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.Â
The NCERT Solutions for Class 11 Statistics Chapter 6 PDF will be uploaded soon.
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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 CurveÂ
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.Â
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.
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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.2Â of TableÂ
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 TableÂ
3. Express frequency in each class as a percentage (%) of total frequency. Thus, obtain Col. (5) of TableÂ
4. Express total income of each class asÂ aÂ percentageÂ (%)Â ofÂ the total income of all classes together. Thus obtained Col. (6) of TableÂ
5. PrepareÂ less than cumulative frequency and Cumulative income tableÂ
6. Col.Â (2)Â TableÂ 6.5Â shows the cumulative frequency of employees.
7. Col.Â (3)Â TableÂ 6.5Â shows the cumulative income going to these persons.
8. DrawÂ aÂ line joiningÂ 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-Â
Range
Quartile Dispersion
Mean Deviation
Standard Deviation.
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