Measures of Dispersion

Nov 29, 2020

Dispersion

• Measure of Dispersion is a way of describing how data is spread around a average value.
• If dataset have large differences between data values then dataset is said as widely scattered dataset.
• If dataset have smmall differences between data value then we can say that dataset is tightly clustered dataset.

How is it useful ?

• Measure of Dispersion represents the variation in the data which provide the information like how well the average of the sample represents the entire data. Less variation gives close representation while with larger variation average may not closely represent all the values in the sample.
• Measures of dispersion enables us to compare two or more series with regard of their variations. It helps to determine consistency.

Range

Range is the difference between largest and lowest data point in a given dataset.

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x = [1,5,23,89,2,12]
Range = 89-1 = 88

Mean Deviation

Average of absolute differences from the mean is the mean Deviation.

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step 1 : Calculate the mean for the given dataset.
step 2 : Substract every datapoint with mean and add them all.(neglect -ve values)
step 3 : divide the sum of all the differences with total number of datapoints.

Variance

• The variance is the average of squared differences from the mean.

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step 1 : Calculate the mean.
step 2 : find the difference of each datapoint from the mean and squared them.
step 3 : divide the step 2 output with total number of data points (count).

Standard deviation

• Standard deviation is the squared root of variance.
• Standard deviation Measures how spread the values of dataset around the mean.

deviation from mean.

Why do we divide by (n-1) instead of n ?

• Read it carefully as it may be too long.
• You have noticed that when we finding the Standard deviation or variance of sample, I am dividing n-1 instead of n why? Because you don't know the true mean of populaion; all you know is the mean of sample.(Except fot the rare cases).Because of that i will not able to get the correct variances. To get the correct variances indirectly to decrease the error or to maintain the degree of freedom , divide by n-1 rather than n .
• It is called bessel correction.

Coefficient of Variance >