area.

Post-occupancy evaluation

After a building is occupied, occupant surveys and environmental monitoring are analysed statistically to judge how it really performs — comfort, satisfaction, energy.[3]

A post-occupancy survey under way in an occupied building.
PhotoA post-occupancy survey under way in an occupied building.
A building energy dashboard — performance, quantified.
PhotoA building energy dashboard — performance, quantified.
Movement in a public plaza — the raw data of space syntax.
PhotoMovement in a public plaza — the raw data of space syntax.
A histogram and a bell curve — describing data at a glance.
PhotoA histogram and a bell curve — describing data at a glance.
Check your understanding

Self-assessment

1. For data with a few extreme outliers, the best 'average' to report is usually the:

2. Standard deviation measures:

3. In a normal distribution, roughly what share of values fall within ±1 standard deviation of the mean?

In a nutshell

Recap

Mean, median and mode are three different 'averages' — pick the one that fits the data.
Range, variance and standard deviation measure how spread out the data are.
In a normal distribution, ~68 / 95 / 99.7% of values lie within ±1 / 2 / 3σ.
Architecture uses statistics in POE, environmental data, structural reliability, planning and space syntax.
The evidence

References & further reading

  1. [1]Measures of central tendency — when to use mean, median, mode. Laerd Statistics. https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php
  2. [2]Variability — range, variance and standard deviation. Scribbr. https://www.scribbr.com/statistics/variability/
  3. [3]Post-occupancy evaluation. Wikipedia / building-performance literature. https://en.wikipedia.org/wiki/Post-occupancy_evaluation
  4. [4]Probability-based load criteria for structural design. NIST. https://nvlpubs.nist.gov/nistpubs/sp958-lide/283-288.pdf
  5. [5]Population forecasting in planning. American Planning Association. https://www.planning.org/pas/reports/report17.htm
  6. [6]The space-syntax approach to movement. Space Syntax Ltd. https://spacesyntax.com/the-space-syntax-approach/

Further reading

  • Groat, L.N. & Wang, D. (2013). Architectural Research Methods (2nd ed.). Hoboken, NJ: Wiley.
  • A standard introductory statistics text (mean/median/mode, dispersion, the normal distribution).

Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.