Chapter - 13
Measures Of Dispersion
Measure of dispersion is a statistical concept that is used to describe how much the data values in a given set are spread out. It is a measure of how far apart the individual data points are from each other and from the mean of the data set.
The measure of dispersion is an important concept in statistics because it provides valuable information about the variability of the data set. In Class 11, we will study the different types of measures of dispersion, such as range, quartiles, variance, and standard deviation.
Understanding measures of dispersion is important in statistics because it allows us to better interpret and analyze data. By knowing how spread out the data is, we can make more informed decisions and draw more accurate conclusions from our analysis. Additionally, measures of dispersion can be used to identify outliers in the data, which can be important in certain applications.
In summary, measures of dispersion are a critical concept in statistics, and in Class 11, we will study the different types of measures of dispersion to gain a deeper understanding of how to analyze and interpret data.
The measure of central tendency gives the information about the concentration of the items around the central value. Again the measure of dispersion gives the concept about the scatterness of the items from the central value.
Though two distribution have the same measure of central tendency (i.e. mean) and the same measure of dispersion (i.e. standard deviation) they may not have the same formation. They may have different graphical formation. Let us see the following two distributions
The mean and the standard deviations of two distributions are the same but their formation shown by their graphs are entirely different. Thus only the measures of central tendency and the measure of dispersion do not give the complete idea about the distribution. For this, we examine whether the dispersed items are symmetrical or not.
A distribution which is not symmetrical is known as skewed. So, skewness is the lack of symmetry. It gives the degree of departure from the symmetry. It relates to the shape of the curve of the frequency distribution than its size. Skewness also tells about the direction along which the tail of the curve of the frequency distribution elongates.
With view of elongation of the tail of the curve of the frequency distribution, skewness can be divided into two types:
i) Positive skewness
ii) Negative skewness
i. Positive Skewness
Skewness is said to be positive when the tail of the curve of the frequency distribution elongates more on the right. Also skewness is positive if mean, median and mode of the frequency distribution satisfy the following condition:
Mean > Median > Mode
ii. Negative Skewness
Skewness is said to be negative when the tail of the curve of the frequency distribution elongates more on the left. Also, skewness is negative if mean, median and mode of the frequency distribution satisfy the condition
Mean < Median < Mode
Measures of Skewness
The absolute measure of skewness are given by the following formula:
i. The first measure of skewness
Mean - Mode or Mean - Median
ii. The second measure of skewness
= (Q₃ - Md) - (Md - Q₁)
= Q₃ + Q₁ - 2Md
The first measure of skewness is based on the assumption that in a skewed distribution, mean, median and mode do not coincide. But the second measure of skewness is based on the assumption that in a skewed distribution, median does not lie in the middle way between the lower and upper quartiles
Exercise - 13.2
In this PDF, you'll only find the solution of class 11 measures of dispersion chapter. It contains all the solutions of exercise- 13.2. If you want the solutions of other exercises then you'll find them above this PDF. Just click on the button and you'll reach your destination.
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Is Class 11 Mathematics Guide Helpful For Student ?
I have published this Notes for helping students who can't solve difficult maths problems. Student should not fully depend on this note for completing all the exercises. If you totally depend on this note and simply copy as it is then it may affect your study.
Student should also use their own will power and try to solve problems themselves. You can use this mathematics guide PDF as a reference. You should check all the answers before copying because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.
How to secure good marks in Mathematics ?
As, you may know I'm also a student. Being a student is not so easy. You have to study different subjects simultaneously. From my point of view most of the student are weak in mathematics. You can take me as an example, I am also weak in mathematics. I also face problems while solving mathematics questions.
If you want to secure good marks in mathematics then you should practise them everyday. You should once revise all the exercise which are already taught in class. When you are solving maths problems, start from easy questions that you know already. If you do so then you won't get bored.
Maths is not only about practising, especially in grade 11 you to have the basic concept of the problem. When you get the main concept of the problem then you can easily any problems in which similar concept are applied.
When your teacher tries to make the concept clear by giving examples then all students tries to remember the same example but you should never do that. You can create your own formula which you won't forget later.
If you give proper time for your practise with proper technique then you can definitely score a good marks in your examination.
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