NCERT Solutions for Exercise 14.2 Class 10 Maths Chapter 14

Q: What do you mean by multimodal data ?

These concepts are discussed in class 10 maths ex 14.2 . T he data which have more than one value which are repeated in same frequency are called multimodal data. Practice the problems to command these concepts.

NCERT Solutions for Exercise 14.2 Class 10 Maths Chapter 14 - Statistics

Updated on 30 Apr 2025, 05:15 PM IST

Knowledge about data patterns in grouped data formats enables better interpretation of real-world trends in the data. This part of the chapter explores mode as a central tendency measure used to determine the most recurrent value in a dataset. The mode is crucial in statistical assessment, especially when data exists in interval groups. We evaluate patterns in the most recurring data points by utilising graphical and algebraic tools in this research. This exercise demonstrates to students how to calculate the mode for grouped data by using an appropriate formula.

This Story also Contains

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2
Assess NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2
Topics Covered in Chapter 13 Statistics: Exercise 13.2
NCERT Solutions for Class 10 Subject Wise
NCERT Exemplar Solutions of Class 10 Subject Wise

exercise 14.2

The NCERT Solutions featured here apply to the latest version of National Council of Educational Research and Training books from the 2025–2026 school year. The solutions guide students to break down the procedure of locating the modal class, then use the proper formula to find the mode. Knowledge mastery of this topic enables students to apply their learned skills in economic research and healthcare, and social science investigations because they need to find and understand dominant patterns. The exercise functions as an essential tool for solidifying the knowledge described in NCERT Books.

NCERT Solutions Class 10 Maths Chapter 13 Exercise 13.2

Download PDF

Assess NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2

Q1 The following table shows the ages of the patients admitted in a hospital during a year:

1640761737516

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer:

To find the modal class: The class having the maximum frequency is the modal class. And, the maximum frequency is 23, and hence the modal class = 35-45

Thus, Lower limit (l) of modal class = 35, class size (h) = 10

Frequency ( $f_{1}$ ) of the modal class = 23

Frequency ( $f_{0}$ ) of class preceding the modal class = 21

Frequency ( $f_{2}$ ) of class succeeding the modal class = 14.

Therefore, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) . h$

$= 35 + (\frac{23 - 21}{2 (23) - 21 - 14}) .10 = 35 + \frac{2}{11} .10$

$= 36.8$

Now,

Age	Number of patients $f_{i}$	Classmark $x_{i}$	$f_{i} x_{i}$
5-15	6	10	60
15-25	11	20	220
25-35	21	30	630
35-45	23	40	920
45-55	14	50	700
55-65	5	60	300
	$\sum f_{i}$ =80		$\sum f_{i} x_{i}$ =2830

Mean,

$\overset{―}{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$= \frac{2830}{80} = 35.37$

Therefore, the maximum number of patients is in the age group of 36.8, whereas the average age of all the patients is 35.37.

Q2 The following data gives information on the observed lifetimes (in hours) of 225 electrical components :

1640761774675

Determine the modal lifetimes of the components.

Answer:

To find the modal class: The class having the maximum frequency is the modal class. And, the maximum frequency is 61, and hence the modal class = 60-80

Thus, Lower limit (l) of modal class = 60, class size (h) = 20

Frequency ( $f_{1}$ ) of the modal class = 61

Frequency ( $f_{0}$ ) of class preceding the modal class = 52

Frequency ( $f_{2}$ ) of class succeeding the modal class = 38.

Therefore, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) . h$

$= 60 + (\frac{61 - 52}{2 (61) - 52 - 38}) .20 = 60 + \frac{9}{32} .20$

$= 65.62$

Thus, the modal lifetime of 225 electrical components is 65.62 hours

Q3 The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

1640761796831

Answer:

To find the modal class: The class having the maximum frequency is the modal class. And, the maximum frequency is 40, and hence the modal class = 1500-2000

Thus, Lower limit (l) of modal class = 1500, class size (h) = 500

Frequency ( $f_{1}$ ) of the modal class = 40

Frequency ( $f_{0}$ ) of class preceding the modal class = 24

Frequency ( $f_{2}$ ) of class succeeding the modal class = 33.

