Statistics (Classification of Data, Tabulation) — ICSE Class 9 Maths Important Questions
13 ICSE Class 9 Maths practice questions on Statistics (Classification of Data, Tabulation), each with a full model answer, covering 5 topics from the chapter in the question formats used in the exam.
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Reviewed by Classmate AI Team · 16 October 2026
Last updated 25 October 2026
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- Key concepts
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ICSE Statistics (classification and tabulation) questions test converting raw data into frequency distributions, forming class intervals with correct class size and class marks, using tally marks, and reading inclusive versus exclusive classes. Expect range, class mark =(lower+upper)/2, class size, and tabulation of ungrouped and grouped data.
About Statistics (Classification of Data, Tabulation)
In the ICSE Class 9 Maths chapter Statistics (Classification of Data and Tabulation) you organise raw data into a readable form. You learn range, tally marks, frequency, discrete and continuous distributions, class intervals, class limits, class size, class marks, and the difference between inclusive and exclusive classes. The chapter builds the frequency tables that later support mean, median and graphical representation.
Key concepts & formulas
Range = (highest observation) - (lowest observation). Class size (width) = upper limit - lower limit of a class.
Class mark (mid-value) =(lower class limit+upper class limit)/2. It represents the whole class in later calculations.
Exclusive classes (e.g. 10–20, 20–30) have no gap and the upper limit belongs to the next class. Inclusive classes (e.g. 10–19, 20–29) leave a gap; adjustment factor =gap/2 converts them to exclusive form.
A frequency distribution lists each value (or class) with its frequency, found using tally marks. The sum of all frequencies equals the total number of observations N.
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Important questions with answers
Try each on paper first, then reveal the model answer to check your method.
Multiple-choice questions (1 mark)
The class mark of the class interval 25–35 is:
- (a)
25
- (b)
30
- (c)
35
- (d)
10
Show model answer
Answer: (b) 30.
Class mark =(25+35)/2=60/2=30.
The range of the data 18, 5, 27, 12, 33, 9 is:
- (a)
33
- (b)
28
- (c)
27
- (d)
14
Show model answer
Answer: (b) 28.
Range = highest - lowest =33-5=28.
In an exclusive frequency distribution with classes 0–10, 10–20, 20–30, the observation 20 is placed in the class:
- (a)
0–10
- (b)
10–20
- (c)
20–30
- (d)
Both 10–20 and 20–30
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Answer: (c) 20–30.
In exclusive classes the upper limit belongs to the next class, so 20 falls in the class 20–30, not in 10–20.
The inclusive class 15–24 is converted to exclusive form. Its true (exclusive) class limits are:
- (a)
15–24
- (b)
14.5–24.5
- (c)
15.5–23.5
- (d)
14–25
Show model answer
Answer: (b) 14.5–24.5.
The gap between 24 and the next lower limit 25 is 1; adjustment factor =1/2=0.5. Subtract 0.5 from the lower limit and add 0.5 to the upper limit: 15-0.5=14.5 and 24+0.5=24.5.
Assertion–Reason questions (1 mark)
Assertion (A): The class marks of the classes 10–20 and 20–30 are 15 and 25.
Reason (R): The class mark of a class is the average of its lower and upper class limits.
- (a)
Both A and R are true and R is the correct explanation of A
- (b)
Both A and R are true but R is not the correct explanation of A
- (c)
A is true but R is false
- (d)
A is false but R is true
Show model answer
Answer: (a) Class mark =(lower+upper)/2, giving (10+20)/2=15 and (20+30)/2=25. R correctly explains how the marks in A are found.
Very short answer questions (2 marks)
For the class interval 47–59, find (i) the class size and (ii) the class mark.
Show model answer
(i) Class size = upper limit - lower limit =59-47=12.
(ii) Class mark =(47+59)/2=106/2=53.
The class marks of a continuous distribution are 12, 17, 22, 27. Find the class size and write the class interval whose class mark is 17.
Show model answer
The class size = difference between consecutive class marks =17-12=5.
For class mark 17 with size 5, half the size =5/2=2.5.
