Statistics - CBSE Class 10 Maths Important Notes

The CBSE Class 10th and Class 12th Term-2 Board Exams are just approaching. The final date sheet for both Class 10th and 12th is available on the official portal of CBSE. Class 10 is crucial in the academic life of the students. It is the first board exam in the life of CBSE students that also plays the role of a deciding factor for their career path. It is important to score well in the Class 10 Term-2 exam. Notably, to score high, students should prepare competently. It is essential to have important notes of each chapter, specifically in a subject like Mathematics, which involves various formulas and theorems.

The important mathematics concepts will also help the students prepare for the NTSE, international mathematical olympiad, JEE 2022, CUCET, NTA, KVPY exam, etc. Chapter 14- Statistics in Class 10th Mathematics is one of the chapters with a high weightage in the Mathematics Term-2 board exam. To help the students prepare for the Statistics Chapter, we will be discussing the important notes of Statistics -CBSE Class 10 Mathematics.

Table of Contents

Weightage of Statistics Chapter in Mathematics Class 10

A Brief Introduction to Statistics

CBSE Class 10 Maths Important Notes of Statistics

Conclusion

Frequently Asked Questions (FAQs)

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The Class 10 syllabus is decreased for the Term-2 exam. There will be a 50:50 ratio of the syllabus for each term. The total marks for CBSE Class 10 Term-2 will be 50 for each subject. The Term-2 Mathematics paper will be a total of 40 marks. The internal assessments will account for the remaining ten marks.

Before heading towards the important notes of Chapter 14, let us crisply review the weightage of this chapter in the Class 10 board exam.

Weightage of Statistics Chapter in Mathematics Class 10

As per the new exam pattern for CBSE Class 10 Term-2 exam 2022, the weightage of the chapters in the reduced syllabus is represented here. Students can check the weightage of Statistics in the Mathematics Class 10 final exam from the table below.

Unit Name	Chapters	Marks
Algebra (Cont.)	Chapter 4 – Quadratic Equations Chapter 5 – Arithmetic Progression	10
Geometry (Cont.)	Chapter 10 – Circles Chapter 11- Constructions	9
Trigonometry (Cont.)	Chapter 9 – Some Applications of Trigonometry	7
Mensuration (Cont.)	Chapter 13 – Surface Areas and Volumes	6
Statistics and Probability (Cont.)	Chapter 14 – Statistics	8

A Brief Introduction to Statistics

Chapter 14 – Statistics involves the introduction of the chapter and topics like the mean of grouped data, mode of grouped data, the median of grouped data, graphical analysis of cumulative frequency distribution, all explained in detail. Then, it includes the exercises for numerical practice. This chapter is an easy and scoring chapter in the Mathematics Term-2 syllabus. Students can secure good marks on the question on Statistics by practising the important topics.

CBSE Class 10 Maths Important Notes of Statistics

Statistics is the chapter of mathematics which entails the collection, organisation, analysis, interpretation, and presentation of data. It is highly useful in real-life situations as it easily comprehends data when it is represented as a particular number, which represents all the numbers. Such a number is known as the measure of central tendency. The typical measures of central tendencies are –

Mean – The average of n numbers is their mean. It is calculated by dividing the sum of all the numbers by the total count of numbers (n).

The mean X̄ of n values –

X̄ = (x1+x2+x3…xn) / n

Median – When we arrange the numbers in an ascending or descending order, the middle value of the series will be the median. It separates the upper half and the lower half of the series.

To find the median, arrange your data and then calculate the middle position based on the number of values in the series (n).

If n is an odd number, the median lies at the position [(n + 1) / 2]. Whereas, if n is an even number, the median is the average of the values of [n / 2]th and [(n + 1) / 2]th observation.

Mode – The value which appears most frequently in the data set is taken as the mode of n numbers.

Mean of Grouped Data

Without Class Interval

In the cases where the data has no class interval, the mean of such data can be calculated as –

x̄ = ∑fixi / ∑fi

where fixi is the sum of the product of x and f for all values and fi is the sum of given frequencies.

With Class Interval

In the cases where the grouping of data is in the form of class intervals, the mean of the data can be calculated by three methods.

1. Direct Method

In the direct method, students have to use a midpoint, which represents the whole class, known as the class mark. It is the mean/average of the upper and lower limit.

Class Mark = (Upper limit + Lower limit) / 2

x̄ = ∑fixi / ∑fi

2. Deviation or Assumed Mean Method

When the data set involves large numbers, we use the Assumed mean method to calculate the mean easily. In this method, we choose one of the values as the assumed mean and denote it as a. Next, we calculate the deviation. The deviation for each x is the difference between the assumed mean (a) and each value(x). Then, we have to calculate the product of d×f, as we calculated in the direct method.