Therefore, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) . h$

$= 1500 + (\frac{40 - 24}{2 (40) - 24 - 33}) .500 = 1500 + \frac{16}{23} .500$

$= 1847.82$

Thus, the Mode of the data is Rs. 1847.82

Now,

Let the assumed mean be a = 2750 and h = 500

Expenditure	Number of families $f_{i}$	Classmark $x_{i}$	$d_{i} = x_{i} - a$	$u_{i} = \frac{d_{i}}{h}$	$f_{i} u_{i}$
1000-1500	24	1250	-1500	-3	-72
1500-2000	40	1750	-1000	-2	-80
2000-2500	33	2250	-500	-1	-33
2500-3000	28	2750	0	0	0
3000-3500	30	3250	500	1	30
3500-4000	22	3750	1000	2	44
4000-4500	16	4250	1500	3	48
4500-5000	7	4750	2000	4	28
	$\sum f_{i}$ =200				$\sum f_{i} x_{i}$ = -35

Mean,

$\overset{―}{x} = a + \frac{\sum f_{i} u_{i}}{\sum f_{i}} \times h$

$= 2750 + \frac{- 35}{200} \times 500 = 2750 - 87.5 = 2662.50$

Thus, the Mean monthly expenditure is Rs. 2662.50

Q4 The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

1640761815121

Answer:

To find the modal class: The class having the maximum frequency is the modal class. And, the maximum frequency is 10, and hence the modal class = 30-35

Lower limit (l) of modal class = 30, class size (h) = 5

Frequency ( $f_{1}$ ) of the modal class = 10

Frequency ( $f_{0}$ ) of class preceding the modal class = 9

Frequency ( $f_{2}$ ) of class succeeding the modal class = 3

Therefore, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) . h$

$= 30 + (\frac{10 - 9}{2 (10) - 9 - 3}) .5 = 30 + \frac{1}{8} .5$

$= 30.625$

Thus, the Mode of the data is 30.625

Now,

Let the assumed mean be a = 32.5 and h = 5

Class	Number of states $f_{i}$	Classmark $x_{i}$	$d_{i} = x_{i} - a$	$u_{i} = \frac{d_{i}}{h}$	$f_{i} u_{i}$
15-20	3	17.5	-15	-3	-9
20-25	8	22.5	-10	-2	-16
25-30	9	27.5	-5	-1	-9
30-35	10	32.5	0	0	0
35-40	3	37.5	5	1	3
40-45	0	42.5	10	2	0
45-50	0	47.5	15	3	0
50-55	2	52.5	20	4	8
	$\sum f_{i}$ =35				$\sum f_{i} x_{i}$ = -23

Mean,

$\overset{―}{x} = a + \frac{\sum f_{i} u_{i}}{\sum f_{i}} \times h$

$= 32.5 + \frac{- 23}{35} \times 5 = 29.22$

Thus, the Mean of the data is 29.22

Q5 The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Find the mode of the data.

Answer:

To find the modal class: The class having the maximum frequency is the modal class. And, the maximum frequency is 18, and hence the modal class = 4000-5000

Lower limit (l) of modal class = 4000, class size (h) = 1000

Frequency ( $f_{1}$ ) of the modal class = 18

Frequency ( $f_{0}$ ) of class preceding the modal class = 4

Frequency ( $f_{2}$ ) of class succeeding the modal class = 9

Therefore, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) . h$

$= 4000 + (\frac{18 - 4}{2 (18) - 4 - 9}) .1000 = 4000 + \frac{14}{23} .1000$

$= 4608.70$

Thus, the Mode of the data is 4608.70

Q6 A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

1640762258431

Answer:

To find the modal class: The class having the maximum frequency is the modal class. And, the maximum frequency is 20, and hence the modal class = 40-50

Lower limit (l) of modal class = 40, class size (h) = 10

Frequency ( $f_{1}$ ) of the modal class = 20

Frequency ( $f_{0}$ ) of class preceding the modal class = 12

Frequency ( $f_{2}$ ) of class succeeding the modal class = 11

Therefore, $M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) . h$

$= 40 + (\frac{20 - 12}{2 (20) - 12 - 11}) .10 = 40 + \frac{8}{17} .10$

$= 44.70$

Thus, the Mode of the data is 44.70

Also Read-

Aakash Repeater Courses

Take Aakash iACST and get instant scholarship on coaching programs.

