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NCERT Solutions for Class 11 Statistics Chapter 6

Q: 1. What are the steps involved in the construction of the Lorenz Curve?

Ans. The procedure involves a set of nine steps.1. Calculate class Midpoints to obtainCol.2 of Table 2. Calculate the estimated total income of employees in each c ss by multiplying the midpoint of the class by the frequency in the class. Thus obtain Col. (4) of Table 3. Express frequency in each class as a percentage (%) of total frequency. Thus, obtain Col. (5) of Table 4. Express total income of each class as a percentage (%) of the total income of all classes together. Thus obtained Col. (6) of Table 5. Prepare less than cumulative frequency and Cumulative income table 6. Col. (2) Table 6.5 shows the cumulative frequency of employees.7. Col. (3) Table 6.5 shows the cumulative income going to these persons.8. Draw a line joining Co-ordinate(0,0) with (100,100). This is called the line of equal distribution.9. Plot the cumulative percentages of employees on the horizontal axis and cumulative income on the vertical axis.

Q: 4. What are the measures of Dispersion according to Chapter 6 of Class 11 Statistics?

The measures of dispersion include:RangeInterquartile rangeQuartile deviation or semi-inter-quartile rangeMean deviationStandard deviationLorenz curve.

NCERT Solutions

NCERT Solutions for Class 11 Statistics Chapter 6 - Measures of Dispersion

The NCERT Solutions for Class 11 Statistics Chapter 6 always focuses on the growth of the students. It makes the students get to understand every topic in detail, which gives sound knowledge and they become experts in that particular topic or chapter or subject. Several subject experts prepared the materials available on the official website of Vedantu.

The NCERT Solutions for Class 11 Statistics Chapter 6 PDF will be uploaded soon.

Last updated date: 01st Jun 2023

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NCERT Solutions for Class 11 Statistics Chapter 6 Measures of Dispersion

Students have tight schedules of going to school, study for hours, etc. So considering the student's comfort, the NCERT Solutions for class 11 statistics chapter 6 are available in the PDF format for free at once at the official website of Vedantu. Students can carry the hardcopy to their convenient place and study along with their friends. Also, it is helpful to revise during the time of board exams and entrance tests.

Measures of Dispersion

1. Introduction

In this section, the NCERT Solutions of class 11th chapter 6 introduce a new topic of dispersion to the students. The students have already learned different topics in statistics like the collection of data, summarizing the data, tools, etc. Here the students will learn what dispersion is. It is explained with illustration in our NCERT Solutions. They also explained that the dispersion is a maximum average value that can differ to an extent it also has certain measures, and the students are going to learn these measures in this chapter in detail.

2. Measures Based upon the Spread of Values

In this section, students will understand numerous measures to calculate the dispersion based on the values. They are the range which is the difference between the largest value and smallest value of the set. The next one is the quartile dispersion. It is a process of dividing the whole set into four equal parts to avoid the maximum values and minimum values which affect the dispersion.

3. Measures of Dispersion from Average

Statistics Class 11 NCERT Solutions' measures of dispersion explain the remaining two measures in this section with enough examples. If the set of values were given, we would use range and quartile dispersion. Whereas if the average needs to be taken to find, then it is better to use standard deviation and mean deviation. And the calculation of mean deviation also includes several variations like finding median using group data and ungrouped data. Also, each concept is explained with two or more examples.

4. Absolute and Relative Dispersion of Measures

Class 11 Statistics NCERT Solutions Chapter 6 teaches another concept in this section. NCERT Solutions explained the meaning and definition of the Coefficient of Mean deviation. It also explains the derived formula and specifies the importance of each term in the formula.

5. Lorenz Curve

NCERT Class 11 Statistics Chapter 6 measures of dispersion explain a new topic to the students, which is nothing but Lawrence curve. The students have learned the measuring of dispersions with sets and averages, deviations, etc. The curve representing all these measurements on graph paper is nothing but the Lorenz curve. Students need to learn about the Lorenz Curve in detail.

