MathsICSE Class 8 · Chapter 22

Data Handling ICSE Class 8: Grouped Data, Bar Graphs, Pie Charts and Averages

Updated 15 October 2026 · Fact-checked

Data handling organises raw numbers so they can be read at a glance. ICSE Class 8 groups large data into class intervals with a frequency table, draws bar graphs of grouped data, draws pie charts with angle = (frequency ÷ total) × 360°, and finds the mean, median and mode of a set of observations.

What Data Handling is about

Data are facts or numbers collected for a purpose: marks in a test, heights of students, votes for a class trip. Raw data in a long list are hard to read, so we organise and represent them.

The CISCE Class VIII curriculum asks you to:

arrange ungrouped data into groups (class intervals) using tally marks and a frequency table,
represent grouped data by bar graphs and interpret them,
draw and interpret simple pie charts,
apply mean, median and mode to data with many observations.

Key words:

Frequency: how many times a value (or values in a class) occurs.
Class interval: a group such as 20–30. Its lower limit is 20, upper limit 30, class size 10, and class mark (mid-point) 25.
In the exclusive form used here, a value equal to the upper limit goes into the next class: 30 goes into 30–40, not 20–30.

Weightage: CISCE publishes no question paper, marking scheme or chapter weightage for Class VIII Mathematics: your school sets and marks the exam. Data Handling sits in the Data Handling theme of the CISCE Curriculum for Upper Primary Classes (VI-VIII).Source: CISCE Curriculum for Upper Primary Classes (VI-VIII), RDCD 2016

Key concepts

Grouping data into class intervals

When there are many different values, group them:
1. Find the range (highest − lowest).
2. Choose a sensible class size (often 5 or 10) and write the classes: 0–10, 10–20, ...
3. Go through the data once, making a tally mark in the right class for each value (group tallies in fives: ||||).
4. Count the tallies to get each frequency; check that the frequencies add up to the total number of observations.

Worked example

The marks (out of 50) of 30 students are: 42, 15, 37, 28, 45, 8, 33, 29, 41, 22, 36, 18, 47, 25, 31, 39, 12, 44, 27, 34, 21, 38, 30, 16, 43, 35, 24, 40, 32, 26. Make a frequency table with classes 0–10, 10–20, ..., 40–50.

Try it first, then show the solutionSolution

0–10: 8 → 1. 10–20: 15, 18, 12, 16 → 4.
20–30: 28, 29, 22, 25, 27, 21, 24, 26 → 8.
30–40: 37, 33, 36, 31, 39, 34, 38, 30, 35, 32 → 10 (30 goes here). 40–50: 42, 45, 41, 47, 44, 43, 40 → 7.
Check: $1 + 4 + 8 + 10 + 7 = 30$ ✓.

Answer: Frequencies 1, 4, 8, 10, 7

Parts of a class interval

For the class 20–30:

lower limit $= 20$ , upper limit $= 30$ ,
class size $=$ upper − lower $= 10$ ,
class mark $= \frac{lower + upper}{2} = 25$ .

In exclusive classes (0–10, 10–20, ...) the upper limit is not included in that class. This avoids counting a value twice.

Worked example

For the class 45–50, give the class size and class mark, and say where the value 50 is counted.

Try it first, then show the solutionSolution

Size $= 50 - 45 = 5$ ; mark $= \frac{45 + 50}{2} = 47.5$ .
50 is the upper limit, so it is counted in 50–55.

Answer: Size 5; mark 47.5; 50 goes into 50–55

Bar graphs of grouped data

To draw a bar graph of grouped data:

class intervals along the horizontal axis, frequency up the vertical axis;
bars of equal width for equal class sizes; for grouped (continuous) data the bars are drawn touching, with no gaps (this is also called a histogram);
a suitable scale (for example 1 cm = 2 students);
a title and labels on both axes.

To interpret: the tallest bar shows the class with the most observations; add bars to answer "how many scored at least 30?".

