Which of the following is an example of unstructured data?

Video recordings of classroom lectures

A table of students' roll numbers and marks

Video recordings of classroom lectures

A railway timetable listing trains and times

A bank statement with date, amount and balance columns

The data 10, 12, 14, 16, 98 contains one extreme value. Which statement is correct?

The mean (30) is pulled far above most values, while the median (14) is not

The median (14) is pulled towards 98, while the mean is unaffected

Both the mean and the median equal 30 here

Neither measure can be calculated when an outlier is present

Assertion (A): If 5 is added to every value in a data set, its standard deviation does not change. Reason (R): Adding the same constant to every value leaves the mean of the data unchanged.

Both A and R are true, and R is the correct explanation of A

Both A and R are true, but R is not the correct explanation of A

Understanding Data

Marks in a register, readings from a weather sensor, the photos on a phone — all of it is data, and almost every program exists to collect, store or process some of it. This chapter looks at what data is and the forms it takes, how it is collected, where it is stored, and what processing turns it into. It then covers the handful of statistical measures used to summarise a set of numbers: three that describe its centre — mean, median and mode — and two that describe how spread out it is — range and standard deviation. The paper asks for these as short calculations, so work each one through on the examples.

Data and Its Types

Data is a collection of raw facts — numbers, text, images, sounds — that by themselves may carry little meaning. When data is organised and processed so that it answers a question, it becomes information: a list of each student's marks is data; the class average and the topper's name, drawn from it, are information. Data helps an organisation take decisions, from a shop deciding what to restock to a government planning schools from census figures.

Structured and unstructured data
Type	What it is	Examples
Structured	organised in a fixed format, typically rows and columns, so it is easy to search and analyse	a marks register, a train timetable, a bank statement, a table in a database
Unstructured	no predefined row-and-column format	photographs, audio and video recordings, e-mails, social-media posts, scanned letters

Collecting, Storing and Processing Data

Data collection means identifying the sources that can supply the data a question needs and gathering it — through forms and surveys, sensors and instruments, transactions recorded by a system, or data already published by organisations and government portals.
Data storage keeps the collected data for later use, as files or in databases, on devices such as hard disk drives, solid state drives, CDs and DVDs, pen drives and memory cards, or on remote servers in the cloud.
Data processing turns data into information through a cycle of input → process → output: data is entered, then classified, sorted, calculated or summarised, and the results are presented — an examination board turning answer-sheet marks into results is one such cycle.

Measures of Central Tendency: Mean, Median, Mode

A measure of central tendency is a single value that represents the centre of a set of data. The mean (arithmetic average) is the sum of the values divided by their number. The median is the middle value once the data is arranged in order; with an even number of values it is the average of the two middle ones. The mode is the value that occurs most often. Take 4, 8, 6, 5, 3, 8, 9: the sum is 43 over 7 values, so the mean is about 6.14; sorted, the data is 3, 4, 5, 6, 8, 8, 9 and the median is the fourth value, 6; 8 appears twice and every other value once, so the mode is 8.

⚠️ Sort before taking the median

The median of 12, 7, 3, 9 is not the average of 7 and 3, the two values that happen to sit in the middle as written. Sorted, the data is 3, 7, 9, 12, and the median is (7 + 9) / 2 = 8.

🎯 Why the median is sometimes preferred

The mean uses every value, so one extreme value drags it. For 10, 12, 14, 16, 98 the mean is 30 — larger than four of the five values — while the median stays at 14. When data has an outlier, such as one very high salary in a small office, the median describes the typical value better.

Measures of Variability: Range and Standard Deviation

Two classes can have the same mean and very different marks — one with everyone near the average, the other split between very high and very low scores. A measure of variability (dispersion) describes that spread. The range is the simplest: largest value minus smallest. For 15, 22, 9, 30, 18 it is 30 − 9 = 21. It uses only two values, so a single outlier changes it completely.

The standard deviation (σ) uses every value. Find the mean x̄; subtract it from each value to get its deviation; square each deviation; take the mean of the squares; and take the square root: σ = √( Σ(x − x̄)² / n ). For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 40 / 8 = 5; the deviations are −3, −1, −1, −1, 0, 0, 2, 4; their squares add to 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32; 32 / 8 = 4; and σ = √4 = 2. A small standard deviation means the values cluster close to the mean; a large one means they are widely spread.

🧠 What shifting the data does

Add the same number to every value and the mean, median and mode all rise by that number, but the range and standard deviation do not change at all — every value has moved together, so the spread is the same. If every value is equal, the standard deviation is 0.

