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:
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, Xl, X2, X3, ..., XN 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 xi
x = the mean,
n = the number of values (data),
x1 = the first data point, x2 = the second data point,....xi = the ith data point,
xi = the ith data point, x1 = the first data point, x2 = the second data point, etc.
The symbol Sigma (`sum` ) is used to indicate summation, and i = 1 to n indicates that the values of xi from i = 1 to i = n are added. The su m of the mean calculated is divided by the number.
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.
Find the mean deviation about the mean for the following data:
12, 6, 18, 15, 12, 6, 20, 16
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 = 105/8= 13.125.
Step 2 The deviations of the respective observations from the mean x, i.e., xi – x are
Step 3 The absolute values of the deviations, i.e.,|xi − x |are
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.