Apply

Topics Covered in Chapter 13 Statistics: Exercise 13.2

1. Understanding Mode for Grouped Data: Learning Mode for Grouped Data shows how this statistical value represents the dominant entry, which occurs most often, especially when data is grouped into intervals.

2. Identifying the Modal Class: A practical method to discover the Modal Class describes the procedure for identifying the class interval with maximum frequency, as it serves as the foundation for calculating the mode.

3. Applying the Mode Formula: Statistical calculation of mode requires the lower class limit of the modal interval alongside the interval width and counts from the modal group, together with adjacent classes.

4. Solving Real-Life Based Word Problems: Students will solve real-life based word problems using frequency tables that originate from survey results or performance scores to establish the most common outcome.

5. Interpreting Data Trends: Those who master the ability to examine organised frequency distributions can form substantial conclusions from original data patterns.

Check Out-

Recommended eBooks

Related eBooks & Sample Papers

CBSE Class 10 Science (Hindi Medium) Sample Paper with Solution 2025-26

110+ Downloads

CBSE Class 10 Social Science (Hindi Medium) Sample Paper with Solution 2025-26

43+ Downloads

NCERT Solutions for Class 10 Subject Wise

Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.

NCERT Exemplar Solutions of Class 10 Subject Wise

Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.

Frequently Asked Questions (FAQs)

Q: How can we measure central tendency of a data as covered in NCERT solutions for Class 10 Maths exercise 14.2?

These concepts are discussed ex 14.2 class 10 comprehensively. With the help of mode , median and mean we can measure central tendency of a data. Practice this exercise to command these concepts.

Q: What do you mean by multimodal data ?

These concepts are discussed in class 10 maths ex 14.2 . The data which have more than one value which are repeated in same frequency are called multimodal data. Practice the problems to command these concepts.

Q: What do you mean by modal class ?

These concepts are discussed in 10th class maths exercise 14.2 answers. Modal class is the class which have maximum frequency or we can say that the class which has highest occurring value in the data. Practice these problems to command the concepts.

Q: Explain the variables covered in the formula of finding mode in grouped data according to NCERT book Class 10 Maths exercise 14.2 .

l = modal class's lowest limit
h = denotes the length of the class interval (assuming all class sizes to be equal)
f ₁ =represents the frequency of the modal class
f ₀ =represents the frequency of the class preceding the modal class
f ₂ = represents the frequency of the class following the modal class.

Q: How many questions are there in Class 10 Maths exercise 14.2 ?

There are six questions in class 10 ex 14.2. Practice these problems to command the concepts.

Q: What do you mean by central tendency ?

This ex 14.2 class 10 discuss about the concept of Central tendency refers to the centre value of all observations.

Q: How many solved examples are there before Exercise 14.2 Class 10 Maths that are based on the mode of grouped data?

There are three problems based on the nature of root that are solved before the Class 10 Mathematics chapter 14 exercise 14.2.