Lower limit =17-2.5=14.5, upper limit =17+2.5=19.5.
The class interval is 14.5–19.5.
Short answer questions (3 marks)
The marks scored by 20 students are:
5, 8, 6, 5, 7, 8, 9, 6, 5, 8, 7, 6, 5, 9, 8, 7, 6, 5, 8, 7.
Make a discrete (ungrouped) frequency distribution table using tally marks.
Show model answer
Counting each value:
| Marks | Tally | Frequency |
|---|---|---|
| 5 | | | | | | 5 |
| 6 | | | | | | 4 |
| 7 | | | | | | 4 |
| 8 | | | | | | 5 |
| 9 | | | | 2 |
Marks 5 occurs 5 times, 6 occurs 4 times, 7 occurs 4 times, 8 occurs 5 times, and 9 occurs 2 times.
Total frequency =5+4+4+5+2=20, which matches the number of students.
The daily wages (in rupees) of 25 workers are:
210, 235, 250, 205, 245, 260, 215, 230, 255, 240, 220, 265, 235, 250, 210, 245, 260, 225, 230, 255, 240, 215, 250, 235, 245.
Form a grouped frequency distribution with class intervals 200–220, 220–240, 240–260, 260–280 (exclusive).
Show model answer
Sorting each wage into the exclusive classes (upper limit belongs to the next class):
| Class (Rs) | Tally | Frequency |
|---|---|---|
| 200–220 | | | | | | 5 |
| 220–240 | | | | | | | | 7 |
| 240–260 | | | | | | | | | | 10 |
| 260–280 | | | | | 3 |
200–220: 210,205,215,210,215 = 5.
220–240: 235,230,220,235,225,230,235 = 7.
240–260: 250,245,255,240,250,245,240,255,250,245 = 10.
260–280: 260,265,260 = 3.
Total =5+7+10+3=25, matching the number of workers.
The following is an inclusive frequency distribution. Convert it to an exclusive (continuous) distribution and write the class marks.
| Class | Frequency |
|---|---|
| 1–10 | 4 |
| 11–20 | 7 |
| 21–30 | 9 |
| 31–40 | 5 |
Show model answer
Gap between classes =11-10=1, so adjustment factor =1/2=0.5. Subtract 0.5 from each lower limit and add 0.5 to each upper limit.
| Exclusive class | Frequency | Class mark |
|---|---|---|
| 0.5–10.5 | 4 | 5.5 |
| 10.5–20.5 | 7 | 15.5 |
| 20.5–30.5 | 9 | 25.5 |
| 30.5–40.5 | 5 | 35.5 |
Each class mark =(lower+upper)/2, e.g. (0.5+10.5)/2=5.5. The frequencies stay unchanged.
Long answer questions (5 marks)
The number of goals scored by a team in 30 matches is:
2, 0, 3, 1, 2, 4, 0, 1, 3, 2, 1, 0, 2, 3, 1, 4, 2, 0, 1, 3, 2, 1, 0, 2, 4, 3, 1, 2, 0, 1.
(i) Make a discrete frequency distribution with tally marks.
(ii) State the range.
(iii) How many matches had at least 2 goals?
(iv) Which score(s) occurred most often?
Show model answer
(i) Frequency distribution:
| Goals | Tally | Frequency |
|---|---|---|
| 0 | | | | | | | 6 |
| 1 | | | | | | | | | 8 |
| 2 | | | | | | | | | 8 |
| 3 | | | | | | 5 |
| 4 | | | | | 3 |
Total =6+8+8+5+3=30 matches.
(ii) Range = highest - lowest =4-0=4.
(iii) At least 2 goals means score 2, 3 or 4: 8+5+3=16 matches.
(iv) The highest frequency is 8, shared by scores 1 and 2, so 1 goal and 2 goals occurred most often (8 matches each).