Draw-and-label checklist: title; both axes labelled with units; scale stated; equal-width bars; each bar's height matching its frequency.

Worked example

From the marks table (1, 4, 8, 10, 7), which class has the tallest bar, and how many students scored 30 or more?

Try it first, then show the solutionSolution

Tallest bar: 30–40 with frequency 10.
30 or more: $10 + 7 = 17$ students.

Answer: 30–40; 17 students

Pie charts

A pie chart shows how a whole is divided into parts, as sectors of a circle. The whole circle ( $360°$ ) stands for the total.

$Angle of a sector = \frac{frequency}{total} \times 360°$ .

Steps: find each angle, check that they add to $360°$ , draw a circle and a radius, and mark the angles one after another with a protractor. Label each sector.

To read a pie chart: $value = \frac{angle}{360°} \times total$ .

Worked example

Of 120 students, 45 like cricket, 30 football, 25 badminton and 20 other games. Find the angles for a pie chart.

Try it first, then show the solutionSolution

Each student $= \frac{360°}{120} = 3°$ .
Cricket $135°$ , football $90°$ , badminton $75°$ , others $60°$ .
Check: $135 + 90 + 75 + 60 = 360$ ✓.

Answer: $135°, 90°, 75°, 60°$

Mean, median and mode

Three ways to describe the centre of data:

Mean (average) $= \frac{sum of observations}{number of observations}$ .
Median: arrange in order; the middle value. With an even number of values, the median is the mean of the two middle values.
Mode: the value that occurs most often. There can be more than one mode, or none.

For a frequency table of values $x$ with frequencies $f$ : mean $= \frac{\sum f x}{\sum f}$ .

Worked example

Find the mean, median and mode of 4, 7, 7, 8, 9.

Try it first, then show the solutionSolution

Mean $= \frac{35}{5} = 7$ .
Already in order: the middle (3rd) value is 7.
7 occurs twice, so the mode is 7.

Answer: Mean 7, median 7, mode 7

Averages from a frequency table

With many repeated values, use a table:

mean $= \frac{\sum f x}{\sum f}$ (multiply each value by its frequency, add, divide by total frequency);
median: use the running total of frequencies to find which value is in the middle position;
mode: the value with the highest frequency.

Worked example

Books read last month by 25 students: 0 books (2 students), 1 (5), 2 (8), 3 (6), 4 (4). Find the mean, median and mode.

Try it first, then show the solutionSolution

$\sum f x = 0 + 5 + 16 + 18 + 16 = 55$ ; mean $= \frac{55}{25} = 2.2$ .
Running totals 2, 7, 15, 21, 25: the middle (13th) value lies in the 2-book group, so the median is 2.
Highest frequency is 8 (for 2 books): mode $= 2$ .

Answer: Mean 2.2, median 2, mode 2

Maths in real life: Data Handling

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Mean, median and mode

Suppose you record your daily screen time for a week: 2, 3, 1, 4, 2, 5 and 4 hours.

Find the mean, median and mode.

Try it first, then show the solutionSolution

Mean $= \frac{21}{7} = 3$ hours. In order: 1, 2, 2, 3, 4, 4, 5, so the median is 3.
2 and 4 each occur twice: two modes, 2 and 4.

Answer: Mean 3 h, median 3 h, modes 2 h and 4 h

Memory hook: Data can have more than one mode.

Pie chart

Imagine 30 classmates vote on a trip: 18 choose a hill station and 12 choose the beach.

Find the sector angles for a pie chart.

Try it first, then show the solutionSolution

Hill station $= \frac{18}{30} \times 360° = 216°$ .
Beach $= \frac{12}{30} \times 360° = 144°$ (check: $216 + 144 = 360$ ).

Answer: $216°$ and $144°$

Memory hook: Fraction of the total × 360°.

Missing value from a mean

Suppose you scored 72, 85 and 78 in three tests and want an average of 80 after the fourth.

