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.

The formula for finding the median:

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

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,

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,

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

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.

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,

## 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:

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 class

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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## NCERT Solutions for Class 10 Subject Wise

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As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

### 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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### Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?

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Hello Aspirant,  Hope your doing great,  your question was incomplete and regarding  what exam your asking.

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

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Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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