# NCERT Solutions for Class 11 Maths Chapter 15

NCERT Solutions for Class 11 Maths Chapter 15 Statistics in PDF for CBSE First Term Exam 2021-2022, Bihar Board, Uttarakhand Board, UP Board and all other board, whoever is following NCERT Textbooks for their board exams.

You can download NCERT Solutions 2021-22 of all subjects as well as other classes free. Clear your doubts through Discussion Forum free. Download UP Board Solutions for class 11 Maths chapter 15 in PDF file format free.## NCERT Solutions for Class 11 Maths Chapter 15

Class: | 11 |

Subject: | Maths |

Chapter 15: | Statistics |

### 11th Maths Chapter 15 Solutions

NCERT Solutions for Class 11 Maths Chapter 15 Statistics all exercises are given below to free download in PDF form updated for new academic session 2021-22. Join the Discussion Forum to ask your doubts related to study. Students can do directly 12th through NIOS after class 10, without doing 11th class.

#### Important Questions on Statistics

1. The variance of 10 observations is 16 and their mean is 12. If each observation is multiplied by 4, what are the new mean and the new variance? [Answer: 48, 256]

2. Find the mean deviation from the mean of A.P: a, a + d, a + 2d… a + 2nd. [Answer: {n(n + 1)/(2n + 1)}d]

3. Mean and standard deviation of the data having 18 observations were found to be 7 and 4 respectively. Later it was found that 12 was wrongly copied as 21 in calculation. Find the correct mean and the correct standard deviation. [Answer: 6.5, 2.5]

##### Questions from Exam Papers

1. Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, find the variance of the numbers so obtained. [Answer: 8.25]

2. Mean and standard deviation of 100 observations were found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively. Find correct standard deviation. [Answer: 10.24]

3. Coefficients of variation of two distributions are 60 and 80 and their standard deviations are 21 and 36. What are their means? [Answer: 35, 45]

###### Questions for Practice

1. The standard deviation of 25 observations is 4 and their mean is 25. If each observation is increased by 10, what are the new mean and the new standard deviation? [Answer: 35, 4]

2. The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6. Find the other two observations. [Answer: 4, 9]

3. In a series of 2n observations, half of them equal ‘a’ and remaining half equal –a. If the standard deviation of the observations is 2, then find the value of |a|. [Answer: 2]

### Important Questions on 11th Maths Chapter 15

##### What are the main methods of measures of dispersion?

The dispersion or scatter in a data is measured on the basis of the observations and the types of the measure of central tendency, used there. There are following measures of dispersion: (i) Range, (ii) Quartile deviation, (iii) Mean deviation, (iv) Standard deviation.

##### What is mean Deviation?

The mean deviation about a central value ‘a’ is the mean of the absolute values of the deviations of the observations from ‘a’. The mean deviation from ‘a’ is denoted as M.D. (a).

##### What do you mean by standard deviation?

The proper measure of dispersion about the mean of a set of observations is expressed as positive square-root of the variance and is called standard deviation. Therefore, the standard deviation, usually denoted by σ.

##### How many exercises are there in chapter 15 of class 11th Maths?

There are 4 exercises in chapter 15 of class 11th Maths.

In the first exercise (Ex 15.1), there are 12 questions.

In the second exercise (Ex 15.2), there are 10 questions.

In the third exercise (Ex 15.3), there are 5 questions.

In the last exercise (Miscellaneous), there are 7 questions.

So, there are in all 34 questions in class 11 Maths Chapter 15 and the third exercise (Ex 15.3) has the least number of questions.

There are in all 19 examples in class 11 Maths Chapter 15.

- Examples 1, 2, 3, 4, 5, 6, 7 are in Ex 15.1.
- Examples 8, 9, 10, 11, 12 are in Ex 15.2.
- Examples 13, 14, 15 are in Ex 15.3.
- Examples 16, 17, 18, 19 are based on Miscellaneous exercise on chapter 15.

##### Which chapter should students revise before starting chapter 15 of class 11th Maths?

Before starting chapter 15 of class 11th Maths, students should revise chapter 14 statistics of class 10th Maths. Chapter 14 statistics of grade 10th Maths works as a base for chapter 15 statistics of grade 11th Maths. If students skip chapter 14 of class 10th Maths, they face problems in chapter 15 of class 11th Maths.

##### Is chapter 15 of class 11th Maths important from the exam point of view?

Yes, chapter 15 of class 11th Maths is important from the exam point of view. This chapter is also useful in class 11th Economics. Some questions of this chapter are very important. These questions are questions 6, 11 of exercise 15.1, questions 6, 9 of exercise 15.2, questions 4, 5 of exercise 15.3, questions 3, 5, 7 of miscellaneous exercise on chapter 15 and example 17.

##### Is chapter 15 of class 11th Math complicated?

Chapter 15 of class 11th mathematics is not easy and not complicated. It lies in the middle of easy and hard because some examples and questions of this chapter are easy, and some are difficult. But, the difficulty level of any chapter varies from student to student. So, Chapter 15 of class 11th mathematics is easy or not depends on students also. Some students find it complex, some find it simple, and some find it in the middle of simple and complex.

##### Can students complete chapter 15 of class 11th Maths in 1 day?

No, students cannot complete chapter 15 of class 11th Maths in 1 day. Students need a maximum of 10-12 days if they seriously and honestly give 1-2 hours per day to chapter 15. This time also depends on student’s efficiency, capability, working speed, etc because no students can have the same working speed, efficiency, capability, etc.