What must you score in the fourth test?

Try it first, then show the solutionSolution

Total needed $= 4 \times 80 = 320$ .
Fourth score $= 320 - (72 + 85 + 78) = 320 - 235 = 85$ .

Answer: 85

Memory hook: Total = mean × number.

Topics in this chapter

Data Handling formula sheet

Class mark: $\frac{lower + upper}{2}$; Mid-point of a class.
Pie-chart angle: $\frac{f}{N} \times 360°$; N = total.
Mean: $\overset{x}{ˉ} = \frac{\sum x}{n}$; For a table: Σfx ÷ Σf.
Median (n odd): $(\frac{n + 1}{2}) th value$; After arranging in order.
Reading a pie chart: $value = \frac{θ}{360°} \times N$; θ = sector angle.

How the school exam asks Data Handling

The question patterns to expect, and the method that works for each.

Question type	How it is asked	Method
Frequency table	Group the given data into classes of size 10 using tally marks.	Exclusive classes; tally once; check the total.
Bar graph	Draw a bar graph for the grouped data and answer questions from it.	Scale, labels, equal-width touching bars; read bar heights.
Pie chart	Draw a pie chart of a budget or survey; or find a value from a sector angle.	Angle = f/N × 360°; check the angles add to 360°.
Mean, median, mode	Find all three for a list or a frequency table.	Sum ÷ count; order for the median; highest frequency for the mode.
Reverse averages	Find a missing value from the mean, or correct a mean after a misread value.	Total = mean × number; adjust the total.

Tricks to remember Data Handling

Short memory aids. Say each one aloud once, then use it on a question the same day.

Mean shares, median middles, mode most
Mean shares the total equally; median is in the middle; mode occurs most.
Use it when: Not mixing up the three.
Upper limit moves up
In 20–30, the value 30 moves up into 30–40.
Use it when: Grouping boundary values.
Pie = 360
Every pie chart's angles must add to exactly 360°.
Use it when: Checking your angles.
Total = mean × number
Most 'missing value' questions start by finding the total.
Use it when: Reverse mean problems.

Data Handling: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Example 1: A simple mean · 1 mark · MCQExam level

The mean of 12, 15, 11, 18 and 14 is:
(a) 13
(b) 14
(c) 15
(d) 70

Try it first, then show the solutionSolution

Sum $= 70$ .
Mean $= 70 \div 5 = 14$ .

Answer: (b)

Example 2: Parts of a class · 3 marks · Short answerExam level

For the class interval 20–30 in an exclusive frequency table, write its lower limit, upper limit, class size and class mark. In which class is the value 30 counted?

Try it first, then show the solutionSolution

Lower limit 20, upper limit 30.
Size $= 10$ ; mark $= 25$ .
30 is counted in 30–40.

Answer: 20, 30, 10, 25; 30–40

Example 3: Grouping heights · 3 marks · Short answerExam level

Heights (cm) of 25 students: 131, 138, 142, 135, 147, 140, 133, 144, 139, 150, 136, 141, 148, 134, 143, 137, 145, 132, 149, 140, 136, 146, 138, 142, 144. Make a frequency table with classes 130–135, 135–140, ..., 150–155.

Try it first, then show the solutionSolution

130–135: 131, 133, 134, 132 → 4. 135–140: 138, 135, 139, 136, 137, 136, 138 → 7.
140–145: 142, 140, 144, 141, 143, 140, 142, 144 → 8. 145–150: 147, 148, 145, 149, 146 → 5. 150–155: 150 → 1.
Check: $4 + 7 + 8 + 5 + 1 = 25$ ✓.

Answer: 4, 7, 8, 5, 1

Example 4: Reading a pie chart · 3 marks · Short answerHarder exam level

In a pie chart of a family's monthly spending of ₹1,800 on snacks and outings, the sector for outings is $72°$ . How much is spent on outings?

