Exercise 9.1 — Presentation of Data
Problems based on presentation of data.
What Exercise 9.1 Tests
Exercise 9.1 in Class 9 Statistics focuses on one central skill: reading, constructing, and interpreting frequency distribution tables. The nine questions move from simple cumulative-to-individual frequency conversion all the way to constructing grouped tables from raw data by calculating the range, class size, and number of classes. These are core 2-mark and 3-mark question types in CBSE, Telangana, and Andhra Pradesh board papers.
- Questions 1: Converting a cumulative frequency table into individual frequencies by subtraction
- Questions 2–4: Building tally-mark frequency tables from raw categorical and discrete data
- Questions 5–6: Reading frequency data from bar graphs and bar charts
- Questions 7–9: Constructing grouped frequency distribution tables with class intervals
Question 1 — Cumulative to Individual Frequencies
The given table shows cumulative totals — "up to 5" means 5 students scored 5 or below, "up to 6" means 11 students scored 6 or below, and so on. To find how many students scored exactly each mark, subtract successive cumulative values.
| Marks | Up to 5 | Up to 6 | Up to 7 | Up to 8 | Up to 9 | Up to 10 |
|---|---|---|---|---|---|---|
| No. of Students | 5 | 11 | 19 | 31 | 40 | 45 |
Solution — Subtract Consecutive Cumulative Values
| Mark | 5 | 6 | 7 | 8 | 9 | 10 | Total |
|---|---|---|---|---|---|---|---|
| Frequency | 5 | 6 | 8 | 12 | 9 | 5 | 45 |
Question 2 — Blood Group Frequency Table
The raw data contains 36 entries — a mix of A, B, O, and AB. Count each blood group using tally marks, where each group of 5 is represented as four vertical strokes crossed by a diagonal.
| Blood Group | Tally Marks | No. of Students (Frequency) |
|---|---|---|
| O | 𝄷𝄷𝄷 (15) | 15 |
| A | 𝄷𝄷 (10) | 10 |
| B | 𝄷𝄷|||| (9) | 9 |
| AB | || (2) | 2 |
| Total | — | 36 |
Question 3 — Coin Toss Experiment
When 3 coins are tossed, the possible outcomes for number of heads are 0, 1, 2, or 3. Count how many times each outcome appeared across the 30 tosses.
| No. of Heads | Tally Marks | Frequency |
|---|---|---|
| 0 | ||| (3) | 3 |
| 1 | 𝄷𝄷 (10) | 10 |
| 2 | 𝄷𝄷 (10) | 10 |
| 3 | 𝄷𝄷|| (7) | 7 |
| Total | — | 30 |
Question 4 — SMS Poll on Smoking Prohibition
This is a real-world application of frequency distribution — political polling uses exactly this method. Count each option letter from the raw data string of 65 responses.
| Option | Meaning | Tally Marks | Frequency |
|---|---|---|---|
| A | Complete prohibition | 𝄷𝄷𝄷𝄷|||| (19) | 19 |
| B | Prohibition in public places only | 𝄷𝄷𝄷𝄷𝄷𝄷𝄷| (36) | 36 |
| C | Not necessary | 𝄷𝄷 (10) | 10 |
| Total | Valid responses received | 65 | |
Question 5 — Reading a Bar Graph into a Table
Read each bar's length on the X-axis and multiply by the scale factor (5 vehicles per cm). This question tests whether you can go in the reverse direction — from a visual graph back to a numerical table.
| Type of Vehicle | Number of Vehicles (Frequency) |
|---|---|
| Cycles | 40 |
| Autos | 30 |
| Bikes | 45 |
| Cars | 25 |
Question 6 — Reading a Histogram into a Table
Reading the scale first is the critical step. The graph shows: X-axis: 1 cm = 1 class and Y-axis: 1 cm = 10 students. Read each bar's height and multiply by the Y-axis scale.
