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Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 15 Statistics, which includes thorough solutions for reference. All of the unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like **JEE mains and advanced**.

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

Following are the topics and subtopics of Class 11 Chapter 15 – Statistics of NCERT Solution:

**15.1 Introduction**

With examples, this section discusses the concepts of central tendency, mean, and median [during even and odd numbers of observations]. It introduces the notion of dispersion measurement.

Measures of central tendency are values that cluster around the middle or center of the distribution. The three terms are mean, median, and mode.

The mean can be used to find the average marks earned by students in a class.

The median can be used to obtain the midway value when calculating student height.

**15.2 Measures of Dispersion**

This section defines dispersion metrics, including the range, quartile deviation, mean deviation, and standard deviation.

The relationship between measures of central tendency and measures of dispersion is explained by measures of dispersion. The spread of data, for example, indicates how well the mean represents the data. The mean is not reflective of data if the spread is big.

**15.3 Range**

The range, its formula, and an example are all defined in this section.

Using the set’s highest and minimum values, the range calculates the variability of scores.

Batsman A’s range in a cricket match is 121 – 0 = 121, while Batsman B’s range is 52 – 22 = 30.

Range A is greater than Range B. As a result, in the instance of A, the scores are dispersed, whereas in the case of B, they are near together.

**15.4 Mean Deviation**

The formula for mean deviation is defined in this section.

Biologists can utilize the notion of mean deviation to compare different animal weights and determine what is a healthy weight.

**15.4.1Mean deviation for ungrouped data**

In this section, we’ll go through how to calculate the mean deviation for ungrouped data.

Find the mean, standard deviations, and absolute deviations, then use the mean deviation formula to calculate the solution.

**15.4.2 Mean deviation for grouped data**

This section explains how to calculate mean deviation for discrete and continuous frequency distributions using solved examples.

**15.4.3 Limitations of mean deviation**

- If there is a lot of variability 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 is unreliable.
- The mean deviation about the mean is not very specific if the sum of deviations from the mean is bigger than the sum of deviations from the median.
- Further algebraic handling of the obtained absolute mean deviation is not possible. It can’t be utilized as a reliable indicator of dispersion.

**15.5 Variance and standard deviation**

**15.5.1 Standard Deviation**

The definitions of variance and standard deviation, as well as formulas and solved examples for discrete and continuous frequency distributions, are covered in this section.

A group of pupils completed a scientific test. On calculation, the test had an average score of 85 percent. The teacher looked up the standard deviation of the other results and discovered that it was relatively minimal, implying that the majority of the kids scored very close to 85 percent.

**15.5.2 Shortcut method to find Variance and standard deviation**

With a few illustrations, this section explains how to calculate the standard deviation in a simplified approach.

**15.6 Analysis of Frequency Distributions**

This section explains how to compare the variability of two series with the same mean, coefficient of variation, and a small number of solved issues.

**Following are the concepts discussed in Chapter 15 Statistics:**

- The difference between the maximum and least value of the given data is defined as the range.
- If two series have the same mean, the one with the lower standard deviation is more stable and less scattered.
- The variance is unaffected by adding or subtracting a positive value from each data point in the data collection.

The solutions provide alternative tactics and clarifications for dealing with problems, allowing the learner to feel confident when taking the first term exam. In addition, dealing with a variety of confusing difficulties improves pupils’ knowledge of mathematical abilities. The answers cover all of the important questions that a student must know in order to appear for the term – I test. The INFINITY learn topic specialists who wrote the NCERT Exemplar Solutions for Class 11 Maths based on the most recent CBSE Syllabus 2021-22 have a thorough understanding of the question paper setting and the distribution of marks throughout the chapters.

**Frequently Asked Questions **

##### Explain the term standard deviation which is discussed in the Chapter 15 of the NCERT Exemplar Solutions for Class 11 Maths.

The measurement of variation or deviation of a given set of values is called standard deviation. The range is determined by the standard deviation level. Students are urged to obtain the PDF of solutions accessible at INFINITY study to better grasp this term. The solutions are presented in a chapter-by-chapter and exercise-by-exercise format to meet the needs of pupils.

##### Are the NCERT Exemplar Solutions for Class 11 Maths Chapter 15 helpful for the students?

The NCERT Exemplar Solutions for Class 11 Maths Chapter 15 provide precise explanations in easy language to assist students in performing well in the first term exams. According to the new CBSE Syllabus 2021-22, the step-by-step manner of solving issues gives students a clear concept of the marks’ weightage. Students will be able to identify their areas of weakness and try to improve them in order to improve their academic performance.

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