Assumed Mean Formula:

x̄ = a + (∑fidi / ∑fi)

3. Step Deviation Method or Short-cut method

This method is an extension of the Assumed mean method. We have to take the assumed mean (a) and calculate the deviation d, as we calculated in the assumed mean method. Then, we have to divide the values of d with a number h, which is the class width, to find u (u= d/h). Then, we have to multiply these values with corresponding frequencies for ∑fiui. Then, put everything into the formula.

x̄ = a + (∑fiui / ∑fi) × h

Mode of Grouped Data

Concerning the ungrouped data, the value that occurs most frequently is the mode of the series. However, in the grouped data we find the class interval, which has the maximum frequency number. It is known as the modal class.

The formula of mode:

Mode = l + [(f1-f0)/(2f1-f0-f2)]×h.

where l = lower class limit of the modal class

h = size of class interval

f1 =frequency of the modal class

f0 =frequency of the preceding class

f2 = frequency of the succeeding class

Median of Grouped Data

Grouped data is data in the form of frequency distribution. To calculate the median of a grouped data, we first have to calculate the cumulative frequency of each class and n/2.

Secondly, we have to find the median class. It is the class whose cumulative frequency is equal to or greater than the (close to) n/2.

To find the Cumulative Frequency, add the frequencies of each class to the sum of its preceding the given class.

After this, put the values in the formula.

Formula of Median:

Median = l+ [(n/2−c)/f] × h

where l = lower limit of the median class

n = no. of observations

c = cumulative frequency of the preceding class

f = frequency of the median class

h = size of class

Fact to Consider

There is an empirical relation between the three measures of central tendency. It can be represented as:

3 Median = Mode + 2 Mean

Conclusion

As the CBSE Class 10 board exams are nearing, the students are now pushing themselves hard to do top-notch preparation for the boards. In such a short duration, the students should regularly revise the important notes for those who have not prepared the important notes during their exhaustive studies. We have provided our high-quality important notes.

Above in this article, we have presented the important notes for the Statistics Chapter in CBSE Class 10 Mathematics Syllabus. Our experts curated our notes and included all key formulas and facts that the students must understand well to solve the questions based on this chapter quickly and accurately. Students can also read Maths concepts for other chapters.

FAQs

1. What is the chapter-specific weightage of Chapter 14-Statistics in Mathematics CBSE Class 10 Term-2 exam?

Concerning the chapter-specific weightage of Statistics, the unit Statistics & Probability (Cont.) will have a weightage of 8 marks, i.e., around 20% of the total marks. The probability chapter was there in the Term-1 syllabus. So, in term-2 only Chapter 14 Statistics is there from this unit. There will be one two-mark question and two three-mark questions from the Statistics Chapter in the CBSE Class 10 Mathematics Term-2 question paper. These three questions will carry eight marks in total. Since statistics is a scoring chapter, students must prepare well for it.

2. Which chapters have the highest weightage in CBSE Class 10 Term-2 Mathematics examination?

This year, the term-2 paper will have a total of 40 marks. The syllabus is also reduced to 50% for all subjects. As per this reduced syllabus pattern, the Algebra unit (chapter 4,5) has the highest weightage in the term-2 question paper. It will carry ten marks, i.e. about 25% of the total marks. After Algebra, other units with high weightage counts of geometry (chapter 10, 11), statistics (chapter 14), and trigonometry (chapter 9). The student should focus more on high-scoring units like algebra & statistics.

3. What is the exam pattern of CBSE Class 10 Mathematics Term-2?

The CBSE Class 10 Mathematics Term-2 will include subjective questions, unlike Term-1. The question paper will have 14 questions across the three sections. Section A will have six two-mark questions (2×6 = 12), Section B will include four three-mark questions (4×3 = 12), and Section C will have four four-mark questions (4×4 = 16). Out of these four, two questions will be based on case studies. Also, there will be two internal choices in Section A, one in Section B, and one in Section C. Attempting all fourteen questions will be compulsory.

4. Can a student change his level from Basic Maths to Standard Maths for the Class 10 Term-2 Exam?

The students can select their preferred level of study in mathematics as basic maths or standard maths only before the beginning of Term-1 exams. The students who have chosen basic maths have attempted their term-1 exams with this level. A student cannot change it till the term-2 exams. But, it is possible to study mathematics in higher studies, as it would be if the student had chosen standard maths. For this, such students will be required to clear the compartment exams for standard mathematics to become eligible to study mathematics in higher classes.

5. From where can I access the important NCERT Questions of CBSE Class 10 Mathematics?

NCERT textbooks as the essential study resources for Class 10. It helps the students understand the core concepts and the crucial parts of the chapters in the Mathematics Syllabus. The students can easily access the NCERT Solutions for Class 10 Maths at our website. While practising the NCERT questions, you can refer to these solutions for the complex questions. It will help the students to achieve good marks. These chapter-wise NCERT solutions come in handy for the preparation. Ultimately, this will help to gain a good command of the topics.