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Statistics Class 10 Notes CBSE Maths Chapter 14 [Free PDF Download]

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Last updated date: 16th May 2024
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Class 10 Maths Revision Notes for Statistics of Chapter 14 - Free PDF Download

Revision plays a crucial role in understanding the concepts and securing good grades in the board exams. To have a revision, it is important to have revision notes of each chapter especially in subjects like Mathematics, as it contains different formulas and facts. To ease your preparation, we at Vedantu are presenting Class 10 Maths Chapter 14 notes on this page in PDF format. Class 10 Maths Statistics notes provided by Vedantu includes all facts and formulas that are important for the students to solve the question given in the chapter quickly and conveniently.

Vedantu also provides NCERT Solution and other study materials for students. You can also download NCERT Solution Class 10 Science to score more marks in the examinations.

Download CBSE Class 10 Maths Revision Notes 2024-25 PDF

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Access Class 10 Maths Chapter 14 – Statistics Notes in 30 Minutes

Statistics

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect and summarize data.


Mean of grouped data

Mean is a measure of central tendency and is defined as an average value of given observations.


There are three methods to find mean of grouped data:

  1. Direct Method:

\[\overline x \; = \;\dfrac{{\sum\limits_{i = 1}^n {{f_i}{x_i}} }}{{\sum\limits_{i = 1}^n {{f_i}} }}\]

Where \[\overline x \] is mean, \[f\] is frequency and \[x\] is the mid-interval

  1. Assumed Mean Method:

\[\overline x \; = \;A\; + \;\dfrac{{\sum\limits_{i = 1}^n {{f_i}{d_i}} }}{{\sum\limits_{i = 1}^n {{f_i}} }}\]

Here, \[A\] is called assumed mean and \[d\; = \;x\; - \;A\]

  1. Step Deviation method:

\[\overline x \; = \;A\; + \;h\; \times \;\dfrac{{\sum\limits_{i = 1}^n {{f_i}{t_i}} }}{{\sum\limits_{i = 1}^n {{f_i}} }}\]

Here, h is called class size and \[t\; = \;\dfrac{d}{h}\]


Mode of Grouped Data:

It is the observation having the highest value of frequency among all observations.

In case of grouped data, firstly modal class is located and then following formula is used to calculate mode:

\[Mode\; = \;l\; + \;\left( {\dfrac{{{f_1}\; - \;{f_0}}}{{2{f_1}\; - \;{f_0}\; - \;{f_2}}}} \right)\; \times \;h\]

\[\;l\]is lower limit of modal class.

\[h\] is upper limit of modal class.

\[{f_1}\] is frequency of the modal class.

\[{f_0}\] is frequency of the class preceding the modal class.

\[f\] is frequency  of the class succeeding the modal class.


Median of Grouped Data:

It is the value of the middlemost observation of the data.

For grouped data, following formula is used to find median of the data but first we find the median class, then apply formula:

\[Median\; = \;l\; + \;\left( {\dfrac{{\dfrac{N}{2}\; - \;c}}{f}} \right)\; \times \;h\]

\[l\] is Lower limit of the median class

\[f\] is Cumulative frequency preceding the median class frequency

\[N\] is Sum of the frequencies

\[h\] is Width of the class interval


Working Rule:

Step 1: Prepare the table of less than the cumulative frequency using the frequency table given in the question. 

Step 2: Find out the cumulative frequency corresponding to the value of \[\dfrac{N}{2}\]. A median class interval is defined as a class interval corresponding to this cumulative frequency.

Step 3: Find the value of lower limit l and frequency f of the median class.

Step 4: Find the width 'h' of the median class interval.

Step 5: Find value of ‘c’, the cumulative frequency of preceding median class 

Step 6: Apply the formula written above.


Graphs in Statistics:

Graphical Representation of Cumulative Frequency Distribution

We find Cumulative frequency by adding the frequencies of the preceding intervals up to that class interval and the frequency of a class interval.


Ogive (Cumulative Frequency Curve)

There are two ways of constructing an Ogive or cumulative frequency curve. 

  1. Less than type Ogive: It is represented by a rising curve.

  2. More than type Ogive: It is represented by a falling curve.

Ogive is pronounced as O-jive and This curve is ‘S-shaped.


To Plot an Ogive: 

  1. We plot the actual limits along the x-axis and the cumulative frequencies along the y-axis. Plot corresponding coordinates of each class interval.

  2. Join the plotted points with a rough hand.

  3. Connect an Ogive to a point on the X-axis which represents the actual lower limit of the first class. 


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Revision Notes Class 10 Maths Chapter 14: Introduction to Statistics

Class 10 Chapter 14 Maths notes are prepared by the subject experience teachers at Vedantu. It includes all statistical concepts like grouped data, ungrouped data, measures of central tendency like mean, median, mode, methods to find mean, median, and mode, and the relationship between them, along with the important facts and formulae that are important to have a proper understanding of the chapter. 

