The NCERT Solutions For Class 11 Maths Chapter 15 – Statistics are available as a pdf on this page. The NCERT Solutions are authored by the most experienced educators in the teaching industry making the solution of every problem straightforward and justifiable. Every solution written in the pdf given underneath empowers the student to get ready for the test and accomplish it. These solutions assist a class 11 student with mastering the idea of Limits and Derivatives.
Access NCERT Solutions for Class 11 Maths Chapter 15 Statistics
NCERT Solutions for Class 11 Maths Chapter 15 – Statistics
The topics of Class 11 Chapter 15 – Statistics of NCERT Solution are as follows:
This section talks about the concept of central tendency, mean and median [during even and the odd number of observations] with examples. It introduces the concept of measure of dispersion.
The values which cluster around the middle or centre of the distribution are measures of central tendency. They are mean, median and mode.
In a class, mean can be used to find the average marks scored by the students.
When calculating the height of students, the median can be used to find the middlemost value.
15.2 Measures of Dispersion
This section defines measures of dispersion, different measures of dispersion [range, quartile deviation, mean deviation, standard deviation]
Measures of dispersion explain the relationship with measures of central tendency. For example, the spread of data tells how well the mean represents the data. If the spread is large, then mean is not representative of data.
This section defines the range, its formula and an example.
The range gives the variability of scores using the maximum and minimum values in the set.
In a cricket match, Batsman A range = 121 – 0 = 121 and Batsman B range = 52 – 22 = 30
Range A > Range B. So, the scores are spread in case of A whereas for B they are close to each other.
15.4 Mean Deviation
This section defines mean deviation, the formula for mean deviation.
The concept of mean deviation can be used by biologists in the comparison of different animal weights and decide what would be a healthy weight.
15.4.1Mean deviation for ungrouped data
The process of obtaining the mean deviation for ungrouped data is elaborated in this section.
Find the mean, deviations from the mean, absolute deviations and substitute the values in the mean deviation formula and arrive at the answer.
15.4.2 Mean deviation for grouped data
The process of obtaining mean deviation for discrete and continuous frequency distributions are elaborated in this section with solved examples.
15.4.3 Limitations of mean deviation
- If in a series the degree of variability is very high, then median will not be a representative of data. Hence the mean deviation calculated about such median cannot be relied on.
- If the sum of deviations from the mean is greater than the sum of deviations from the median, then the mean deviation about mean is not very specific.
- The absolute mean deviation calculated can’t be subjected to further algebraic treatment. It can’t be used as an appropriate measure of dispersion.
15.5 Variance and standard deviation
15.5.1 Standard Deviation
This section involves the variance and standard deviation definition, formula and solved examples on the discrete and continuous frequency distribution.
A science test was taken by a class of students. The mean score of the test was 85% on calculation. The teacher found the standard deviation of other scores and noticed that a very small standard deviation exists which suggests that most of the students scored very close to 85%.
15.5.2 Shortcut method to find Variance and standard deviation
This section deals with the simpler way of calculating the standard deviation with a few illustrations.
15.6 Analysis of Frequency Distributions
This section deals with the process of comparing the variability of two series having the same mean, coefficient of variation with few solved problems.
Get detailed solution for all the questions listed under below exercises:
Exercise 15.1 Solutions : 12 Questions
Exercise 15.2 Solutions : 10 Questions
Exercise 15.3 Solutions : 5 Questions
Miscellaneous Exercise Solutions: 7 Questions
A few points on Chapter 15 Statistics
- Range is defined as the difference between the maximum and minimum value of the given data.
- If there exists series with equal means, then the series with lesser standard deviation is more consistent or less scattered.
- The addition or subtraction of a positive number to each data point of the data set will not affect the variance.
The solutions give substitute strategies and clarifications to take care of problems which makes the student feel sure while taking the test. Additionally, taking care of many muddled issues upgrades the information on mathematical ability in the students. The solutions cater to all the vital inquiries which a student should and ought to have aced to show up for the test. The BYJU’S subject specialists who have written these solutions have complete knowledge about the question paper setting and the marks distributed across the chapters.