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Introduction to Measure of Dispersion

What is Measure of Dispersion?

The measure of central tendency tells something about the general level of a frequency distribution but it fails to give its complete description. This does not tell how the items are scattered around it. Sometimes it might happen that averages of two set of data are equal but the scattering of the observations from the mean and internal variations among individual observation could be different. So the direct comparison of two set of data on the basis of mean without truly estimating the variation is not feasible.

Range and Co-efficient of Range

Range is the simplest method of studying Dispersion. Range is defined as the difference between te value of the smallest observation and the value of the largest observation present in the distribution and it is denoted by R.

To calculate Range, R = L – S

Calculate Range and Co-efficient of Range for Ungrouped, Discrete series and Continuous series

Interquartile Range and Quartile Deviation and Co-efficient of Quartile Deviation

Calculate Q.D. (Quartile Deviation) and Co-efficient of Q.D. from Ungrouped Data

Calculate Q.D. and Co-efficient of Q.D. from Discrete Series

Calculate Q.D. and Co-efficient of Q.D. from Continuous Series

What is Standard Deviation ?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.  It is useful in comparing sets of data which may have the same mean but a different range. 

To calculate Standard Deviation,

Step 1: Find the mean.

Step 2: For each data point, find the square of its distance to the mean.

Step 3: Sum the values from Step 2.

Step 4: Divide by the number of data points.

Calculate Standard Deviation/Variance using Direct Method

Calculate Standard Deviation/Variance using square of value method and shortcut method

Calculate Combined Standard Deviation

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