To have a quick overview of the important concepts of the chapter before the exams, download Class 10 Chapter 14 Maths notes free PDF through the link given here.


A Quick Overview of Class 10 Maths Chapter 14

In Class 10 Maths Chapter 14, students will learn the three measures of central tendency that are mean, median, and mode from ungrouped data to that of grouped data. Students will also understand the concepts of cumulative frequency, the cumulative frequency distribution, and how to draw cumulative frequency known as ogives. 


Mean of Grouped Data

The mean of the observation is the sum of all the values given in the observations divided by the total number of observations.

If y₁,y₂, y₃, y₄...yₙ are observation with respective frequencies f1, f2, f3, f4, ….,fn

Then, the mean of the yof the data is given by:

\[\bar{y}\] = \[\frac{f_{1}y_{1}, f_{2}y_{2}, f_{3}y_{3}, f_{4}y_{4},+.....+y_{n}}{f_{1}, f_{2}, f_{3}, f_{4},....f_{n} }\]


Mode of Grouped Data

The mode of the is that value among the observations which occurs most frequently and is also defined as the value of the observation having a maximum frequency.


Median of Grouped Data

Median is defined as the measure of central tendency which obtains the value of the middlemost observation in the data.

If n is odd, then the median is the \[\left ( \frac{n+1}{2} \right )^{th}\]term of the observations.

If n is even, then the median is defined as the average of the \[\left ( \frac{n}{2} \right )^{th}\] and the \[\left ( \frac{n+1}{2} \right )^{th}\] term of the observations.


Cumulative Frequency

The cumulative frequency of the class is the frequency that is received by adding the frequencies of all the classes above the given class.


List of the Topics and Subtopics Covered in Class 12 Maths Chapter 14

14.1:  Introduction

14.2:  Mean of Grouped Data

14.3:  Mode of Grouped Data

14.4:  Median of Grouped Data

14.5:  Graphical Representation of Cumulative Frequency Distribution

To have a detailed understanding of all the above topics discussed above, download Class 10 Maths Statistics Notes free PDF now.


Benefits of Class 10 Maths Chapter Statistics Notes

Here are some of the benefits of referring to Class 10 Maths Chapter Statistics notes:

  • The Class 10 Maths Chapter Statistics notes are 100% accurate as the notes are prepared by the experts after having extensive research of the topics.

  • The Class 10 Maths Statistics notes are available in a PDF format that helps students to revise the notes anytime and at any place as per their comfort.

  • The Class 10 Maths Chapter 14 notes enable students to recall all the previously learned concepts of the chapter quickly and conveniently especially during the exams when they have to revise the whole syllabus in a limited period.

  • Class 10 Maths Statistics notes enable students to get acquainted with the topics and also helps to identify the key elements of the chapter

  • Class 10 Maths Chapter 14 notes curbs the activities of referring to the multiple study material for preparing the chapter during revision.


Solved Examples

1. The daily expenditure on food for 25 households in a locality is depicted in the table given below. Determine the mean of daily expenditure on food using an appropriate method.

Daily expenditure(in Rs)

100-150

150-200

200-250

250-300

300-350

Number of households

4

5

12

2

2

 

Solution:

Determine the mid-point of the given interval using the formula.

Midpoint (xi) = (upper limit + lower limit)/2

Let the mean (A) be equal to 225.

Class size (h) = 50

Class Interval

Number of households (fi)

Mid-point (xi)

fi.xi

100-150

4

125

500

150-200

5

175

875

200-250

12

225

2700

250-300

2

275

550

300-350

2

325

650


Σ fi = 25


Σ fi.xi =  5275

 

Mean = Σ fi.xi / Σ fi

 = 5275 / 25 = 211

Hence, the mean of daily expenditure on food comes out to be 211.

 

2. Information on the observed lifetimes (in hours) of 225 electrical components is given in the following data. Calculate the modal lifetimes of the components.

Lifetime (in hours)

0-20

20-40

40-60

60-80

80-100

100-120

Frequency

10

35

52

61

38

29

 

Solution:

Based on the given data, the modal class is 60–80 as the frequency of this interval is maximum..

So, lower limit of modal class l = 60,

The frequencies are as follows:

fm = 61, f1 = 52, f2 = 38 and h = 20

Mode = l+ [(fm-f1)/(2fm-f1-f2)]×h

Substituting the values in the formula, we obtain

Mode =60+[(61-52)/(122-52-38)]×20

Mode = 60+((9 x 20)/32)

Mode = 60+(45/8) = 60+ 5.625

Hence, the modal lifetime of the components is computed to be 65.625 hours.

 

What are the Benefits of Referring to Vedantu’s Revision Notes for Class 10 Maths Chapter 14 - Statistics

  • Provides quick, clear summaries of key concepts.

  • Simplifies complex topics for better understanding.

  • Efficient tool for last-minute exam prep.

  • Enhances retention of crucial information.

  • Supports effective exam preparation with key points and tips.

