Introduction
HSA Notes brings short, clear, exam focused notes designed to help Class 9 SSC Part One Matric students score 90 plus marks in Punjab Board exams under the New Book 2026 to 2027 session. This page covers Unit 12, Information Handling, from Exercise 12.1, 12.2 & Review Exercise 12 including reading class limits, midpoints, frequencies, and class size directly from a grouped frequency distribution table.
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HSA Notes Features
- Short, easy to remember definitions.
- Step by step solutions for every question.
- Tricks and memory aids for faster revision.
- Exact alignment with the PCTB and PECTAA textbook.
- Statistics simplified into a clear, repeatable method.
- Past paper pattern questions included throughout.
- A fast revision format built for last minute review.
- Trusted by Punjab students.
Available Across All Punjab Boards and Top Schools
These notes are built for students across all Punjab Boards, including Lahore, Gujranwala, Rawalpindi, Faisalabad, Bahawalpur, Multan, Sargodha, Sahiwal, and DG Khan, and are used at top schools including The City School, Beaconhouse, Roots International, Lahore Grammar School, Karachi Grammar School, Froebel’s, The Educators, Army Public School, Divisional Public School, and Government Model School.
Exercise 12.1, Frequency Distribution
| No. | Question | Answer |
|---|---|---|
| i | Upper limit of the last class | 53 |
| ii | Lower limit of the class 39–43 | 39 |
| iii | Midpoint of the class 34–38 | 36 |
| iv | Frequency of the class 29–33 | 6 |
| iv | Frequency of the class 44–48 | 15 |
| v | Class size | 5 |
| vi | Class with the minimum number of students | 24–28 |
| vii | Lower limit of the class with a frequency of 15 | 44 |
View the PDF for the full frequency distribution table.
How to Read Class Limits, Midpoints, and Class Size
A grouped frequency distribution organises raw data into classes, or intervals, such as 29–33 or 44–48, each covering a fixed range of values. The lower limit of a class is the smallest value it can contain, shown as the first number in the interval, while the upper limit is the largest value it can contain, shown as the last number.
The midpoint, also called the class mark, is found by adding the lower and upper limits together and dividing by 2; for the class 34–38, this gives (34 + 38) divided by 2, which equals 36. The class size, sometimes called the class width, is the difference between the lower limits of two consecutive classes, or equivalently the upper limit minus the lower limit plus 1 when the data is made up of whole numbers; here, moving from one class to the next, such as from 29–33 to 34–38, shows a consistent class size of 5 throughout the table.
How to Read Frequencies from the Table
The frequency of a class is simply the count of data values, often the number of students, that fall within that class’s range, and it is read directly from the frequency column next to the matching class interval.
To answer a question that gives a frequency and asks for the class, scan down the frequency column until the matching number is found, then read across to that row’s class interval; for a frequency of 15, this points to the class 44–48, giving a lower limit of 44.
To answer a question that asks which class has the fewest or most students, compare every value in the frequency column directly rather than estimating, since classes with similar-looking frequencies are a common source of small mistakes under exam pressure; scanning the full column here shows that 24–28 holds the smallest frequency of all the listed classes.
Why This Unit Matters for Your Overall Score
Information handling turns raw, unsorted data into a form that is easy to read and compare, and every later topic in statistics, including measures of central tendency and measures of dispersion, is built on being able to read a frequency distribution table correctly first.
Getting comfortable with class limits, midpoints, class size, and frequency now means later calculations, such as finding the mean or the mode from grouped data, go smoothly instead of being slowed down by basic table-reading errors.
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Frequently Asked Questions
How do I find the midpoint of a class? Add the lower limit and the upper limit of the class together, then divide the sum by 2.
How do I find the class size? Subtract the lower limit of one class from the lower limit of the next consecutive class; the result is the same for every class in a properly constructed table.
What does the frequency of a class represent? It is the number of data values, such as students or observations, that fall within that class’s range.
Are these notes aligned with the PCTB and PECTAA textbook? Yes, these notes are built to exactly match the PCTB and PECTAA New Book for Class 9 Mathematics for the 2026 to 2027 session.
Conclusion
With Exercise 12.1 fully solved, covering class limits, midpoints, class size, and frequency readings, Class 9 students have a strong foundation for Unit 12, Information Handling. Use these notes alongside regular practice with past papers to build the confidence needed for 90 plus marks in your Punjab Board exam.
Best of luck for your Class 9 Mathematics exam!