Articles

NCERT Exemplar Class 10 Science Solutions Chapter 2 Acids Bases And Salts

1 day ago

NCERT Resources

NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes

3 days ago

NCERT Resources

NCERT Solutions for Class 10 Maths Chapter 14 Probability

4 days ago

NCERT Resources

NCERT solutions for class 10 maths Chapter 13 Statistics

4 days ago

NCERT Resources

Certifications By Top Providers

People Management with Impact

Via Indian Institute of Management Bangalore

Forensic Science DNA Analysis

Via University of Cambridge, Cambridge

Basic 3D Animation using Blender

Via Indian Institute of Technology Bombay

Preparing for the AP English Language and Composition Exam

Via Tennessee Board of Regents

Consumer Behaviour

Via Indian Institute of Management Bangalore

Certificate Course Animation Technology

Via Manipal Institute of Communication, Manipal

1078 courses

816 courses

394 courses

281 courses

Harvard University, Cambridge

96 courses

University of Michigan, Ann Arbor

83 courses

IT & Software

Teaching and Academics

Programming and Development

Health, Fitness and Medicine

Business and Management

Engineering and Architecture

General Management

Financial Management

Environmental Studies

History

Psychology

Artificial Intelligence

Explore Top Universities Across Globe

University of Essex, Colchester

Wivenhoe Park Colchester CO4 3SQ

University College London, London

Gower Street, London, WC1E 6BT

The University of Edinburgh, Edinburgh

Old College, South Bridge, Edinburgh, Post Code EH8 9YL

University of Delaware, Newark

Newark, DE 19716

University of Nottingham, Nottingham

University Park, Nottingham NG7 2RD

Bristol Baptist College, Bristol

The Promenade, Clifton Down, Bristol BS8 3NJ

PR in Ireland After Study: Eligibility, Steps to Apply, Document Required

12 min ⋆ Sep 01, 2025 05:09 AM IST

Advantages and Disadvantages of Studying MBBS in Abroad 2025-26

9 min ⋆ Sep 01, 2025 05:09 AM IST

IELTS 2025 Exam: Test Dates (September), Registration, Syllabus, Fees

20 min ⋆ Sep 01, 2025 05:09 AM IST

PG in Abroad After MBBS for Indian Students 2025: Fees and Courses

11 min ⋆ Sep 01, 2025 05:09 AM IST

MCAT Syllabus 2025 - Check Section-wise Exam Syllabus & Pattern

8 min ⋆ Sep 01, 2025 05:09 AM IST

Is Studying MBBS Abroad in 2025 Worth It for Indian Students?

12 min ⋆ Sep 01, 2025 05:09 AM IST

Questions related to CBSE Class 10th

On Question asked by student community

Have a question related to CBSE Class 10th ?

25.05.2013 date of birth and i am studying in class 9th therefore I can gives the CBSE board exam on 2027....

Hello,

Yes, you can give the CBSE board exam in 2027.

If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.

Hope it helps !

Read Complete Answer

Prachi Kumari

27 Aug'25

My school has asked to create apaar id.. but I selected none and forgot to put CBSE as institution will it affect any way?

Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.

Read Complete Answer

Chelsie G

23 Aug'25

i want to know my class 10th registration number

Hello Aspirant,

Here's how you can find it:

School ID Card: Your registration number is often printed on your school ID card.
Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.
School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.
Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.

Your school is the best place to get this information.

Read Complete Answer

SHUBHRADIP ROY

20 Aug'25

Currently I passed my 10 in 2024-2025 session can I fill form

Hello,

It appears you are asking if you can fill out a form after passing your 10th grade examination in the 2024-2025 academic session.

The answer depends on what form you are referring to. Some forms might be for courses or examinations where passing 10th grade is a prerequisite or an eligibility criteria, such as applying for further education or specific entrance exams. Other forms might be related to other purposes, like applying for a job, which may also have age and educational requirements.

For example, if you are looking to apply for JEE Main 2025 (a competitive exam in India), having passed class 12 or appearing for it in 2025 are mentioned as eligibility criteria.

Let me know if you need imformation about any exam eligibility criteria.

good wishes for your future!!

Read Complete Answer

sadafreen356

20 Aug'25

CBSE board real paperAnd notes

Hello Aspirant,

"Real papers" for CBSE board exams are the previous year's question papers . You can find these, along with sample papers and their marking schemes , on the official CBSE Academic website (cbseacademic.nic.in).

For notes , refer to NCERT textbooks as they are the primary source for CBSE exams. Many educational websites also provide chapter-wise revision notes and study material that align with the NCERT syllabus. Focus on practicing previous papers and understanding concepts thoroughly.

Popular CBSE Class 10th Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Read Complete Answer

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

Read Complete Answer

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Read Complete Answer

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Read Complete Answer

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Read Complete Answer

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Read Complete Answer

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Read Complete Answer

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Read Complete Answer

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Read Complete Answer

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is