| Class | Number of Students (Frequency) | Bar Height (cm) |
|---|---|---|
| I Class | 40 | 4 cm |
| II Class | 55 | 5.5 cm |
| III Class | 65 | 6.5 cm |
| IV Class | 50 | 5 cm |
| V Class | 30 | 3 cm |
| VI Class | 15 | 1.5 cm |
Question 7 — Grouped Frequency Table (Test Marks)
The hint tells us to use class width = 10. Since the maximum mark appears to be 61, we need classes up to 70–80 to safely cover all values. Go through each data point and place it in the correct class.
| Marks (Class Interval) | Tally Marks | No. of Students (Frequency) |
|---|---|---|
| 0 – 10 | | (1) | 1 |
| 10 – 20 | |||| (4) | 4 |
| 20 – 30 | ||| (3) | 3 |
| 30 – 40 | 𝄷𝄷|| (7) | 7 |
| 40 – 50 | 𝄷𝄷|| (7) | 7 |
| 50 – 60 | 𝄷𝄷|| (7) | 7 |
| 60 – 70 | | (1) | 1 |
| 70 – 80 | — (0) | 0 |
| Total | — | 30 |
Question 8 — Electricity Bills: Calculating Number of Classes
This question introduces the important formula for calculating how many classes you need. Always compute the range first, then divide by the class size.
Range = Maximum − Minimum = 724 − 170 = 554Number of classes = Range ÷ Class size = 554 ÷ 75 = 7.3 ≈ 8
Since 7.3 classes are needed, we round up to 8 classes to ensure all data is covered. Start the first class just below the minimum value at 150.
| Electricity Bill (₹) | Tally Marks | No. of Houses (Frequency) |
|---|---|---|
| 150 – 225 | |||| (4) | 4 |
| 225 – 300 | ||| (3) | 3 |
| 300 – 375 | 𝄷𝄷|| (7) | 7 |
| 375 – 450 | 𝄷𝄷|| (7) | 7 |
| 450 – 525 | — (0) | 0 |
| 525 – 600 | | (1) | 1 |
| 600 – 675 | | (1) | 1 |
| 675 – 750 | || (2) | 2 |
| Total | — | 25 |
Question 9 — Car Battery Life: Exclusive Classes with Decimal Intervals
This question uses decimal data and exclusive class intervals — the upper boundary of each class is not included, so 2.5 goes into the 2.5–3.0 class, not 2.0–2.5. The class width is 0.5 years.
| Lifetime (years) | Tally Marks | No. of Batteries (Frequency) |
|---|---|---|
| 2.0 – 2.5 | || (2) | 2 |
| 2.5 – 3.0 | 𝄷𝄷| (6) | 6 |
| 3.0 – 3.5 | 𝄷𝄷𝄷𝄷|||| (14) | 14 |
| 3.5 – 4.0 | 𝄷𝄷| (11) | 11 |
| 4.0 – 4.5 | |||| (4) | 4 |
| 4.5 – 5.0 | ||| (3) | 3 |
| Total | — | 40 |
Exercise 9.1 — All Questions at a Glance
What Exercise 9.1 Prepares You For
Constructing frequency distribution tables is the essential first step for everything that follows in statistics. In the next part of Chapter 9, you will use these same tables to draw histograms and frequency polygons — visual representations of grouped data. The grouped tables from Questions 7, 8, and 9 feed directly into histogram construction.
In Class 10 Statistics, the frequency distribution table is used to calculate mean (by the assumed mean and step deviation methods), median (using the median formula and cumulative frequency), and mode (from the modal class). Getting comfortable with class intervals and tally marking in Class 9 makes these Class 10 calculations straightforward.
For Telangana and Andhra Pradesh SSC exams, Exercise 9.1 style questions — particularly building a grouped table from raw data (like Q7, Q8, Q9) — appear as 4-mark questions. The formula Number of classes = Range ÷ Class size from Question 8 is a frequently tested 1-mark fill-in-the-blank item.