Try it first, then show the solutionSolution

Value $= \frac{72}{360} \times 1800$ .
$= \frac{1}{5} \times 1800$ .
$= ₹360$ .

Answer: ₹360

Example 5: Averages from a table · 4 marks · Long answerHarder exam level

In 20 matches a team scored: 0 goals in 3 matches, 1 goal in 6, 2 goals in 5, 3 goals in 4 and 4 goals in 2. Find the mean, median and mode.

Try it first, then show the solutionSolution

$\sum f x = 0 \times 3 + 1 \times 6 + 2 \times 5 + 3 \times 4 + 4 \times 2 = 36$ .
Mean $= 36 \div 20 = 1.8$ goals.
Running totals 3, 9, 14, 18, 20: the 10th and 11th values are 2, so median $= 2$ .
Mode $= 1$ (frequency 6).

Answer: Mean 1.8; median 2; mode 1

Example 6: A budget pie chart · 4 marks · Long answerHarder exam level

A family's monthly budget of ₹24,000 is: food ₹9,000, rent ₹7,200, education ₹3,600, savings ₹2,400, others ₹1,800. Find the angle of each sector.

Try it first, then show the solutionSolution

Food $= \frac{9000}{24000} \times 360° = 135°$ ; rent $= 108°$ .
Education $= 54°$ ; savings $= 36°$ .
Others $= 27°$ .
Check: $135 + 108 + 54 + 36 + 27 = 360$ ✓.

Answer: $135°, 108°, 54°, 36°, 27°$

Example 7: A misread value and an even median · 5 marks · Long answerHOTS / competency

(i) The mean of 10 numbers was found to be 15. Later it was found that 24 had been copied as 42. Find the correct mean. (ii) Find the median of 3, 5, 8, 9, 11, 14.

Try it first, then show the solutionSolution

(i) Wrong total $= 10 \times 15 = 150$ .
Correct total $= 150 - 42 + 24 = 132$ .
Correct mean $= 132 \div 10 = 13.2$ .
(ii) Six values (even): the middle two are 8 and 9.
Median $= \frac{8 + 9}{2} = 8.5$ .

Answer: (i) 13.2 (ii) 8.5

Case-study practice (Section B style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 10-mark question split into 3 + 3 + 4 marks.

The class test

Suppose these are the marks (out of 50) of 30 students in a second class test: 42, 17, 30, 25, 7, 36, 21, 45, 13, 28, 33, 40, 23, 19, 38, 9, 26, 48, 31, 22, 11, 35, 44, 29, 14, 39, 24, 46, 27, 34. The pass mark is 30.

(i) · 3 marks
Make a frequency table with classes 0–10, 10–20, 20–30, 30–40, 40–50.
Answer
Answer: 2, 5, 9, 8, 6
Tally each value into its class (30 and 40 go into 30–40 and 40–50): 0–10: 7, 9 → 2; 10–20: 17, 13, 19, 11, 14 → 5; 20–30: 25, 21, 28, 23, 26, 22, 29, 24, 27 → 9; 30–40: 30, 36, 33, 38, 31, 35, 39, 34 → 8; 40–50: 42, 45, 40, 48, 44, 46 → 6. Total 30 ✓.
(ii) · 3 marks
Find the angle of each sector if the table is shown as a pie chart.
Answer
Answer: $24°, 60°, 108°, 96°, 72°$
Each student $= \frac{360°}{30} = 12°$ . Angles: $24°, 60°, 108°, 96°, 72°$ (sum $360°$ ).
(iii) · 4 marks
How many students passed, and what percentage is that? Which class is the modal class (highest frequency)?
Answer
Answer: 14 students, about 46.7%; 20–30
Passed $= 8 + 6 = 14$ . Percentage $= \frac{14}{30} \times 100 \approx 46.7%$ . The class 20–30 has the highest frequency (9).

