Data

What this unit covers

The topics below follow the published CS Principles course framework for Unit 2. This unit is worth 17–22% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Lessons in this unit

• Binary & Number Representation13 min · 3 objectivesExplain why computers represent all data using bits (binary) · Convert numbers between binary and decimal · Relate the number of bits to the range of values that can be represented
• Data Compression13 min · 3 objectivesDistinguish lossless from lossy compression and their trade-offs · Explain why compression reduces storage and transmission costs · Compute and interpret a compression ratio
• Extracting Information from Data13 min · 3 objectivesExplain how patterns and correlations are found in large data sets · Distinguish correlation from causation · Describe the roles of metadata, cleaning, and filtering in analysis
• Bias in Data Collection12 min · 3 objectivesExplain how the way data is collected can introduce bias · Describe how a non-representative sample skews conclusions · Recognize privacy and consent issues in gathering data

Formulas in Unit 2

Every term in Unit 2

All 36 terms we publish for Data, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Data abstraction

Using a name to represent a collection of data — a list rather than many separate variables. It lets a program work with any number of items using the same code.

Bit

A single binary digit, 0 or 1. The smallest unit of digital data.

Byte

Eight bits. Enough to represent 256 distinct values.

Binary number system

Base 2, using only 0 and 1. Place values are 1, 2, 4, 8, 16, 32, 64, 128 reading right to left.

Converting binary to decimal

Add the place values wherever there is a 1. So 1011 is 8 + 0 + 2 + 1 = 11.

Converting decimal to binary

Repeatedly subtract the largest power of 2 that fits, writing 1 for each one used and 0 otherwise. Or divide by 2 repeatedly and read the remainders bottom to top.

Number of values in n bits

2 to the power n. Four bits give 16 values, eight bits give 256 — and this is the calculation behind almost every "how many bits do you need" question.

Why digital data is discrete

Computers store finite sequences of bits, so they can only represent a finite set of values. Continuous real-world quantities must be approximated.

Analog vs digital data

Analog data varies continuously — sound pressure, light intensity. Digital data is discrete. Converting analog to digital always involves sampling and therefore approximation.

Sampling

Measuring an analog signal at regular intervals to make it digital. More frequent samples and more bits per sample give a closer approximation and a larger file.

Round-off error

Error from storing a number with limited precision. It accumulates over repeated calculations, which is why floating-point sums can drift.

Overflow vs round-off

Overflow is a number too large to store at all. Round-off is a number stored with insufficient precision. Different failures, and the exam distinguishes them.

Abstraction

Removing detail to manage complexity, and the central idea of the whole course. A variable name, a procedure, and a high-level language are all abstractions.

Lossless compression

Reducing file size with no information lost; the original is exactly recoverable. Used where every bit matters — text, code, archives.

Lossy compression

Reducing file size by discarding information, so the original cannot be exactly recovered. Achieves far smaller files, and is acceptable where human perception will not notice.

Choosing lossy or lossless

Lossy when the file is large, perception-limited and will not be edited further — streaming video, photographs. Lossless when exactness is required or the file will be re-edited.

Metadata

Data about data — file size, creation date, author, image dimensions, location. It can reveal more than the file itself, which is why it is a privacy topic as well as a data topic.

Information vs data

Data is raw values. Information is what those values mean once they are collected, cleaned and interpreted. The exam asks what can and cannot be concluded.

Data cleaning

Removing errors, duplicates and inconsistencies before analysis — standardizing formats, handling missing values. Skipping it produces confident wrong conclusions.

Filtering data

Selecting a subset that meets a condition. Reduces the data to what a question actually needs.

Data visualization

Presenting data graphically to reveal patterns. A well-chosen chart makes a trend visible; a poorly chosen one can imply a relationship that is not there.

Correlation vs causation

Two things moving together does not mean one causes the other. A standard exam trap on the data-analysis questions.

Bias in data collection

When a dataset systematically misrepresents the population — a survey reaching only smartphone users, a sensor only in wealthy neighborhoods. The conclusions inherit the bias.

Bias in a program

Bias can enter from the data used, from the assumptions built into the algorithm, or from who was in the room when it was designed. All three are examinable.

Scalability

Whether an approach still works as the data grows. Something manageable for a hundred records may be impossible for a hundred million.

Cleaning vs filtering

Cleaning fixes bad data. Filtering removes data you do not need. Cleaning improves quality; filtering narrows scope.

Why large datasets need programs

Volume beyond human reading. Programs can search, sort, filter and summarize at a scale a person cannot, which is exactly why bias in those programs is consequential.

Open data

Data made freely available for anyone to use. Enables collaboration and verification, and raises questions about consent and privacy for the people in it.

Personally identifiable information (PII)

Data that can identify a specific individual — name, address, biometrics, and combinations that become identifying together. Location plus timestamp is often PII even when neither is alone.

Aggregating data

Combining records to produce a summary such as a count, average or total. Aggregation can protect privacy — or fail to, when the group is small enough to identify.

Text as binary

Characters are stored as numbers under an encoding such as ASCII or Unicode, and those numbers are stored as bits. There is no text at the hardware level.

Images as binary

An image is a grid of pixels, each stored as numbers for its color components. More bits per pixel means more distinguishable colors and a larger file.

Sound as binary

Sound is sampled at intervals, each sample stored as a number. Sample rate and bit depth together determine fidelity and file size.

Why the same bits can mean different things

A sequence of bits has no meaning without a convention for reading it. The same byte can be a number, a character or part of a color depending on the program.

Data compression ratio

Compressed size divided by original size. A smaller ratio means more compression; the exam usually asks you to compare two schemes rather than compute one.

Extracting information from data

Using filtering, sorting, aggregating and visualizing to answer a question the raw data does not answer directly. Name the operation, not just the conclusion.

What examiners penalize here

• Watch for **overflow**: with a fixed number of bits, the representable range is 0 to 2ⁿ − 1. A value past the top cannot be stored, so the exam expects you to say it overflows — not that it rounds or is stored fine.
• Remember the trade-off in one line: **lossless = exact but larger; lossy = smaller but permanent loss.** For a compression ratio, divide original by compressed — a bigger ratio means a smaller file.
• A correlation in data never by itself proves causation. On the exam, the safe reading of "X and Y rise together" is that they are *associated* — a possible hidden variable or reversed direction must be ruled out before claiming cause.
• When a scenario describes collecting data, scan for two things: is the **sample representative**, and was there **consent/privacy** protection? Those are the two questions the exam repeatedly rewards you for asking.

Practice CS Principles

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

Questions about this unit

All 5 units of AP Computer Science Principles

1. Unit 1 · Creative Development
2. Unit 2 · Data
3. Unit 3 · Algorithms & Programming
4. Unit 4 · Computer Systems & Networks
5. Unit 5 · Impact of Computing