Key takeaways

Data is raw facts; processed to answer a question, it becomes information.
Structured data sits in rows and columns; images, audio, video and e-mail are unstructured.
Processing follows input → process → output; data is stored in files or databases on disks, drives or the cloud.
Mean is the average, median the middle value after sorting (average of two middles if the count is even), mode the most frequent value.
An outlier pulls the mean far more than the median.
Range = largest − smallest; standard deviation = √(Σ(x − x̄)² / n); adding a constant to every value changes neither.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

For the data 4, 8, 6, 5, 3, 8, 9, what are the median and the mode?
1. Median 6, mode 8
2. Median 5, mode 8
3. Median 6, mode 9
4. Median 8, mode 6
Show answer
Answer: A — Median 6, mode 8
Sorted, the seven values are 3, 4, 5, 6, 8, 8, 9, so the median is the fourth, 6; 8 occurs twice and every other value once, so the mode is 8. Median 5 is the middle of the data as written, before sorting. Mode 9 picks the largest value instead of the most frequent, and median 8 with mode 6 swaps the two measures.
What is the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9, taking σ = √(Σ(x − x̄)² / n)?
1. 4
2. 5
3. 7
4. 2
Show answer
Answer: D — 2
The mean is 40 / 8 = 5; the squared deviations are 9, 1, 1, 1, 0, 0, 4 and 16, adding to 32; dividing by 8 gives 4, and the square root is 2. Answering 4 stops one step early, giving the mean of the squared deviations rather than its root. 5 is the mean itself, and 7 is the range, 9 − 2, a different measure of spread.
What is the median of the values 12, 7, 3, 9?
1. 5
2. 7.75
3. 8
4. 9
Show answer
Answer: C — 8
Sorted, the values are 3, 7, 9, 12; with an even count the median is the average of the two middle values, (7 + 9) / 2 = 8. Five is the average of 7 and 3, the middle pair before sorting. 7.75 is the mean, 31 / 4, and 9 picks just one of the middle pair instead of averaging them.
Which of the following is an example of unstructured data?
1. A table of students' roll numbers and marks
2. Video recordings of classroom lectures
3. A railway timetable listing trains and times
4. A bank statement with date, amount and balance columns
Show answer
Answer: B — Video recordings of classroom lectures
A video has no predefined rows and columns that a program can search directly, which is what makes it unstructured. The marks table, the timetable and the bank statement are all organised into fixed fields — the defining feature of structured data — even though they look very different from one another.
The data 10, 12, 14, 16, 98 contains one extreme value. Which statement is correct?
1. The mean (30) is pulled far above most values, while the median (14) is not
2. The median (14) is pulled towards 98, while the mean is unaffected
3. Both the mean and the median equal 30 here
4. Neither measure can be calculated when an outlier is present
Show answer
Answer: A — The mean (30) is pulled far above most values, while the median (14) is not
The sum is 150, so the mean is 30, larger than four of the five values, because every value — including 98 — enters the average. The median is the middle value after sorting, 14, and would be the same if 98 were 20. Claiming the median is pulled while the mean is not reverses the two measures' sensitivity, and an outlier never prevents either from being calculated.
What is the range of the data 15, 22, 9, 30, 18?
1. 15
2. 18.8
3. 3
4. 21
Show answer
Answer: D — 21
The range is the largest value minus the smallest: 30 − 9 = 21. 15 is the difference between the first and last values as written, which ignores where the extremes actually are. 18.8 is the mean, 94 / 5, a measure of centre rather than spread, and 3 is not any measure of this data.
Assertion (A): If 5 is added to every value in a data set, its standard deviation does not change. Reason (R): Adding the same constant to every value leaves the mean of the data unchanged.
1. Both A and R are true, and R is the correct explanation of A
2. Both A and R are true, but R is not the correct explanation of A
3. A is true, but R is false
4. A is false, but R is true
Show answer
Answer: C — A is true, but R is false
Adding 5 to every value raises the mean by 5 as well, so each deviation x − x̄ is exactly what it was and the standard deviation is unchanged: A is true. R is false — the mean does change, by 5. It is precisely because the mean moves along with the data that the deviations stay the same, so a candidate who thinks the mean stays fixed has the right conclusion for the wrong reason.
Which of the following is a measure of variability (spread) rather than of central tendency?
1. Mean
2. Median
3. Standard deviation
4. Mode
Show answer
Answer: C — Standard deviation
Standard deviation measures how far the values lie from the mean, which is a description of spread; range is the other spread measure in the syllabus. Mean, median and mode each give a single value representing the centre of the data — two classes can share all three and still differ completely in how spread out their marks are.