Introduction to Measures of Dispersion

What is Dispersion?

Dispersion is the state of getting dispersed or spread. Dispersion meaning in the extent to which a numerical data is likely to vary about an average value.

Dispersion - Simplified

Measures of Dispersion: 

The distribution of the value of a variable about its mean or median. It shows how squeezed or scattered the variable is. Measure of dispersion in statistics:

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  1. Range ­ it is simply the difference between the maximum value and the minimum value given in a data set. Eg – 1, 3,5 ,6 ,7.  Range = 7­-1= 6
  2. Variance – deduct the mean from each data in the set then squaring each of them and adding each square and finally dividing them by the total no of values in the data set.  Variance \((\sigma ^{2}) = \sum \frac{(X-\mu)^{2}}{N}\)
  3. Standard deviation – it is the square root of the variance.

An absolute measure of dispersion contains the same unit as the original data set. It includes range, standard deviation, quartile deviation relative measure of depression includes pure numbers 1, coefficient of range 2 and coefficient of variance.

Example:

Find the variance and standard deviation of the following numbers: 1, 3, 5, 5, 6, 7, 9, 10 .

The mean = 46/ 8 = 5.75

Step 1: (1 – 5.75), (3 – 5.75), (5 – 5.75), (5 – 5.75), (6 – 5.75), (7 – 5.75), (9 – 5.75), (10 – 5.75)
= -4.75, -2.75, -0.75, -0.75, 0.25, 1.25, 3.25, 4.25

Step 2:  Squaring the above values we get, 22.563, 7.563, 0.563, 0.563, 0.063, 1.563, 10.563, 18.063

Step 3: 22.563 + 7.563 + 0.563 + 0.563 + 0.063 + 1.563 + 10.563 + 18.063
= 61.504

Step 4: n = 8, therefore variance (\(\sigma ^{2}\)) = 61.504/ 8 = 7.69 (3sf)

Now, Standard deviation (\(\sigma\)))= 2.77 (3sf)

Stay tuned with byju’s to learn more about measures of dispersion, variance and many more.


Practise This Question

If a red light ray falls on the following system of prisms then after dispersion how many colours do we see in the emergent ray?