Data Types, Measurement Scales, and Descriptive Statistics

What Are Data Types and Why Do They Matter?

Before you can summarize, visualize, or model data, you need to know what kind of data you are working with. Using the wrong statistical technique on the wrong type of data produces misleading results. This lesson gives you the vocabulary and the arithmetic you need to describe any dataset accurately.

Data variables fall into two broad families: categorical (qualitative) and numerical (quantitative). Categorical variables place observations into groups or labels. Numerical variables record amounts or counts that can be measured on a number line.

The Four Measurement Scales

Stanley Smith Stevens described four levels of measurement that are now standard across statistics and data science. Each level adds a property that the level below it lacks.

Nominal scale — Labels only; no natural order. You can count how many observations fall in each category, but arithmetic such as addition or averaging is meaningless. Examples: inspection district name, sensor manufacturer brand, survey respondent's city.

Ordinal scale — Categories that have a meaningful order, but the gaps between categories are not guaranteed to be equal. A Likert-item response (Strongly Disagree / Disagree / Neutral / Agree / Strongly Agree) is ordinal. You know Agree ranks higher than Neutral, but you cannot claim the psychological distance from Neutral to Agree is identical to the distance from Disagree to Neutral. Other examples: restaurant star ratings, letter grades.

Interval scale — Ordered categories with equal, meaningful gaps, but no true zero point. The absence of a true zero means ratios are not interpretable. Temperature in Fahrenheit or Celsius is the classic example: 40 °F is not "twice as warm" as 20 °F. Sensor timestamps expressed as calendar dates are also interval.

Ratio scale — Interval properties plus a true, meaningful zero that represents the complete absence of the quantity. Ratios are now fully interpretable. Revenue in dollars, weight in kilograms, inspection scores on a 0–100 scale, and count of code violations are all ratio variables. Most numerical data you encounter in business analytics is ratio scale.

Measures of Central Tendency

Descriptive statistics summarize a dataset with a small number of values. The three measures of central tendency locate the "center" of a distribution.

Mean (arithmetic average): Add all values and divide by the count (n). The mean uses every data point, so it is sensitive to extreme values (outliers).

Median: Sort the values from smallest to largest. For an odd count, the median is the middle value. For an even count, it is the average of the two middle values. The median is resistant to outliers, which is why income distributions are usually reported with the median rather than the mean.

Mode: The value that appears most often. A dataset can have no mode, one mode, or multiple modes. Mode is the only measure of central tendency appropriate for nominal data.

Measures of Spread

Central tendency alone is incomplete. Two datasets can share the same mean yet differ dramatically in how spread out their values are.

Range: Maximum minus minimum. Simple but heavily influenced by outliers.

Variance (s²): The average of the squared deviations from the mean. For a sample, divide the sum of squared deviations by (n − 1) rather than n; this gives an unbiased estimate of the population variance.

Standard deviation (s): The square root of the variance. It is expressed in the same units as the original data and is the most commonly reported measure of spread.

Interquartile range (IQR): The difference between the 75th percentile (Q3) and the 25th percentile (Q1). Because it captures the middle 50 % of the data, it is resistant to outliers and is often paired with the median.

Accuracy and Integrity in Descriptive Reporting

A persistent real-world error is reporting the mean when the median is the more honest summary. When a distribution is strongly skewed — for example, a neighborhood where most households earn modest wages but a handful earn very high incomes — the mean is pulled toward the tail and overstates the "typical" value. Always inspect the shape of your distribution before choosing which statistic to report.

When you share descriptive statistics, also state the sample size (n), the time period the data covers, and the source. Open datasets from portals such as the NYC or Chicago open data portals are citable public records; always confirm the data dictionary so you know whether a score column is truly ratio scale or has a bounded maximum that limits its interpretation.

Working Safely with Data

Data science does not involve physical hazards in the same way a construction trade does, but professional data handling carries its own safety obligations. Always verify you are authorized to access and use a dataset before downloading it. Municipal open datasets are public by design, but datasets containing personal identifiers require careful handling under applicable privacy regulations. Never share raw data files that contain personally identifiable information (PII) via unsecured channels. Lock your workstation when you step away from it, and store project files in access-controlled locations. These practices protect the people whose data you are analyzing and protect you professionally.

Using Spreadsheet Functions

In Microsoft Excel or Google Sheets the key functions for this lesson are: `AVERAGE()`, `MEDIAN()`, `MODE.SNGL()`, `MAX()`, `MIN()`, `VAR.S()`, `STDEV.S()`, and `QUARTILE.INC()` or `QUARTILE()`. Always verify at least one result by hand to confirm you have selected the correct cell range. A common mistake is including a header row in the range, which inserts a text value and silently distorts the result.