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Wednesday, March 22, 2017

Measures of Data Spread in Stats

What do we mean by SPREAD? - The measures which can tell us the variability of a dataset, width, average distribution falls into this category.

Let's see which measures we are taking about-

Input: 45, 67, 23, 12, 9, 43, 12, 17, 91
Sorted: 9, 12, 12, 17, 23, 43, 45, 67, 91

It is the simplest measures of Spread. It is the difference between max and min value of a dataset but this will not give you the idea about the data distribution. It may be given a wrong interpretation if our dataset is having outliers.

Range - Max - Min = 91 - 9 = 82

Interquartile Range (IQR):
IQR is the middle 50 percentile data which is difference between 75 percentile and 25 percentile. It is used in boxplot plotting. 

IQR = Q3 - Q1 = 56 - 12 = 44

Variance shows the distance of each element from its mean, If you simply sum this it will be zero and that is why we use squared distance to calculate it.

Standard Deviation (`\sigma` or s):
This measure is square root of Variance, the only difference between Variance and Standard deviation is the output unit as Variance.

`Variance = \sigma^2 or s^2 = \frac{\Sigma_{i=1}^N(x_i-\barx)^2}{N}`

`Standard Deviation = \sigma or s = \root{2}{\sigma^2} = \root{2}{\frac{\Sigma_{i=1}^N(x_i-\barx)^2}{N}}`

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