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

**Range:**

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:**

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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