Statistics Class 11th Notes - Free NCERT Class 11 Maths Chapter 15 notes - Download PDF

We are surrounded by data, from the scores of a Football match to the marks obtained by a student in an examination, data is everywhere. Ever thought about how we can knit all these data together, so that they all make perfect sense? Well, this is where statistics come into the picture. From NCERT Class 11 Maths, the chapter Statistics contains the concepts of Measures of Dispersion, Grouped and Ungrouped Data, Variance and Standard Deviation, etc. These concepts will help the students grasp more advanced Statistics concepts easily and enhance their problem-solving ability in real-world applications.

This article on NCERT notes Class 11 Maths Chapter 13 Statistics offers well-structured NCERT notes to help the students grasp the concepts of Statistics easily. Students who want to revise the key topics of Statistics quickly will find this article very useful. It will also boost the exam preparation of the students several times. These notes of NCERT Class 11 Maths Chapter 13 Statistics are made by the Subject Matter Experts according to the latest CBSE syllabus, ensuring that students can grasp the basic concepts effectively. NCERT solutions for class 11 maths and NCERT solutions for other subjects and classes can be downloaded from the NCERT Solutions.

NCERT CLASS 11 CHAPTER 13 NOTES

Statistics:

Collecting and analysing data in different forms is called statistics.

Measure of dispersion:

Measuring the difference or the variations in the values is called dispersion measurement.

Range:

The difference between the highest and the lowest values gives us the range.

Mean:

Mean is generally the ratio between the sum of observations to the number of observations.

Denoted by $x$.

Mathematical representation: $\frac{1}{n}\sum_{i=1}^{n} x_i$

n denotes the number of observations.

$x_i$ denotes $i$ th observations.

Median:

The middlemost term in all the observations, after arranging them in either ascending or descending order, denotes the Median.

For the odd number of observations :

Median = $(\frac{n+1}{2})$ th observation

For an even number of observations:

It is the mean of $(\frac{n}{2})$ th and $(\frac{n+1}{2})$ th observation.

Mode:

The observation that repeats most frequently is the mode of the data.

Mean Deviation for ungrouped data:

Let n be the observation: x₁, x₂, x₃, ............, x_n

Mean Deviation about Mean:

$M D(\bar{x})=\frac{\sum\left|x_i-x\right|}{n}$

Here, x is the mean.

Steps to calculate mean deviation about a mean:

Step 1: Calculate the mean value $\bar{x}$ using the formula.

$\frac{1}{n} \sum_{i=1}^n x_i$

Step 2: Find the value of deviation from x_i to x.

Step 3: Find the value of mean of absolute value from the formula specified above under the definition.

Mean deviation about Median:

$M D(M)=\sum \frac{\left|x_i-M\right|}{n}$

Here M is the median.

Mean Deviation for grouped data:

It can be of two types:

1. Discrete distribution

2. Continuous distribution

Mean Deviation about the mean for a discrete distribution:

Let n be the observation: x₁, x₂, x₃, ............, x_n, and the frequencies are

f₁, f₂, f₃, ............., f_n respectively.

$M D(\bar{x})=\frac{\sum f_i\left|x_i-\bar{x}\right|}{\sum f_i}=\frac{\sum f_i\left|x_i-\bar{x}\right|}{N}$

Here, x_i and f_i are respective observations and frequencies.

N is the sum of frequencies.

Mean Deviation about median for a discrete distribution:

$M D(M)=\frac{\sum f_i\left|x_i-M\right|}{\sum f_i}=M D(\bar{x})=\frac{\sum f_i\left|x_i-M\right|}{N}$

Here, M denotes the median.

Mean Deviation about the mean for a continuous distribution:

Let n be the observation: x₁,x₂,x₃,............,x_n, and the frequencies are

f₁,f₂,f₃,.............,f_n respectively.

$\begin{aligned} & M D(\bar{x})=\frac{\sum f_i\left|x_i-\bar{x}\right|}{\sum f_i}=M D(\bar{x})=\frac{\sum f_i\left|x_i-\bar{x}\right|}{N} \\ & \text { Step deviation : } x=a+\frac{\sum_{i=1}^n f_i d_i}{N} h\end{aligned}$

Where we have $d_i = \frac{(x_i-A)}{h}$

Here, $a$ is the assumed mean, $h$ is the interval between the upper and lower class frequencies.

