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Edited By Ramraj Saini | Updated on Mar 22, 2022 05:45 PM IST

Class 11 Math chapter 15 notes are regarding statistics. In chapter 15 we will be going through the mean, mode, and median concepts in Statistics Class 11 notes. This Class 11 Maths chapter 15 notes contains the following topics: statistics, range, mean, median, mode, mean deviation about mean and median in grouped and ungrouped data, continuous, discrete distributions, the standard deviation for ungrouped, continuous, discrete distributions, variance, coefficient of variance with standard formulas. NCERT Class 11 Math chapter 15 contains a detailed explanation of topics like - mean, median, mode, frequency, variation. Important topics are explained in CBSE Class 11 Maths chapter 15 notes in a very simple and detailed way. All these notes can be downloaded from Class 11 Maths chapter 15 notes pdf download, Statistics Class 11 notes, and Class 11 Statistics notes pdf download.

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**Also, students can refer,**

- NCERT Solutions for Class 11 Maths Chapter 15 Statistics
- NCERT Exemplar Class 11 Maths Chapter 15 Statistics

**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:

n denotes the number of observations.

x_{i} denotes i th observations.

**Median:**

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

For the odd number of observations :

Median = {n+1}/2 th observation

For an even number of observations:

It is the mean of n/2 th and {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: x_{1},x_{2},x_{3},............,x_{n}

**Mean Deviation about Mean:**

Here x is the mean.

Steps to calculate mean deviation about a mean:

Step 1: Calculate the means value x‾ the formula.

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:**

Here M is the median.

**Mean Deviation for grouped data:**

It can be of two types:

Discrete distribution

Continuous distribution

**Mean Deviation about mean for discrete distribution:**

Let n be the observation: x_{1}, x_{2}, x_{3},............,x_{n}, and the frequencies are

f_{1},f_{2},f_{3},.............,f_{n} respectively.

Here, x_{i} and f_{i} are respective observations and frequencies.

N is the sum of frequencies.

**Mean Deviation about median for discrete distribution:**

Here, M denotes the median.

**Mean Deviation about mean for continuous distribution:**

Let n be the observation: x_{1},x_{2},x_{3},............,x_{n}, and the frequencies are

f_{1},f_{2},f_{3},.............,f_{n} respectively.

Where we have d_{i} = {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:**

Here, M denotes median.

Here, l is the lowest boundary value

N is the sum of frequencies

C is the value of cumulative frequency of 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.

σ^{2}= variance

x¯ = mean

n = sum of frequencies

**Standard Deviation:**

It is the square root of variance.

**Standard deviation of discrete frequencies:**

**Standard deviation of continuous frequencies:**

Another formula:

Here,

h is the width of the class

d_{i} = (x_{i}-A)/h where A is assumed mean

**Coefficient of variance:**

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

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

The link for NCERT textbook pdf is given below:

URL: ncert.nic.in/textbook/pdf/kemh115.pdf

NCERT Class 11 Maths chapter 15 notes will be very much helpful for students to score maximum marks in their 11 board exams. In Statistics Class 11 chapter 15 notes we have discussed many topics: statistics, range, mean, median, mode, mean deviation about mean and median in grouped and ungrouped data, continuous, discrete distributions, the standard deviation for ungrouped, continuous, discrete distributions, variance, coefficient of variance with standard formulas. NCERT Class 11 Maths chapter 15 is also very useful to cover major topics of the Class 11 CBSE Maths Syllabus.

The NCERT Class 11 Maths chapter 15 notes are in compact form. The statistics chapter is explained in detail in the notes. Most useful topics and formulas are explained in an easy manner. The students can download pdf from the Statistics Class11 chapter 15 pdf download link.

NCERT Class 11 Maths Chapter 3 Notes |

- 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

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

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Download EBook1. What is the use of Statistics Class 11 notes in real life?

They are useful in weather forecasts, for maintaining records of the stock market, for appropriate comparison and data collection.

2. Who invented Class 11 Math chapter 15 notes?

John Graunt, along with William Petty first invented and used statistics and census.

3. How many types of statistics do we have in NCERT Class 11 Math chapter 15?

Even though we don't use any such types and the definitions in NCERT Class 11 Math chapter 15 for the information we have 2 types of statistics.

They are - descriptive and inferential statistics.

4. What are the important and basic terms in Class 11 Maths chapter 15 notes?

We have the most important and basic terms in statistics: mean, mode, median.

Detailed information regarding all the terms and the formulas are explained above in the notes.

5. What are the advantages of statistics in our daily life according to ncert notes for Class 11 Maths chapter 15?

a) For storing and displaying large and complex data easily in the prescribed form.

b) For weather and stock market measurements.

c) To draw conclusions on any topic seeing statistics

d) For showing the trends growth

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