Statistics is the collection of enormous masses of numerical information that is summarized and then analyzed for the point of making decisions; that is, the use of past information is used to predict future actions.

In other words, statistics is a scheme or technique which will enable us to approach a problem of formative a course of action in a systematic manner in order to reach the desired results. The statics are most commonly used to find the mean and variability of population.

**Uses of Statisticals:**

**MEAN: **

One of the most use of statistics is to find the mean value of a set of measurements. The term "Mean" is used to state the "average" value of a set of data. The mean also found in the same way as the "average" of a group of numbers is determined.

The mean of a set of N measurements, X_{l}, X_{2}, X_{3}, ...,
X_{N} is equal to the sum of the measurements divided by the number of data points, N. Mathematically, this is expressed by the following equation:

**
Mean ** **x= (1/n) _{i=1}∑^{n} x_{i}**

where,

*x* = the mean,

*n* = the number of values (data),

*x*1 = the first data point, *x*2 = the second data point,....*x*i = the ith data point,

*x*i = the ith data point, *x*1 = the first data point, *x*2 = the second data point, etc.

The symbol Sigma (`sum` ) is used to indicate summation, and *i* = 1 to n indicates that the values of *x*i from *i* =
1 to *i* = *n* are added. The su m of the mean calculated is divided by the number.

**Variance:**

We have discussed the averages and the means of groups of values. While the mean is a useful tool in describing a characteristic of a set of numbers, sometimes it is valuable to obtain information about the mean. There is a subsequent number that indicates how representative the mean is of the data.

**
Variance= x- xi.**

**Example1: **

Find the mean deviation about the mean for the following data:

12, 6, 18, 15, 12, 6, 20, 16

**Solution: **

We proceed step-wise and get the following:

**Step 1** Mean of the given data is `barx`

* ** `barx` =* 12+6+18+15+12+6+20+16/8

**Step 2** The deviations of the respective observations from the mean *x*, i.e., *x*i – *x* are

12–11,6–11,18–11,15–11,12–11,6–11,20–11,16–11,

or 1,–5,7,4,1,–5,9,5

**Step 3** The absolute values of the deviations, i.e.,|*xi* − *x |*are

1,5,7,4,1,5,9,5

**Step 4** The required mean deviation of the mean is

M.D. ( `barx` ) = `sum` ^{8} _{i-1} |xi-x| / 8

=`(1+5+7+4+1+5+9+5)/8` = `37/8` = 4.625.