Statisticc Definition

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http://en.wikipedia.org/wiki/Mathematical_statistics

Mathematical statistics

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Mathematical statistics is the study ofstatisticsfrom a mathematical standpoint, using

probability theoryas well as other branches ofmathematicssuch aslinear algebraandanalysis.

The term "mathematical statistics" is closely related to the term "statistical theory" but alsoembraces modelling foractuarial scienceand non-statisticalprobability theory, particularly in

Scandinavia.

Statistics deals with gaining information from data. In practice,dataoften contain some

randomnessoruncertainty. Statistics handles such data using methods ofprobability theory.

[edit] Introduction

Statistical science is concerned with the planning of studies, especially with thedesign ofrandomized experimentsand with the planning ofsurveysusingrandom sampling. The initial

analysis of the data from properly randomized studies often follows the study protocol.

Of course, the data from a randomized study can be analyzed to consider secondary hypotheses

or to suggest new ideas. A secondary analysis of the data from a planned study uses tools from

data analysis.

Data analysis is divided into:

descriptive statistics- the part of statistics that describes data, i.e. summarises the dataand their typical properties.

inferential statistics- the part of statistics that draws conclusions from data (using somemodel for the data): For example, inferential statistics involves selecting a model for the

data, checking whether the data fulfill the conditions of a particular model, and withquantifying the involved uncertainty (e.g. usingconfidence intervals).

While the tools of data analysis work best on data from randomized studies, they are also applied

to other kinds of data --- for example, fromnatural experimentsandobservational studies, inwhich case the inference is dependent on the model chosen by the statistician, and so

subjective.[1]

Mathematical statistics has been inspired by and has extended many procedures inapplied

statistics.
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[edit] Statistics, mathematics, and mathematical statistics

Mathematical statistics has substantial overlap with the discipline ofstatistics.Statistical

theoristsstudy and improve statistical procedures with mathematics, and statistical research oftenraises mathematical questions. Statistical theory relies onprobabilityanddecision theory.

Mathematicians and statisticians likeGauss,Laplace, andC. S. Peirceuseddecision theorywithprobability distributionsandloss functions(orutility functions). The decision-theoretic approachto statistical inference was reinvigorated byAbraham Waldand his successors.

[2][3][4][5][6][7][8],

and makes extensive use ofscientific computing,analysis, andoptimization; for thedesign of

experiments, statisticians usealgebraandcombinatorics.
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http://www.tutorvista.com/math/definition-of-statistics-in-mathematics

Introduction to definition of statistics in mathematics:

Statistics is a study of numerical facts systematically collected with some definite object

in view, in any field of enquiry, whatsoever of observation, measurement or experiment.Statistical method is a technique used to obtain, analyze, summaries, compare and present the

numerical data or statistics. Statistics classified into two types i) Pure statistics ii) Applied

statistics. Pure statistics deals with general theories, formula, equations and their derivations.

Applied statistics deals with measurement of economic, commercial, agriculture, industrial, etc.

Example Problems for the Definitions of Statistics in

Mathematics

Example Problems for the definitions of Statistics in Mathematics are given below:

Problem 1: 7 students were asked about the time in a week they spend in doing study. They said14, 11, 17, 24, and 19 hours, respectively. Find the mean time in a week spent by them for study.

And also find the median.

Solution:

Mean:

Let x1=14, x2=11, x3=17, x4=24, x5=19

The formula for find the mean is( Sum of all the observations/ Total number ofobservations)

Therefore, the mean x (x1+x2+x3+x4+x5 / 5)

= (14+11+17+24+19/5) = (85/5) = 17

Median:

Arrange the observations in ascending order

11, 14, 17, 19, 24

Total number of observations is 5(odd).

Therefore center of the observations 17 is the median.

Problem 2:
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Consider the following three data sets A, B and C.

A = {13, 14, 15, 11, 17}

Calculate the standard deviation of each data set.

Solution:

Standard deviation, =( (x-m)2/(n))

Where m is the mean, n is the total number of elements in set, x is the elements in a set.

Here the mean is 14.

Standard Deviation Data set A

= [ ( (13-14)2

+(14-14)

2

+(15-14)

2

+(11-14)

2

+(17-14)

2

)/5 ]

= [ ( (-1)2+(0)2+(1)2+(-3)2+(3)2 )/5 ]

= [ ( 1+1+9+9 )/5 ]

= 2

Problem 3: Find the median for the following series: 7, 9, 11, 13, 19, 20

Solution:

First count the numbers, it is 6(even).

Since there is no middle number so take the middle numbers 11 and 13.

Add those two numbers and divide by two to get

(11 + 13) / 2 = 24 / 2 = 12

The median is 12.

Practice Problems for Solving Definition of Statistics inMathematics:

Practice Problems for solving definition of statistics in mathematics are given below:

Problem 1: Find the standard deviation. 8, 10, 12, 14


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Answer: 5.

Problem 2: Find the mean and median: 17, 18, 20, 19, 27, 28, and 35

Answer: Mean= 23.43, Median = 20

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Statisticc Definition