NCERT Solutions for Class 11 Statistics Chapter 6 also provided information regarding the construction of the Lorenz curve. As it plays a crucial role in the field of statistics, students can understand it as a step-by-step procedure that involves many things to learn. To provide better knowledge on these steps of the Lorenz curve, these Solutions also give an illustration in detail.

Conclusion

This is the ending part of the chapter. Here the NCERT Solutions Class 11 Statistics Chapter 6 available on Vedantu explains the importance of dispersion and the measures, different cases of dispersion like deviations, average, etc with proper examples and exercises also.

An exercise with the 12 Long answer type questions

Key takeaways of the NCERT Solutions for class 11 statistics chapter 6-measures of dispersion free pdf

NCERT Solutions of Class 12 English Chapter 6 available on the official website of Vedantu is a good choice for students to prepare for their examinations. It benefits -

NCERT Solutions provide a free download for PDF. A group of language experts are available to clarify the doubts of students through live chat.
Students can post their doubts in a chatbox on the official website.
It is useful to gain a sound knowledge and can make them attend entrance exams where English is mandatory.
It helps in enhancing their knowledge and improving their scores.

FAQs on NCERT Solutions for Class 11 Statistics Chapter 6

1. What are the steps involved in the construction of the Lorenz Curve?

Ans. The procedure involves a set of nine steps.

1. Calculate class Midpoints to obtainCol.2 of Table

2. Calculate the estimated total income of employees in each c ss by multiplying the midpoint of the class by the frequency in the class. Thus obtain Col. (4) of Table

3. Express frequency in each class as a percentage (%) of total frequency. Thus, obtain Col. (5) of Table

4. Express total income of each class as a percentage (%) of the total income of all classes together. Thus obtained Col. (6) of Table

5. Prepare less than cumulative frequency and Cumulative income table

6. Col. (2) Table 6.5 shows the cumulative frequency of employees.

7. Col. (3) Table 6.5 shows the cumulative income going to these persons.

8. Draw a line joining Co-ordinate(0,0) with (100,100). This is called the line of equal distribution.

9. Plot the cumulative percentages of employees on the horizontal axis and cumulative income on the vertical axis.

2. What are the measures used for the Dispersion of Values?

Ans. We have four different measures users further dispersion of spread values. They are-

Range
Quartile Dispersion
Mean Deviation
Standard Deviation.

3. A measure of Dispersion is a good supplement to the central value in understanding a frequency distribution. Comment according to Chapter 6 of Class 11 Statistics.

Knowledge of only the average will not give the variation in values. The measure of dispersion increases the understanding of distribution because it gives information about how much the actual value of terms in a series deviates from the central value e.g. per capita income, only gives the average income but the measure of dispersion can help you understand income inequalities.

4. What are the measures of Dispersion according to Chapter 6 of Class 11 Statistics?

The measures of dispersion include:

Range
Interquartile range
Quartile deviation or semi-inter-quartile range
Mean deviation
Standard deviation
Lorenz curve.

5. Which are the characteristics of a good measure of Dispersion according to Chapter 6 of Class 11 Statistics?

In Chapter 6 of NCERT Class 11 Statistics, the measure of dispersion is of two types: Absolute and Relative. The characteristics of a good measure of dispersion are:

It should be done based on all observations.
It should be defined rigidly.
It can be calculated and understood easily.
It should not be affected by the fluctuations of sampling and also by extreme fluctuations.
It should help in further mathematical or algebraic treatment.

6. What is the measure of Dispersion in statistics?

The measures of dispersion help to explain the variability of data. It gives information about the disparity of data from one another giving precise information of the data distribution. The measure of dispersion explains and gives an idea about the variation and the core value of an individual item. It means dispersion is the extent to which values in a distribution can change from the average of the distribution.

7. What is Dispersion? Explain the need to study it in Class 11 Statistics?

Dispersion in Class 11 Statistics is defined as the state of getting dispersed or spread. In statistics, dispersion means the extent to which a given numerical data can vary from an average value. Dispersion is important to study in Class 11 because it helps to understand how the given data is distributed. All Solutions are given in a simple language and are free of cost. These are available on Vedantu’s website(vedantu.com) Mobile app as well.