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
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
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