Mean Deviation about median for continuous distribution:

$M D(M)=\frac{\sum f_i\left|x_i-M\right|}{\sum f_i}=M D(\bar{x})=\frac{\sum f_i\left|x_i-M\right|}{N}$

Here, M denotes median.

$M=l+\frac{\frac{N}{2}-C}{f} h$

Here, $l$ is the lowest boundary value

N is the sum of frequencies

C is the value of the cumulative frequency of the selected class

$f$ is selected frequency

$h$ is the interval between the upper and lower class frequencies.

To overcome a few limitations of the mean deviation, we use the concepts called variance and standard deviation.

Variance:

It is the square of Standard deviation.

$\sigma^2=\frac{1}{n} \sum\left|x_i-\bar{x}\right|^2$

$σ^2$ = variance

$\bar{x}$ = mean

$n$ = sum of frequencies

Standard Deviation:
It is the square root of variance.

$\sigma=\sqrt{\frac{1}{n} \sum\left|x_i-\bar{x}\right|^2}$

Standard deviation of discrete frequencies:

$\sigma=\sqrt{\frac{1}{N} \sum f_i\left|x_i-\bar{x}\right|^2}$

Standard deviation of continuous frequencies:

$\sigma=\frac{1}{N} \sqrt{\sum N f_i x_i^2-\sum\left(f_i x_i\right)^2}$

Another formula:

$\sigma=\frac{h}{N} \sqrt{\sum N f_i d_i^2-\sum\left(f_i d_i\right)^2}$

Here, $h$ is the width of the class

$d_i = \frac{(x_i-A)}{h}$, where A is assumed mean

Coefficient of variance:

$\begin{aligned} C V & =\frac{\text { Standar d deviation }}{\text { Mean }} 100 \\ C V & =\frac{\sigma}{\bar{x}} 100\end{aligned}$

Note: When the CV is the coefficient of variance is greater then we have greater variance than that of a smaller variance.

With this topic, we conclude the NCERT Class 11 chapter 15 notes.

Importance of NCERT Class 11 Maths Chapter 13 Notes:

NCERT Class 11 Maths Chapter 13 Notes play a vital role in helping students grasp the core concepts of the chapter easily and effectively, so that they can remember these concepts for a long time. Some important points of these notes are:

• Effective Revision: These notes provide a detailed overview of all the important theorems and formulas, so that students can revise the chapter quickly and effectively.
• Clear Concepts: With these well-prepared notes, students can understand the basic concepts effectively. Also, these notes will help the students remember the key concepts by breaking down complex topics into simpler and easier-to-understand points.
• Time Saving: Students can look to save time by going through these notes instead of reading the whole lengthy chapter.
• Exam Ready Preparation: These notes also highlight the relevant contents for various exams, so that students can get the last-minute minute very useful guidance for exams.

NCERT Class 11 Notes Chapter Wise

Subject-Wise NCERT Notes

Given below are some subject-wise links for the NCERT Notes for class 11.

• NCERT Notes Class 11 Physics
• NCERT Notes Class 11 Chemistry
• NCERT Notes Class 11 Biology

Subject-Wise NCERT Exemplar Solutions

After finishing the textbook exercises, students can use the following links to check the NCERT exemplar solutions for a better understanding of the concepts.

• NCERT Exemplar Class 11 Solutions
• NCERT Exemplar Class 11 Maths
• NCERT Exemplar Class 11 Physics
• NCERT Exemplar Class 11 Chemistry
• NCERT Exemplar Class 11 Biology

Subject-Wise NCERT Solutions

Students can also check these well-structured, subject-wise solutions.

• NCERT Solutions for Class 11 Mathematics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Physics

• NCERT Solutions for Class 11 Biology

NCERT Books and Syllabus

Students should always analyze the latest CBSE syllabus before making a study routine. The following links will help them check the syllabus. Also, here is access to more reference books.

• NCERT Book for Class 11
• NCERT Syllabus for Class 11

Important points to note:

• NCERT problems are very important in order to perform well in the exams. Students must try to solve all the NCERT problems, including miscellaneous exercises, and if needed, refer to the NCERT Solutions for Class 11 Maths.
• Students are advised to go through the NCERT Class 11 Maths Chapter-Wise Notes before solving the questions.
• To boost your exam preparation as well as for a quick revision, these NCERT notes are very useful.

Happy learning!