NCERT Solutions for Class 11 Mathematics Chapter 15 Statistics
If you’re a Class 11 student studying Mathematics from the NCERT Textbook, you would have probably come across Chapter 15 Statistics. Statistics is concerned with the gathering of information for specific purposes. Decisions can be made through analysing and interpreting facts. This chapter discusses measures of dispersion, range, mean deviation, variance, and standard deviation, as well as frequency distribution analysis.
You’ve already learned how to express data graphically and tabularly in previous classes. In Chapter 15 Class 11 Mathematics, you will learn about data representation, as well as specific prominent elements and qualities of the data. This is a chapter with a medium weightage for JEE Main.
Class 11 Mathematics Chapter 15 – Topics
In the financial and economic industries, statistics is one of the most extensively used disciplines for planning and forecasting. They assist in the development of mathematical models and the analysis of time-series data. Therefore, students should extensively practise with the NCERT Solutions Class 12 Mathematics Chapter 15 and revise these concepts. The solutions include answers, illustrations, and explanations for the entire chapter 15 titled Statistics, which is taught in Class 11.
Let’s go over the sections in this chapter before diving into the NCERT Solutions for Class 11 Mathematics Chapter 15:
|15.2||Measures of Dispersion|
|15.4.1||Mean Deviation for Ungrouped Data|
|15.4.2||Mean Deviation for Grouped Data|
|15.4.3||Limitations of Mean Deviation|
|15.5||Variance and Standard Deviation|
|15.5.2||Standard Deviation of a Discrete Frequency Distribution|
|15.5.3||Standard Deviation of a Continuous Frequency Distribution|
|15.5.4||Shortcut method to find Variance and Standard Deviation|
|15.6||Analysis of Frequency Distributions|
|15.6.1||Comparison of Two Frequency Distributions with same Mean|
With examples, this section discusses the concepts of central tendency, mean, and median [during even and odd number of observations]. It introduces the notion of dispersion measurement. Measures of central tendency are values that cluster around the middle or centre of the distribution. It includes the mean, the median, and the mode. In a class, mean can be used to calculate the average of the students’ grades.
15.2 Measures of Dispersion
This section discusses measurements of dispersion, including range, quartile deviation, mean deviation, and standard deviation.
Measures of dispersion explain the link with measures of central tendency. The spread of data, for example, indicates how well the data is represented by the mean. If the spread is high, the mean is not indicative of the data.
This section explains the range, its calculation, and provides an example. The range represents the variety of scores by utilising the set’s highest and minimum values.
15.4 Mean Deviation
This section defines mean deviation and its formula. For example, biologists can utilise the notion of mean deviation to compare different animal weights and determine the weight that is considered healthy.
15.4.1 Mean Deviation – Ungrouped Data
This section describes how to calculate the mean deviation for ungrouped data. Students will have to calculate the mean, deviations from the mean, and absolute deviations, then enter the numbers into the mean deviation formula to get the result.
15.4.2 Mean Deviation – Grouped Data
This section explains how to calculate mean deviation for continuous and discrete frequency distributions using solved examples.
15.4.3 Mean deviation limitations
This section will cover the limitations of using mean deviation. Students will learn that:
- If there is a lot of variation in a series, the median will not be a good representation of the data. As a result, the mean deviation derived around such a median cannot be trusted.
- The mean deviation from the mean is not very specific if the sum of deviations from the mean is larger than the sum of deviations from the median.
- Further algebraic handling of the obtained absolute mean deviation is not possible. It cannot be used as an accurate measure of dispersion.
15.5 Standard Deviation and Variance
15.5.1 Standard Deviation
This section defines variance and standard deviation, as well as provides formulae and solved examples for discrete and continuous frequency distributions.
15.5.2 Standard Deviation of a Discrete Frequency Distribution
Students will learn that standard deviation can be determined by one of two methods based on the frequency distribution of the dataset. One of such methods is when the pieces of the data presented are discontinuous (discrete) in which there are no observation groups, and each element is assigned a specific frequency value.
15.5.3. Standard Deviation of a Continuous Frequency Distribution
The second method is when the data is provided, i.e., the elements or observations are displayed in a continuous or grouped format. It means that instead of providing a specific value to each frequency, a ‘class’ or ‘group’ of a specific element range is provided.