  • Saves time by consolidating information.

  • Prioritizes important topics and questions.

  • Offers practical examples for real-world connections.

  • Boosts student confidence for exams.


Other Maths Related Links

CBSE Syllabus for Class 10

CSBE Sample Papers for Class 10

RS Aggarwal Solutions for Class 10

Important Questions for Class 10

Lakhmir Singh Class 10 Solutions

NCERT Books for Class 10

CSBE Previous Year Question Papers for Class 10

Maths formulas for Class 10

RD Sharma Class 10 Solutions

NCERT Exemplar Class 10 Solutions

NCERT Solutions for Class 10

Revision Notes for Class 10


CBSE Class 10 Revision Notes - Other Chapters (Maths)

Chapter 1 - Real Numbers Revision Notes

Chapter 2 - Polynomials Revision Notes

Chapter 3 - Pair of Linear Equations in Two Variables Revision Notes

Chapter 4 - Quadratic Equations Revision Notes

Chapter 5 - Arithmetic Progressions Revision Notes

Chapter 6 - Triangles Revision Notes

Chapter 7 - Coordinate Geometry Revision Notes

Chapter 8 - Introduction to Trigonometry Revision Notes

Chapter 9 - Some Applications of Trigonometry Revision Notes

Chapter 10 - Circles Revision Notes

Chapter 11 - Constructions Revision Notes

Chapter 12 - Areas Related to Circles Revision Notes

Chapter 13 - Surface Areas and Volumes Revision Notes

Chapter 15 - Probability Revision Notes

 

Conclusion

Statistics is one of the most important and easy to understand the chapter in the CBSE Class 10 Maths syllabus. Learning statistics will enable students to properly collect and use data, make accurate analyses, and prepare a great presentation of results. Solved examples and revision notes help students achieve desired results in their exams in terms of scoring and we take pride in improving the conceptualisation of topics in students. We advise students to go through these revision notes along with the other related links that have been provided in this article so that they can make full use of the materials provided by Vedantu.

FAQs on Statistics Class 10 Notes CBSE Maths Chapter 14 [Free PDF Download]

1. Is Vedantu's Class 10 Maths Chapter 14 notes available free of cost?

Yes,  Vedantu's revision notes are available free of cost in the PDF format and students can download them at no time by clicking on the PDF link given above on this page.

2. What is the importance of referring to Vedantu's Class 10 Chapter 14 Maths notes?

The Class 10 Chapter 14 Maths notes are prepared as per the latest syllabus issued by the CBSE board so that any changes made in the syllabus are also considered well. These CBSE Class 10 Maths Chapter 14 notes are one of the best tools to prepare the chapter effectively as the content is presented in an easy-to-read format. Furthermore, all the important topics of the chapter are summarised in a few lines. All the relevant formulae are also illustrated with examples.

3. What is data according to Revision Notes of Chapter 14 of Class 10 Maths?

Every day, we are presented with a lot of numbers and figures. We see a lot of information displayed to us on the news. These facts or figures may simply be the scores of a cricket match or the results of an election. All this information that has been collected with a definite purpose is called data. Data derives its name from the Latin word datum, which is generally used as the singular form of data. 


4. What is the branch of statistics all about according to Revision Notes of Chapter 14 of Class 10 Maths?

The method of extracting meaningful information out of the data that is given is studied in a branch of mathematics called Statistics. Statistics not only involve the collection, organisation, analysis and interpretation of data, but it also is used to infer collected data. The subject can hold different meanings in different contexts, as has been explored in Revision Notes of Chapter 14 of Class 10 Maths given by Vedantu. The solutions are free of cost and also available on Vedantu Mobile app.


5. What are the steps involved in the study of statistics according to Revision Notes of Chapter 14 of Class 10 Maths?

To master the study of statistics, you need to follow a series of sequential steps. The first step is all about collecting accurate data while the second step involves the presentation of the collected data. After you have presented your data properly, you need to represent it in a graphical manner. This is the third step. The graphical representation can be in the form of bar graphs, pie charts, and so on.

6. What is a bar graph according to Revision Notes of Chapter 14 of Class 10 Maths?

Students are already familiar with bar graphs. Here, we shall take a look at the proper way of constructing these bar graphs. A bar graph is basically just a pictorial representation of data. It is drawn in such a manner that there are bars of uniform width drawn with equal spacing between them. One variable is plotted on one axis along with its values on the other. The heights of the bars drawn represent the value of the data.

7. How many exercises are there in Chapter 14 of Class 10 Maths?

Overall, there are four exercises in the Maths chapter of Statistics. Exercise 1 assigns students with tasks of collecting data. Exercise 2 makes them represent this data in the form of frequency distribution tables. Exercise 3 deals with making bar graphs and histograms using the data presented. In contrast to this, Exercise 4 is all about using the measures of central tendency in statistical analysis. For notes on these topics and a clearer understanding of the subject, refer to Vedantu.