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Statistics isn’t tough when you have the right notes. 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. These NCERT notes for class 11 Maths help to make learning uncomplicated, simple, and easy in a stress-free environment.
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This article on NCERT notes for Class 11 Maths Chapter 13 Statistics provides well-structured NCERT notes to help students easily grasp the concepts of Statistics. Students who want to revise the key topics of Statistics quickly will find this article very useful. It will also significantly boost the exam preparation of students. These NCERT Class 11 Maths Chapter 13 notes on Statistics are made by the Subject Matter Experts of Careers360 following the latest CBSE syllabus, ensuring that students can grasp the basic concepts effectively. For syllabus, notes, and PDF, refer to this link: NCERT.
Students who wish to access the Statistics Class 11 Maths notes can click on the link below to download the entire notes in PDF.
Careers360 experts have curated these Statistics Class 11 Notes to help students revise quickly and confidently.
Collecting and analysing data in different forms is called statistics.
Measuring the difference or the variations in the values is called dispersion measurement.
The difference between the highest and the lowest values gives us the range.
Mean is generally the ratio between the sum of observations to the number of observations.
Denoted by
Mathematical representation:
n denotes the number of observations.
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
For an even number of observations:
It is the mean of
The observation that repeats most frequently is the mode of the data.
Let
Here, x is the mean.
Steps to calculate the mean deviation about a mean:
Step 1: Calculate the mean value
Step 2: Find the value of deviation from
Step 3: Find the value of the mean of absolute value from the formula specified above under the definition.
Here, M is the median.
It can be of two types:
Discrete distribution
Continuous distribution
Let
Here,
Here,
Let n be the observation:
Where we have
Here,
Here, M denotes median.
Here,
C is the value of the cumulative frequency of the selected class
To overcome a few limitations of the mean deviation, we use the concepts called variance and standard deviation.
It is the square of the Standard deviation.
It is the square root of variance.
Another formula:
Here,
Note: When the CV is the coefficient of variance is greater than we have greater variance than that of a smaller variance.
With this topic, we conclude the NCERT Class 11 Statistics notes.
Question 1:
If xi’s are the midpoints of the class intervals of grouped data, fi’s are the corresponding frequencies and
(A) 0 (B) –1 (C) 1 (D) 2
Solution:
Mean: It is the average of the given numbers/observations. It is easy to calculate the mean. First of all, add up all the observations and then divide by the total number of observations.
That is mean
By cross multiplication, we get,
= 0
Hence, the correct answer is 0.
Question 2:
The abscissa of the point of intersection of the less-than-type and the more-than-type cumulative frequency curves of a grouped data gives its
(A) mean
(B) median
(C) mode
(D) all three above
Solution:
Frequency distribution: It tells how frequencies are distributed over values in a frequency distribution. However, mostly we use frequency distribution to summarise categorical variables.
If we make a graph of less than type and of more than type grouped data and find the intersection point, then the value at the abscissa is the median of the grouped data.
Hence, option (B) is correct.
Question 3:
For the following distribution:
Class |
0-5 |
5-10 |
10-15 |
15-20 |
20-25 |
Frequency |
10 |
15 |
12 |
20 |
9 |
The sum of the lower limits of the median class and the modal class is
(A) 15
(B) 25
(C) 30
(D) 35
Solution:
Frequency distribution: It tells how frequencies are distributed over values in a frequency distribution. However, mostly we use frequency distribution to summarise categorical variables.
Class |
Frequency |
Cumulative Frequency (C.F) |
0-5 |
10 |
10 |
5-10 |
15 |
(10+15=25) |
10-15 |
12 |
(25+12=37) |
15-20 |
20 |
(37+20=57) |
20-25 |
9 |
(57+9=66) |
|
N=66 |
|
Hence, the median class is 10 – 15.
The class with the maximum frequency is the modal class, which is 15 – 20
The lower limit of the median class = 10
The lower limit of the modal class = 15
Sum = 10 + 15 = 25
Hence, the correct answer is 25.
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:
For students' preparation, Careers360 has gathered all Class 11 Maths NCERT Notes here for quick and convenient access.
Given below are some subject-wise links for the NCERT Notes for class 11.
After finishing the textbook exercises, students can use the following links to check the NCERT exemplar solutions for a better understanding of the concepts.
Students can also check these well-structured, subject-wise solutions.
Students should always analyse 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.
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