15.5.4 Quick Technique for Calculating Variance and Standard Deviation
With a few illustrations, this section discusses the simpler method of determining the standard deviation.
15.6 Frequency Distribution Analysis
This section explains how to compare the variability of two series with the same mean, coefficient of variation, and a few solved issues.
15.6.1 Comparison of Two Frequency Distributions with Same Mean
To compare the variability or dispersion of two series, the coefficient of variance for each series should be estimated. It is calculated by dividing the standard deviation by the mean and finding its percentage.
NCERT Solutions for Class 11 Mathematics Chapter 15 – Statistics
You must be seeking answers to the questions after you have completed Chapter 15 Mathematics Class 11. The solutions provide alternative solutions and clarifications, making students feel more confident when appearing in the exam. In case, students aren’t able to derive the answer or are unsure if their answer/approach is correct, solutions by Extramarks will prove to be of great help. The subject matter experts from Extramarks have designed the Class 11 Mathematics NCERT Solutions Chapter 15 based on the most recent CBSE Syllabus 2022-23, keeping in mind the question paper setting and the distribution of marks throughout the chapters. You can access and download these solutions and practise them offline as well.
Access NCERT Solutions for Class 11 Mathematics Chapter 15 – Statistics
Class 11 Mathematics NCERT Solutions Chapter 15
As students move through their educational journey, the concepts provided in this chapter will serve as the foundation for the introduction of more complex topics. As a result, students should make it a point to be well-versed in the formulas and theories of Statistics, as these will undoubtedly make their way into future board exams. These NCERT Solutions offer a variety of practical examples to deliver an engaging lesson, guaranteeing that students gain a solid statistical foundation and also download the exercise-by-exercise solutions given in the links below.
Mean Deviation About Mean
In the following chapter, we go over all of the exercises:
How is Statistics Class 11 Mathematics NCERT Solutions Advantageous to Students?
If you ask any top student what their secret to success is, they will undoubtedly answer that they extensively read the NCERT textbooks. All of the fundamentals are covered in these textbooks. After you have finished the theories, it is critical that you solve the NCERT questions thoroughly. This is essential for both – board exams and competitive tests such as JEE Main and JEE Advanced.
The NCERT Solutions for Class 11 Mathematics Chapter 15 have exact explanations in easy language to assist students in performing well in their first term exams. Before moving on to more difficult topics, basic concepts are thoroughly explained so that students’ doubts or confusion are cleared.
The step-by-step manner of problem-solving offers students a thorough understanding of the mark weightage as per the new CBSE Syllabus 2022-23. Students will be able to identify their areas of weakness and try to improve them in order to improve their academic performance.
You now have access to all of the Class 11 Mathematics NCERT Solutions Chapter 15 on Statistics. Use these solutions to your advantage and master the chapter.
Q.1 Find the mean deviation about the mean for the data in Exercises 1 and 2.
Q.1: 4, 7, 8, 9, 10, 12, 13, 17
Q.2: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Thus, the mean deviation is 3.
Q.2 Find the mean deviation about the median for the data in Exercises 3 and 4.
3. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
4. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Q.3 5. Find the mean deviation about the mean for the data in Exercises 5 and 6.
Q.4 Find the mean deviation about the median for the data in Exercises 7 and 8.
Q.5 Find the mean deviation about the mean for the data in Exercises 9 and 10.
|Income per day||0-100||100-200||200-300||300-400||400-500||500-600||600-700||700-800|
|Number of persons||4||8||9||10||7||5||4||3|
|Height in cms||95-105||105-115||115-125||125-135||135-145||145-155|
|Number of boys||9||13||26||30||12||10|
Q.6 Find the mean deviation about median for the following data :
|Number of Girls||6||8||14||16||4||2|
Q.7 Calculate the mean deviation about median age for the age distribution of 100 persons given below:
The given table can be arranged as given below:
Q.8 Find the mean and variance for each of the data in Exercies 1 to 5.
Q1. 6, 7, 10, 12, 13, 4, 8, 12
Q2. First n natural numbers.
