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NCERT Solutions for Exercise 14.4 Class 10 Maths Chapter 14 - Statistics

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NCERT Solutions for Exercise 14.4 Class 10 Maths Chapter 14 - Statistics

Edited By Sumit Saini | Updated on Jul 12, 2022 02:57 PM IST | #CBSE Class 10th

NCERT Solutions for Class 10 Maths exercise 14.4 - Cumulative frequency is calculated by adding all frequencies up to a certain threshold. We calculate the cumulative frequency by adding each and every frequency from the frequency distribution table given to us to the sum of its predecessor.

In NCERT solutions for Class 10 Maths chapter 14 exercise 14.4 we are introduced to ‘ogives’. An 'ogive of the less than type' is a graph of a cumulative frequency distribution of the less than type. An ‘ogive of the more than type' is a graph depicting a cumulative frequency distribution of the more than type. The median of the grouped frequency distribution is determined by the point of intersection of the ogives of more than and less than types.

The formula for finding the median:

1639046081922

Where,
l = lower limit of median class,
n = number of observations,
cf = cumulative frequency of class preceding the median class,
f = frequency of median class,
h = class size (assuming class size to be equal).

Along with NCERT book Class 10 Maths chapter 14 exercise 14.4, the following exercises are also present.

Benefits of NCERT Solutions for Class 10 Maths Exercise 14.4

Q1 The following distribution gives the daily income of 50 workers of a factory.

1640762580356 Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Answer:

Daily Income

(Upper-Class Limit)

Cumulative

Frequency

Less than 120

12

Less than 140

26

Less than 160

34

Less than 180

40

Less than 200

50

Now,

Taking upper-class interval on the x-axis and their respective frequencies on the y-axis,

1640762619994

Q2 During the medical check-up of 35 students of a class, their weights were recorded as follows:


1640762636273 Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Answer:

Taking upper-class interval on the x-axis and their respective frequencies on the y-axis,

1640762661028

N= 35 \implies \frac{N}{2} = 17.5

Marking a point on the curve whose ordinate is 17.5 gives an x-ordinate= 46.5.

Hence, the Median of the data is 46.5

Now,

Weight

(Class)

Frequency

Cumulative

Frequency

>38

0

0

38-40

3

3

40-42

2

5

42-44

4

9

44-46

5

14

46-48

14

28

48-50

4

32

50-52

3

35

N= 35 \implies \frac{N}{2} = 17.5
\therefore Median class = 46-48; Lower limit, l = 46;

Cumulative frequency of preceding class, c.f. = 14; f = 14; h = 2
Median = l + \left (\frac{\frac{n}{2}-c.f}{f} \right ).W
\\ = 46+ \left (\frac{17.5-14}{14} \right ).2 \\ \\ = 46+\frac{7}{14}

= 46.5

Thus, the median using formula is 46.5 which verifies the result.

Q3 The following table gives production yield per hectare of wheat of 100 farms of a village.


1640762676580 Change the distribution to a more than type distribution, and draw its ogive.

Answer:

Production yield

(Upper-Class Limit)

Cumulative

Frequency

More than or equal to 50

100

More than or equal to 55

98

More than or equal to 60

90

More than or equal to 65

78

More than or equal to 70

54

More than or equal to 75

16

Now,

Taking lower class limit on the x-axis and their respective frequencies on the y-axis,

1640762700208

More About NCERT Solutions for Class 10 Maths Exercise 14.4

The modal class is the class with the highest frequency in grouped data. The following formula can be used to determine the mode. When the modal class is unique, the formula is valid for equal class intervals.

The formula for finding the mode:

1639046081094

Where,
l = lower limit of modal class
h = class width
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeeding the modal class1639046080913

Also Read| Statistics Class 10 Notes

Benefits of NCERT Solutions for Class 10 Maths Exercise 14.4

  • Exercise 14.4 Class 10 Maths, gives us a concept on STATISTICS and its uses to a board-level of graphs like ogives.

  • NCERT syllabus Class 10 Maths chapter 14 exercise 14.4 teaches us about the new formula of mode and median.

  • The concepts from Class 10 Maths chapter 14 exercise 14.4 will give us a vivid image of the graphical representation of Cumulative Frequency Distribution, which is very effective if ogives are given to us in any question.

Also, See:

NCERT Solutions for Class 10 Subject Wise


Frequently Asked Question (FAQs)

1. What is the main concept used to solve Class 10 Maths chapter 14 exercise 14.4?

To learn about graphical representation of cumulative frequency distribution. To find the median and mode using graphical method.

2. What do you understand by median?

The middle term of a sorted list is called as median. It may be the mean of the data set or close to the mean of the data set.

3. What do you understand by Cumulative Frequency Table for a set of data?

Cumulative frequency is a running total or the sum of the frequencies. This can be represented on a graph by plotting the upper boundary of the groups.

4. What do you understand by mode?

Any value that appears the most in the value set is called as the mode of the data set.

5. Write the formula for finding the mode of a set of data?

Any value that appears the most in the value set is called as the mode of the data set.

6. what is the relation between mean median and mode?

Generally



Mean – Mode = 3 (Mean – Median)

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Thanking you

The eligibility age criteria for class 10th CBSE is 14 years of age. Since your son will be 15 years of age in 2024, he will be eligible to give the exam.

According to CBSE norms, a student must be 14 years old by the end of the year in which the exam will be held in order to sit for the 10th board exam. If your age is greater than 14, however, there are no limits. Therefore, based on your DOB, you will be 12 years and 6 months old by the end of December 2022. After the actual 16 June 2024, you'll be qualified to take your 10th board.

Hello aspirant,

Central Board Of Secondary Education(CBSE) is likely to declare class 10 and 12 terms 2 board result 2022 by July 15. The evaluation process is underway. Students are demanding good results and don't want to lack behind. They are requesting the board to use their best scores in Term 1 and Term 2 exams to prepare for the results.

CBSE concluded board exams 2022 for 10, and 12 on June 15 and May 24. Exams for both classes began on April 26. A total of 35 lakh students including 21 lakh class 10 students and 14 lakh class 12 students appeared in exams and are awaiting their results.

You can look for your results on websites- cbse.gov (//cbse.gov) .in, cbseresults.nic.in

Thank you

Sir, did you get any problem in result
I have also done this same mistake in board 2023 exam
Please reply because I am panic regarding this problem
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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

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 3.8×107 J 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

 

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

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

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 .

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

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.

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.

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

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

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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Metallurgical Engineer

A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment. 

2 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
QA Manager
4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
ITSM Manager
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
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