**Descriptive statistics :-**

First hand tools which gives first hand information.

- Central tendency of data (Mean, median, mode, geometric mean, harmonic mean etc.)
- Variation in data (variance, standard deviation, standard error, mean deviation etc.)

**Central tendency of the data**

Gives an idea about the mean value of the data

The data is clustered around what value?

**Data**: 𝒳1, 𝒳2, ......,𝒳n

x : Data vector

**mean (x)**

prod (x) ^ (1/length (x) )

(length (x) is equal to the number of elements in x)

**Median :-**

Value such that the number of observation above it is equal to the number of observation below it.

median (x)

Example :-

**Variability**

spread and scatterdness of data around any point, preferably the mean value.

Data set 1: 360, 370, 380

mean = (360 + 370 + 380) /3 = 370

Data set 2: 10, 100, 1000

mean = (10 + 100 + 1000) /3 = 370

How to differentiate between the two data sets?

x : data vector

var (x)

positive square root of variance :

__standard deviation__

sqrt (var (x) )

Variance

Another variant,

If we want divisor to be n, then use

( (n-1) /n) * var (x)

where n = length (x)

**Range:**

maximum(x1, x2, ....., xn) - minimum(x1, x2, ...., xn)

max (x) - min (x)

**Interquartile range:**

Third quartile (x1, x2, ..., xn) - First quartile (x1, x2, ...., xn)

IQR (x)

**Quartile deviation:**

[Third quartile (x1, x2, ..., xn) - First quartile (x1, x2, ..., xn)]/2

= Interquartile range/2

IQR (x) /2

Example :-

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