Q3. First 10 multiples of 3.
Q.9 Find the mean and standard deviation using short-cut method.
Q.10 Find the mean and variance for the following frequency distributions in Exercises 7 and 8.
Q.11 Find the mean, variance and standard deviation using short-cut method
|Height in cms||70-75||75-80||80-85||85-90||90-95||95-100||100-105||105-110||110-115|
|No. of children||3||4||7||7||15||9||6||6||3|
Q.12 The diameters of circles (in mm) drawn in a design are given below:
|No. of circles||15||17||21||22||25|
Calculate the standard deviation and mean diameter of the circles.
Q.13 From the data given below state which group is more variable, A or B?
For group A:
Since, both groups have equal mean. Group B has greater standard deviation. So, group B is more variable than group A.
Q.14 From the prices of shares X and Y below, find out which is more stable in value:
For prices of share X:
For prices of share Y:
Q.15 An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
Firm A Firm B
No. of wage earners 586 648
Mean of monthly wages Rs. 5253 Rs. 5253
Variance of distribution of wages 100 121
1. Which firm A or B pays larger amount as monthly wages?
2. Which firm, A or B, shows greater variability in individual wages?
Q.16 The following is the record of goals scored by team A in a football session:
|No. of goals scored||0||1||2||3||4|
|No. of matched||1||9||7||5||3|
For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?
Q.17 The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
Q.18 The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
Let remaining two observations be x and y.
Q.19 The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.
Let remaining two observations be x and y.
Q.20 The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
Q.22 The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
(i) If wrong item is omitted.
(ii) If it is replaced by 12.
Q.23 The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject Mathematics Physics Chemistry
Mean 42 32 40.9
Standard 12 15 20
Which of the three subjects shows the highest variability in marks and which shows the lowest?
Q.24 The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.
Thus, the new mean and new standard deviation are 20 and 3.036 respectively.
FAQs (Frequently Asked Questions)
1. What are the key formulas in Statistics Class 11?
Mean, median, variance, and standard deviation formulae are important in Class 11. You’ll be able to develop a clear knowledge of the topics contained in the Chapter 15 Class 11 Mathematics once you’ve completed them. To do so, use the examples and activities in the NCERT Class 11 Mathematics CBSE book to solve and practise each sum.
2. Explain the concept of standard deviation, which is covered in Chapter 15 of the NCERT Solutions for Class 11 Mathematics.
The measurement of variation or deviation of a given set of values is dealt with by standard deviation. The range is determined by the standard deviation level. Students should obtain the solutions accessible at Extramarks to better grasp this term. Based on the needs of the students, they are presented in chapter and exercise format.
3. From where and how can I get the NCERT solutions for CBSE Mathematics Class 11 Chapter 15 Statistics?
The NCERT Solutions for Class 11 Chapter 15, which can be found in this post, is created by subject experts and professionals affiliated with Extramarks who have considerable experience in the field of teaching and are well-versed in the entire course. The solutions are specifically created with NCERT recommendations in mind. Because they are written by subject-matter experts, these answers and notes save time and are reliable for preparation.
4. How much should you practise Mathematics for NCERT Class 11?
While there is no set time for practising equations, the time required varies from person to person. Students are advised to select and practise challenging sums and equations from the Class 11 Mathematics NCERT Solutions Chapter 15. It’s also vital to set aside a few hours each week to practise those difficult equations, since this will help you study in the most efficient way possible.
5. Do I have to practise all of the questions in NCERT Solutions Class 11 Mathematics Statistics?
Constant practise is the key to mastering Ch 15 Mathematics Class 11 on Statistics. Students must memorise a number of formulas and conduct extensive calculations. A simple error while solving these problems can cost the entire mark of that question. As a result, students should review these answers on a frequent basis to keep their skills sharp.
6. What is the total number of questions in NCERT Solutions Class 11 Mathematics Chapter 15 Statistics?
In Chapter 15 Class 11 Mathematics, there are 34 problems divided among three exercises and one miscellaneous exercise. These questions, handpicked by Mathematics professionals, provide children with a 360-degree picture of the entire chapter. They range from simple formula-based to complex word problems.