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Find the mean, median and mode of 3, 5, 5, 6, 8, 9, 13. (3 marks)

Step	Marks
Mean $= \frac{49}{7} = 7$	1
Median (4th value in order) $= 6$	1
Mode $= 5$	1

Group these 12 values into classes 0–10, 10–20, 20–30: 5, 12, 18, 23, 7, 15, 28, 21, 9, 26, 14, 19. Name the class with the highest frequency. (4 marks)

Step	Marks
Classes written correctly with tally columns	1
0–10: 5, 7, 9 → 3	1
10–20: 12, 18, 15, 14, 19 → 5; 20–30: 23, 28, 21, 26 → 4	1
Total 12 ✓; highest frequency: 10–20	1

In a survey of 72 students, the fruits liked best were: mango 24, apple 18, banana 12, grapes 18. Find the angles for a pie chart and describe how to draw it. (5 marks)

Step	Marks
Each student $= \frac{360°}{72} = 5°$	1
Mango $120°$ , apple $90°$	1
Banana $60°$ , grapes $90°$	1
Check: $120 + 90 + 60 + 90 = 360$ ✓	1
Draw a circle and a radius; mark each angle in turn with a protractor; label each sector	1

Where students lose marks in Data Handling

The slips examiners see most often, and what to write instead.

Mistake: Putting a boundary value in the wrong class
In exclusive classes the upper limit belongs to the next class.
Wrong working
30 counted in 20–30
Right working
30 counted in 30–40
Do this: Write the rule at the top of your table.
Usually costs: 1 mark, and a wrong total.
Mistake: Finding the median without ordering
The median is the middle of the ordered data.
Wrong working
Median of 7, 2, 9, 4, 5, 8, 1 is 4 (the middle as written)
Right working
Ordered: 1, 2, 4, 5, 7, 8, 9; median 5
Do this: Always arrange the data first.
Usually costs: 1 mark.
Mistake: Pie-chart angles that do not add to 360°
Usually an arithmetic slip or rounding.
Do this: Add the angles before drawing; fix any error.
Usually costs: Accuracy marks.
Mistake: Gaps between bars for grouped data
Grouped classes run on continuously.
Do this: Draw bars of grouped data touching, with equal widths.
Usually costs: 1 mark.
Mistake: Dividing by the wrong number for the mean
For a frequency table, divide by the total frequency, not by the number of rows.
Wrong working
Mean $= 36 \div 5$
Right working
Mean $= 36 \div 20 = 1.8$
Do this: Divide by Σf.
Usually costs: The answer.