The heights (in cm) of 40 saplings are recorded. A grouped distribution is given below, but two frequencies are missing. If the total frequency is 40 and the class 30–40 has twice the frequency of class 10–20, find the missing frequencies and the class marks.
| Class (cm) | Frequency |
|---|---|
| 0–10 | 5 |
| 10–20 | a |
| 20–30 | 11 |
| 30–40 | b |
| 40–50 | 6 |
Show model answer
Total frequency: 5+a+11+b+6=40, so a+b=18. \quad(1)
Given the class 30–40 has twice the frequency of 10–20: b=2a. \quad(2)
Substitute (2) into (1): a+2a=18⇒3a=18⇒ a=6. Then b=2×6=12.
So the missing frequencies are a=6 (class 10–20) and b=12 (class 30–40).
Class marks =(lower+upper)/2:
| Class | Frequency | Class mark |
|---|---|---|
| 0–10 | 5 | 5 |
| 10–20 | 6 | 15 |
| 20–30 | 11 | 25 |
| 30–40 | 12 | 35 |
| 40–50 | 6 | 45 |
Check: 5+6+11+12+6=40.
Case-based questions (4 marks)
A shopkeeper records the amount (in rupees) spent by 30 customers in a morning:
120, 85, 60, 150, 95, 45, 110, 130, 75, 90, 55, 140, 100, 65, 115, 80, 125, 50, 105, 70, 135, 90, 60, 145, 85, 100, 55, 120, 95, 75.
Use class intervals 40–70, 70–100, 100–130, 130–160 (exclusive).
(i) State the range of the data.
(ii) What is the class size?
(iii) Prepare the grouped frequency table.
(iv) How many customers spent Rs 100 or more?
Show model answer
(i) Range = highest - lowest =150-45=105.
(ii) Class size =70-40=30.
(iii) Grouped frequency table (the upper limit goes to the next class, so 70 belongs to 70–100):
| Class (Rs) | Frequency |
|---|---|
| 40–70 | 7 |
| 70–100 | 10 |
| 100–130 | 8 |
| 130–160 | 5 |
40–70: 60, 45, 55, 65, 50, 60, 55 = 7.
70–100: 85, 95, 75, 90, 80, 70, 90, 85, 95, 75 = 10.
100–130: 120, 110, 100, 115, 125, 105, 100, 120 = 8.
130–160: 150, 130, 140, 135, 145 = 5.
Total =7+10+8+5=30.
(iv) Rs 100 or more falls in classes 100–130 and 130–160: 8+5=13 customers.
All ICSE Class 9 Maths Chapters
Frequently asked questions
What are the important questions in ICSE Class 9 Statistics (classification and tabulation)?
Range, class size and class marks, frequency distributions with tally marks, converting inclusive classes to exclusive ones, and finding missing frequencies. This page has 13 questions with answers, including a shopkeeper's customer-spending case study.How do you find the class mark and class size?
Class mark =(lower limit+upper limit)/2, so 25–35 has class mark 30. Class size is the difference between consecutive class marks or limits; class marks 12, 17, 22, 27 give a size of 5 and classes 9.5–14.5, 14.5–19.5, and so on.How do you convert inclusive classes to exclusive classes?
Find the gap between one class's upper limit and the next class's lower limit, halve it, then subtract that from every lower limit and add it to every upper limit. With a gap of 1, the class 15–24 becomes 14.5–24.5.In which class does an observation on a boundary go?
In an exclusive distribution such as 0–10, 10–20, 20–30, the upper limit is not included, so the value 20 is counted in 20–30. Getting this right matters when you tally raw data.Which ICSE Class 9 chapter comes after classification of data?
Mean and Median (Chapter 19) uses the frequency tables you build in Statistics (Chapter 18) to calculate averages. Both have important-questions pages on Classmate AI, linked from the ICSE Class 9 Maths chapter list.What do statistical calculations on classified data depend on?
On class marks: once data is grouped, each class is represented by its mid-value, so every later calculation of mean or median uses class marks and frequencies rather than the original observations. Choosing sensible, equal class sizes keeps those results reliable.Can I download ICSE Class 9 Statistics tabulation questions?
Yes. Enter your email in the free PDF box on this page and the 13 tabulation questions, raw-data tables included, open with full answers as a printable worksheet to save as a PDF.
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