Statistics NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.1 15.2 15.3 Miscellaneous Free pdf Notes Study Material download-Anand Classes |
NCERT solutions for class 11 maths chapter 15 statistics is a chapter that students have encountered throughout their school career in different ways. Statistics deals with data collected for specific purposes. We can make decisions about the data by analyzing and interpreting it. Students have already been introduced to methods of representing data graphically and in tabular form. Along with that, they have also studied the various measures of central tendency such as arithmetic mean, median, and mode. In the NCERT solutions class 11 maths chapter 15 students are now educated on how the data collected is scattered or how much it is bunched around a measure of central tendency. Statistics is one of the most widely used topics in the financial and economic industries for planning as well as forecasting.
Download the pdf of NCERT Solutions for Class 11 Maths Chapter 15 – Statistics
Download the NCERT Book for Class 11 Maths Chapter 15 – Statistics
Number of questions in each exercise of NCERT Solutions Class 11 Maths Chapter 15 Statistics
Class 11 maths NCERT solutions chapter 15 is not only an important chapter for examinations but is also required by students in class 12th. The concepts that are presented in this chapter will be used as the building bricks for the introduction of more complicated topics as students progress through their educational journey. Hence, students should make it a point to be well-versed with the formulas and theories of Statistics as these will inevitably make their way into the future board exams. NCERT Solutions Chapter 15 Statistics uses various practical examples to deliver an impactful chapter thus, ensuring that students of all intelligence quotas can instill a crystal clear statistical foundation and also download the exercise-wise solutions provided in the links below.
- NCERT Solutions Class 11 Maths Chapter 15 Ex 15.1
- NCERT Solutions Class 11 Maths Chapter 15 Ex 15.2
- NCERT Solutions Class 11 Maths Chapter 15 Ex 15.3
- NCERT Solutions Class 11 Maths Chapter 15 Miscellaneous Ex
In the NCERT solutions class 11 maths students take a deeper look at the various statistical measures such as mean deviation, standard deviation, and variance of grouped, as well as ungrouped data. There are a number of formulas that have been outlined in this chapter for finding the values of the above-stated concepts. This is an immaculately crafted chapter that combines the basics of statistics with higher-level topics. Given below are the links to all the exercise-wise solutions to all NCERT textbook questions.
As this chapter will be seen further in a child’s educational career it is imperative for her to periodically revise the solutions so as to recall the concepts immediately when required. These solutions come with tips and tricks that can help to streamline the studying process thus, students should keep a lookout for the same. The detailed analysis of NCERT Solutions Class 11 Maths Chapter 15 statistics is given below.
- Class 11 Maths Chapter 15 Ex 15.1 – 12 Questions
- Class 11 Maths Chapter 15 Ex 15.2 – 10 Questions
- Class 11 Maths Chapter 15 Ex 15.3 – 5 Questions
- Class 11 Maths Chapter 15 Miscellaneous Ex – 7 Questions
Important Topics and Subtopics of NCERT Solutions for Class 11 Maths Chapter 15 – Statistics
Topics Covered: Measures of dispersions, mean deviation, and variance of grouped as well as ungrouped data, are the topics under class 11 maths NCERT solutions chapter 15. Other sections also include variance and standard deviation of discrete as well as continuous frequency distribution and coefficient of variation.
Total Questions: Class 11 maths chapter 15 Statistics has 34 questions in total out of which 14 are straightforward, 15 are slightly difficult while 5 are complex higher-order thinking sums.
The topics of Class 11 Chapter 15 – Statistics of NCERT Solution are as follows:
15.1 Introduction
This section talks about the concept of central tendency, mean and median [during even and the odd number of observations] with examples. It introduces the concept of measure of dispersion.
The values which cluster around the middle or centre of the distribution are measures of central tendency. They are mean, median and mode.
In a class, the mean can be used to find the average marks scored by the students.
When calculating the height of students, the median can be used to find the middlemost value.
15.2 Measures of Dispersion
This section defines measures of dispersion, different measures of dispersion [range, quartile deviation, mean deviation, standard deviation]
Measures of dispersion explain the relationship with measures of central tendency. For example, the spread of data tells how well the mean represents the data. If the spread is large, then the mean is not representative of the data.
15.3 Range
This section defines the range, its formula and an example.
The range gives the variability of scores using the maximum and minimum values in the set.
In a cricket match, Batsman A range = 121 – 0 = 121 and Batsman B range = 52 – 22 = 30
Range A > Range B. So, the scores are spread in the case of A, whereas for B, they are close to each other.
15.4 Mean Deviation
This section defines mean deviation, the formula for mean deviation.
The concept of mean deviation can be used by biologists in the comparison of different animal weights and deciding what would be a healthy weight.
15.4.1 Mean deviation for ungrouped data
The process of obtaining the mean deviation for ungrouped data is elaborated in this section.
Find the mean, deviations from the mean, and absolute deviations and substitute the values in the mean deviation formula and arrive at the answer.
15.4.2 Mean deviation for grouped data
The process of obtaining mean deviation for discrete and continuous frequency distributions is elaborated in this section with solved examples.
15.4.3 Limitations of mean deviation
- If, in a series, the degree of variability is very high, then the median will not be representative of the data. Hence, the mean deviation calculated about such a median cannot be relied on.
