dispersion

Dispersion, according to Gujarat education board, is the name of the method that is used for finding the difference between the maximum and minimum value that is also defined in terms of range, means if we want to define the range of set of values then it can be denoted as:

range = maximum value - minimum value that is also explained through the example as if there is variable that is denoted as v and it has three different values that are 50 , 51 and 53 then the range for the variable v is defined as the range = maximum value - minimum value
Range = 53 – 51
Range = 2 .
There is one another example in which value of variable v are randomly chosen that are 45 , 76 , 95 then the range defined for the variable v = maximum value - minimum value
Range = 95 – 45
Range = 50
So by using the above two examples we can define dispersion as in the very first example there is little dispersion in the values but in the later example dispersion is bigger in the values.
If we talk about the different types of dispersion than there are basically three types are defined that are IQR (Interquartile range) that defined as IQR = Q3-Q1 that is a process for elimination .IQR is come in existence to overcome the effect of outliers on the range.
Another method of dispersion is Standard Deviation that is more use than any other of dispersion method. Standard deviation is calculated by the variance and it is denoted by sigma (σ²) and the expression is denoted as σ² = ∑ (X – μ )² / N and Standard deviation ( σ ) is σ = ∑ [(X - μ)² / N ]^1/2

In upcoming posts we will discuss about Correlation coefficient and area of an ellipse calculator. Visit our website for information on Binomial Probability Formula

Measures of central tendency

Hello students, in this blog we are going to discuss the measures of central tendency that are the very important concept in the statistics. The most important central tendency measures are mean, median and mode. We calculate the mean, median and mode for the ungrouped data and we can calculate the mean, median and mode also for grouped data. Let’s discuss the all measure one by one.
Mean: - It means average of the whole numbers, like we have 9 numbers then we will add the 9 numbers together and divide by the 9, 9 is because total number are 9. For example: -
8, 7, 6, 8, 7, 5, 7, 6, 5, 6
Then add the all number and divide the total sum by 10, because 10 numbers are there.
8 + 7 + 6 + 8 + 7 + 5 + 7 + 6 + 5 + 6 / 10,
6.5 is mean,
This example was for the ungrouped data. We can calculate the mean when we have grouped data, to do this we have three methods they are: -
-Direct method.
-Shortcut method.
-Step-deviation method.
The all three methods have their respected formulas.
Medan (from CBSE Books): - Median is the middle value in the number distribution. Like we have 7 numbers then the median will be 4^th number and if we have 6 number then add the 3^rd and 4^th number and divide it by the 2, then he result will be median. For example 6, 7, 5, 4, 2 then the median is 5.
Mode: - The mode or mode value of a distribution is that value of the variable for which the frequency is maximum. For example 2, 6, 7, 2, 5, in this 2 is mode, because it is occurring at 2 times.


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Measures of dispersions in Grade XI

Measure of dispersions (for more visit here) in the simplest form is the difference between the maximum and the minimum values which is defined in terms of range. We can write it as
Range = Maximum value – minimum value
If a variable x has three different values 39, 40, 41 then Range is 41 – 39 = 2. In another example if x has values 18, 40, 60 than range is 60 – 18 = 42. In first example x has small dispersion and in another example x has large dispersion. So it is the simplest form of dispersion.
But sometimes it is affected by the outliers and that time it will be a false measure of dispersion.
Another type of measuring statistics dispersion is IQR that is inter-quartile range that is defined as IQR = Q3-Q1
IQR is come in existence to overcome the effect of outliers on the range. IQR is the process that eliminates the outlier from the data in the way that it removes the lowest 25% of the values in ordered and also removing the 25% of the highest ordered values and then range of the remaining data is the Q3 – Q1.
One of the measures of dispersion is Standard Deviation. It is used more than any other dispersion method. It is described as it is the deviation of every value of the actual data from the mean of all the data. For avoiding the zero as sum, square the deviation. Now the question is How to Calculate Standard Deviation? For standard deviation first we calculate the variance and it is denoted by sigma ( σ² ) and the expression is
σ² = ∑ (X – μ )² / N and Standard deviation ( σ ) is σ = ∑ [(X - μ)² / N ]^1/2
Where μ is mean and σ² is variance.
Sometimes we want to compare the two sets of data, that time we use the relative measure of dispersion and we cannot compare the two sets of data until their units of measurement are not same. So by using the relative measure of dispersion we compare it easily as by calculating the coefficient of variation (CV) and it is calculated as CV= S / X * 100. Here s is standard deviation and x is mean of data set. So above are some measures of dispersions that are defined for grade XI.

In upcoming posts we will discuss about Measures of central tendency in Grade XI and Basic constructions. Visit our website for information on CBSE 11th syllabus