Practice questions on Data Handling

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQExam level
The mode of 2, 3, 3, 5, 5, 5, 6 is:
(a) 3
(b) 4
(c) 5
(d) 6
Hint
Most frequent value.
Answer
(c)
Q2 · 1 mark · Very short answerExam level
Find the mean of 2, 4, 6, 8, 10.
Hint
Sum ÷ 5.
Answer
6.
Q3 · 2 marks · Short answerExam level
Find the median of 7, 2, 9, 4, 5, 8, 1.
Hint
Order first.
Answer
1, 2, 4, 5, 7, 8, 9; median 5.
Q4 · 2 marks · Short answerHarder exam level
In a pie chart, an item makes up 25% of the total. What is its sector angle?
Hint
25% of 360°.
Answer
$90°$ .
Q5 · 1 mark · Assertion-reasonHarder exam level
Assertion (A): The sector angles of a pie chart always add up to $360°$ .
Reason (R): The whole circle represents the total of the data.
(a) (A) is true and (R) is false.
(b) (A) is false and (R) is true.
(c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
(d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).
Hint
Parts of the whole.
Answer
(c)
Q6 · 3 marks · Short answerHarder exam level
Find the mean and the median of 45, 50, 55, 60, 65, 70.
Hint
Even count: average of the middle two.
Answer
Mean $= 345 \div 6 = 57.5$ ; median $= \frac{55 + 60}{2} = 57.5$ .
Q7 · 2 marks · Short answerHarder exam level
A pie chart shows how 1440 students travel to school. The sector for cycling is $40°$ . How many students cycle?
Hint
$\frac{40}{360} \times 1440$ .
Answer
160 students.
Q8 · 3 marks · Short answerHarder exam level
Group 31, 44, 38, 52, 47, 35, 59, 41, 33, 56, 49, 42 into classes 30–40, 40–50, 50–60.
Hint
Tally each value.
Answer
30–40: 31, 38, 35, 33 → 4; 40–50: 44, 47, 41, 49, 42 → 5; 50–60: 52, 59, 56 → 3 (total 12).
Q9 · 3 marks · Short answerHarder exam level
The mean of 8 numbers is 12 and the mean of another 5 numbers is 9. Find the mean of all 13 numbers.
Hint
Find both totals.
Answer
Totals 96 and 45; combined mean $= \frac{141}{13} \approx 10.85$ .
Q10 · 2 marks · Short answerHarder exam level
The mean of 10, 20, 30, 40, 50 is 30. What is the mean if 5 is added to every number? Explain.
Hint
The total grows by 5 × 5.
Answer
35: the total rises by 25, so the mean rises by $25 \div 5 = 5$ .
Q11 · 3 marks · Short answerHOTS / competency
The mean of six numbers is 20. Five of them are 17, 23, 19, 21 and 22. Find the sixth.
Hint
Total = 6 × 20.
Answer
Total $= 120$ ; known sum $= 102$ ; sixth $= 18$ .
Q12 · 4 marks · Long answerHOTS / competency
The mean of five numbers is 40. If one of them is increased by 10, what is the new mean? Would the median always change too? Explain.
Hint
New total = 210.
Answer
New mean $= 210 \div 5 = 42$ . The median need not change: if the increased number was already above the middle value (and stays above it), the middle value is the same.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What is frequency?Show answer
The number of times a value (or values in a class) occurs.
2.Class mark of 40–50?Show answer
45.
3.Angles of a pie chart add up to?Show answer
360°.
4.Mean of 2, 4, 9?Show answer
5.
5.Median of 3, 1, 7?Show answer
3.
6.Mode of 4, 6, 6, 7, 4, 6?Show answer
6.
7.A sector of 90° shows what fraction of the total?Show answer
One-quarter.
8.Size of class 15–20?Show answer
5.

Best order to study it

Learn frequency, tally marks and the parts of a class interval.
Group raw data into exclusive classes and check totals.
Draw and read bar graphs of grouped data.
Draw and read pie charts.
Finish with mean, median and mode, including from tables and reverse problems.

Quick revision checklist

The night before the exam: can you do each of these without looking?

Did you put upper-limit values into the next class?
Do your frequencies add up to the total?
Are your bars equal in width, touching, with a stated scale?
Do your pie-chart angles add to 360°?
Did you order the data before finding the median?
For a table, did you divide Σfx by Σf?

Data Handling: frequently asked questions

Why do we group data?

With many different values, a list or a one-value-per-row table is hard to read. Grouping into classes shows the pattern at a glance.

What is the difference between a bar graph and a pie chart?

A bar graph compares amounts using bar heights. A pie chart shows how a whole is divided, using sector angles out of 360°.

Can there be no mode?

Yes. If every value occurs the same number of times (for example once each), there is no single mode.

Which average should I use?

The mean uses every value; the median is not pulled by a few very large or small values; the mode tells you the most common value.

What are exclusive and inclusive classes?

Exclusive classes share limits (10–20, 20–30) and exclude the upper limit. Inclusive classes do not share limits (10–19, 20–29). This page uses exclusive classes, as is usual for continuous data.

Based on: CISCE Curriculum for Upper Primary Classes (VI-VIII), Mathematics (Class VIII); CISCE RDCD: Curriculum Pre-School to Class VIII