- If the sum of deviations from the mean is greater than the sum of deviations from the median, then the mean deviation from the mean is not very specific.
- The absolute mean deviation calculated can’t be subjected to further algebraic treatment. It can’t be used as an appropriate measure of dispersion.
15.5 Variance and standard deviation
15.5.1 Standard Deviation
This section involves the variance and standard deviation definition, formula and solved examples of the discrete and continuous frequency distribution.
A science test was taken by a class of students. The mean score of the test was 85% on calculation. The teacher found the standard deviation of other scores and noticed that a very small standard deviation exists, which suggests that most of the students scored very close to 85%.
15.5.2 Shortcut method to find Variance and standard deviation
This section deals with the simpler way of calculating the standard deviation with a few illustrations.
15.6 Analysis of Frequency Distributions
This section deals with the process of comparing the variability of two series having the same mean, coefficient of variation with few solved problems.
List of Formulas in NCERT Solutions Class 11 Maths Chapter 15 – Statistics
NCERT solutions class 11 maths chapter 15 are based on formulas as well as a child’s ability to understand what the question is asking. Formulas can be seen as an easy way of solving an otherwise difficult sum. Statistics not only call for the use of formulas but also help in enhancing a child’s calculation skills. Students are advised to make formula charts as well as solve all sums by hand as this can increase the speed and accuracy in performing calculations that can be vital while appearing for exams. Given below are some of the formulas used in this chapter.
- Range = Maximum Value – Minimum Value.
- Mean deviation for ungrouped data: x̅ = ∑|xi – x̅| / n
- Mean deviation for grouped data: x̅ = ∑|xi x̅| / N; N = ∑fi
- Variance for ungrouped data: σ2 = ∑(xi – x̅)2/ n
- Variance for grouped data: σ2 = ∑fi(xi – x̅)2/ N
- The range is defined as the difference between the maximum and minimum values of the given data.
- If there exists a series with equal means, then the series with a lesser standard deviation is more consistent or less scattered.
- The addition or subtraction of a positive number to each data point of the data set will not affect the variance.
The solutions give substitute strategies and clarifications to solve problems which makes the student feel confident while taking the exam. Additionally, solving and practising new problems upgrades the understanding of Mathematical concepts among students. The solutions help with inquiries that a student has on the questions asked in the exam. The ANAND CLASSES’S subject specialists who have written the NCERT Solutions for Class 11 Maths, according to the latest CBSE Syllabus, have in-depth knowledge about the question paper setting and the marks distributed across the chapters.
Frequently Asked Questions (FAQs) on NCERT Solutions for Class 11 Maths Chapter 15 – Statistics
Q1
Why are NCERT Solutions Class 11 Maths Chapter 15 Important?
NCERT Solutions Class 11 Maths Chapter 15 has been prepared by mathematical experts who are geniuses in their field. The solutions have been explained in a step-wise and detailed manner that can be understood by all students. students not only get an idea of how to clearly present their answers in examinations but are also able to clear their concepts making these solutions a very important source of learning.
Q2
Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Statistics?
The key to being successful in the NCERT Solutions Class 11 Maths Statistics is constant practice. Students are required to memorize several formulas and perform lengthy calculations. If a child makes a silly mistake while going through these steps then the entire sum will be marked incorrect. Hence, students need to regularly revise these solutions to brush up on their skills.
Q3
What are the Important Topics Covered in NCERT Solutions Class 11 Maths Chapter 15?
All the topics covered in NCERT Solutions Class 11 Maths Chapter 15 are equally important. Each exercise targets a different subject matter. The easier questions help students build their foundation and memorize formulas while the tougher ones aid in harnessing up their mathematical acumen. Additionally, this chapter will be further used in class 12. Thus, students should not skip any section.
Q4
How Many Questions are there in NCERT Solutions Class 11 Maths Chapter 15 Statistics?
There are 34 sums in the NCERT Solutions Class 11 Maths Chapter 15 Statistics that are divided into 3 exercises and one miscellaneous exercise. These questions give a 360-degree view to students of the entire chapter and have been curated by math experts. They range from easy formula-based questions to complicated word problems.
Q5
What are the Important Formulas in NCERT Solutions Class 11 Maths Chapter 15?
The formulas in NCERT Solutions Class 11 Maths Chapter 15 that are based on calculating the mean, variance, and standard deviation of different types of data are vital. As there are a lot of formulas that need to be learned students should proceed through them in a step-wise manner as well as note them down in their formula sheet.
Q6
How CBSE Students can utilize NCERT Solutions Class 11 Maths Chapter 15 effectively?
To effectively utilize NCERT Solutions Class 11 Maths Chapter 15 the most important point is to understand the derivations of all the formulas outlined before the exercises. students should also recall all the concepts that they have learned in Statistics in previous classes. Additionally, they should also understand the theory. Once they are comfortable with these three tools they can proceed to solve the exercise questions.
Q7
What are the topics discussed in Chapter 15 of NCERT Solutions for Class 11 Maths?
2. Methods of Dispersion
3. Range
4. Mean Deviation
5. Variance and Standard Deviation
6. Analysis of Frequency Distributions
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