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

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.

This Story also Contains
  1. Benefits of NCERT Solutions for Class 10 Maths Exercise 14.4
  2. More About NCERT Solutions for Class 10 Maths Exercise 14.4
  3. Benefits of NCERT Solutions for Class 10 Maths Exercise 14.4
  4. NCERT Solutions for Class 10 Subject Wise

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.

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Also, See:

NCERT Solutions for Class 10 Subject Wise


Frequently Asked Questions (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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