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

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

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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NCERT CLASS 11 CHAPTER 15 NOTES
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NCERT Class 11 Notes Chapter Wise.

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NCERT CLASS 11 CHAPTER 15 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: $\frac{1}{n} \sum_{i=1}^nx_i$

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: x₁,x₂,x₃,............,x_n

Mean Deviation about Mean:

$MD ( \bar{x} ) = \frac{ \sum |x_i-x|}{n}$

Here x is the mean.

Steps to calculate mean deviation about a mean:

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

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

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:

$MD (M) = \sum \frac {|x_i-M|}{n}$

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: x₁, x₂, x₃,............,x_n, and the frequencies are

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

$MD (\bar{x}) = \frac{ \sum f_i |x_i-\bar{x}|}{\sum f_i} = \frac{\sum f_i |x_i-\bar{x}|}{N}$

Here, x_i and f_i are respective observations and frequencies.

N is the sum of frequencies.

Mean Deviation about median for discrete distribution:

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

Here, M denotes the median.

Mean Deviation about mean for continuous distribution:

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

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

$MD (\bar{x}) = \frac{ \sum f_i |x_i-\bar{x}|}{\sum f_i} = MD (\bar{x}) = \frac{ \sum f_i |x_i-\bar{x}|}{N}$

$Step\ deviation : x = a+ \frac{\sum_{i=1}^n f_id_i}{N} h$

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:

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

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 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.

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

σ²= variance

x¯ = mean

n = sum of frequencies

Standard Deviation:

It is the square root of variance.

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

Standard deviation of discrete frequencies:

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

Standard deviation of continuous frequencies:

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

Another formula:

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

Here,

h is the width of the class

d_i = (x_i-A)/h where A is assumed mean

Coefficient of variance:

$\\ CV = \frac{Standard \ deviation} {Mean} 100 \\ \\ CV = \frac{\sigma}{\bar{x}} 100$

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

Significance of NCERT Class 11 Maths Chapter 15 Notes:

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 Notes Chapter Wise.

NCERT Class 11 Maths Chapter 1 Notes

NCERT Class 11 Maths Chapter 2 Notes

NCERT Class 11 Maths Chapter 3 Notes

NCERT Class 11 Maths Chapter 4 Notes

NCERT Class 11 Maths Chapter 5 Notes

NCERT Class 11 Maths Chapter 6 Notes

NCERT Class 11 Maths Chapter 7 Notes

NCERT Class 11 Maths Chapter 8 Notes

NCERT Class 11 Maths Chapter 9 Notes

NCERT Class 11 Maths Chapter 10 Notes

NCERT Class 11 Maths Chapter 11 Notes

NCERT Class 11 Maths Chapter 12 Notes

NCERT Class 11 Maths Chapter 13 Notes

NCERT Class 11 Maths Chapter 14 Notes

NCERT Class 11 Maths Chapter 15 Notes

NCERT Class 11 Maths Chapter 16 Notes

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