Class 10 Maths Chapter 11 Exercise 11.1 Solutions 2026 – Information Handling Notes PDF

Unit 11: Information Handling | Exercise 11.1 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 11.1 solutions for Information Handling have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Turning Raw Data into a Running Total

A frequency table shows how often each value or class occurs, but it doesn’t immediately show how many data points fall below a certain point. Exercise 11.1 introduces cumulative frequency — a running total of frequencies — along with the ogive, a graph that turns this running total into a visual tool for finding quartiles, deciles, and percentiles.

Key Concepts Covered in Exercise 11.1

Cumulative Frequency

The cumulative frequency of a class is the sum of its own frequency and the frequencies of every class before it. This running total shows exactly how many data points fall at or below the upper boundary of each class.

The Ogive (Cumulative Frequency Curve)

An ogive is a smooth curve or polygon plotted with class upper boundaries on the x-axis and cumulative frequencies on the y-axis. Because cumulative frequency only increases, an ogive always rises from left to right.

Quartiles, Deciles, and Percentiles

These are values that divide ordered data into equal parts: quartiles divide it into 4 parts, deciles into 10, and percentiles into 100. The median is the same as the second quartile (Q2), splitting the data exactly in half.

Reading Values Off the Ogive

Once an ogive is drawn, quartiles and other measures can be read directly from the graph: locate the required cumulative frequency on the y-axis, trace across to the curve, then down to the x-axis to read the corresponding value.

Step-by-Step Solved Examples

Q. No. 1: Complete the cumulative frequency column for the frequencies 5, 8, 12, 10, 5 (total = 40).

Class 1: cf = 5

Class 2: cf = 5 + 8 = 13

Class 3: cf = 13 + 12 = 25

Class 4: cf = 25 + 10 = 35

Class 5: cf = 35 + 5 = 40 (matches the total, confirming the table is correct)

Q. No. 2: For a data set of 40 values, find the position of the median (Q2) and the first quartile (Q1) in terms of cumulative frequency.

Median (Q2) position: n/2 = 40/2 = 20th value

First quartile (Q1) position: n/4 = 40/4 = 10th value

Q. No. 3: Using the cumulative frequency table from Q. No. 1, identify which class contains the median (the 20th value).

The cumulative frequency reaches 13 by the end of Class 2, and 25 by the end of Class 3.

Since the 20th value falls between 13 and 25, the median lies within Class 3.

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 11.1 in the same numbered, step-by-step format, including full ogive diagrams.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on what fraction of the data a given quartile or percentile represents
• Short Questions: Completing a cumulative frequency column, like Q. No. 1 above
• Long Questions: Drawing a full ogive and reading off quartiles graphically

Where This Matters Beyond This Exercise

Cumulative frequency and the ogive are the graphical foundation for the measures of central tendency and dispersion covered in the next exercise, since several of those measures can be estimated directly from the ogive as a visual check. Cumulative data and percentiles are also used constantly in real-world reporting — exam result distributions, income brackets, and growth charts all rely on this exact idea.

Common Mistakes Students Make in Exercise 11.1

• Forgetting that cumulative frequency only ever increases, never decreases, down the table
• Plotting the ogive against the class midpoint instead of the upper class boundary
• Confusing the position formula for the median (n/2) with quartile positions (n/4, 3n/4)
• Misreading which class an estimated value falls into when the target frequency lands exactly on a class boundary

Why This Exercise Matters for the Board Exam

Cumulative frequency tables and ogive-reading questions are graded on accuracy and correct labeling, and are a common, reliable long-question type in the statistics section. Since much of the answer depends on correctly locating the target row in the table, careful, methodical calculation matters more than speed here.

Quick Links – Chapter 11: Information Handling

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 11.1 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. What is the difference between a quartile, a decile, and a percentile?

All three divide ordered data into equal parts — quartiles into 4 parts, deciles into 10 parts, and percentiles into 100 parts. They all describe the same underlying idea of position within a data set, just at different levels of detail.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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