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Introduction to Statistics

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Information about Introduction to Statistics
Education

Published on March 2, 2014

Author: sauravchaser

Source: slideshare.net

Description

A brief introduction to statistics.
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INTRODUCTION TO STATISTICS

Statistics  Singular sense(Cowden & Oxden)  A statistical tool  Used for collection, presentation, analysis & interpretation of numerical data

Statistics  Plural sense(Proff. Horace Secrist)  Aggregate of facts  Affected by multiplicity of causes  Numerically expressed  Collected for predetermined purpose  Comparable

Importance and Scope of Statistics  Statistics in Planning  Statistics in State  Statistics in Mathematics  Statistics in Economics

Importance and Scope of Statistics  Statistics in Business and Management  Statistics in Accountancy and Auditing  Statistics in Industry  Statistics in Insurance  Statistics in Astronomy

Importance and Scope of Statistics  Statistics in Physical Sciences  Statistics in Social Sciences  Statistics in Biological and Medical Sciences  Statistics in Psychology and Education  Statistics in War

Measures of Central Tendency  Arithmetic Mean  Geometric Mean  Harmonic Mean  Median  Mode

Arithmetic Mean  Sum of set of observations divided by number of observations

Arithmetic Mean Single Discrete Continuous

Geometric Mean  Set of n observations in nth root

Harmonic Mean  Reciprocal of arithmetic mean

Median  Value of the variable which divides the group into two equal parts

Median Single/Discrete Continuou s Exact Median

Mode  Value which has greatest frequency density

Measures of Dispersion  Range  Quartile Deviation  Mean Deviation  Standard Deviation

Range  Difference between two extreme observations  Range = Xmax - Xmin

Merits of Range  Easiest to compute  Rigidly defined  Requires very less calculation

Demerits of Range  Not based on entire data  Affected by fluctuations of sampling  Cannot be used with open end classes  Not suitable for mathematical treatment

Quartile Deviation  Measure of dispersion based on upper quartile and lower quartile

Merits of Quartile Deviation  Makes use of 50% of data, which is better than range  Can be used with open end classes

Demerits of Quartile Deviation  Affected by fluctuation of sample  Not suitable for further mathematical treatment

Mean Deviation  Arithmetic deviations mean of the absolute

Merits of Mean Deviation  Based on all observations  Less affected by extreme observations than S.D.  Better measure of comparison

Demerits of Mean Deviation  Ignores sign of deviation  Rarely used in sociological studies  Cannot be used with open end classes

Standard Deviation  Positive square root of the arithmetic mean of the squares of the deviations from their mean  Considered as most important and widely used measure of dispersion

Merits of Standard Deviation  Rigidly defined  Based on all observations  Suitable for further mathematical treatment  Least affected by fluctuations of sampling

Demerits of Standard Deviation  More affected by extreme items  Relatively difficult to calculate and understand

Correlation A statistical measure  Used to study degree of relationship between two or more variables

Types of Correlation

Simple Correlation  Study under only two variables. Example,  Height & Weight of person  Family income & Expenditure  Price & demand

Positive and Negative Correlation  Positive if both variables moves in same direction. Example,  Day temp. & Sales of ice-cream  Height & Weight

Positive and Negative Correlation  Negative if variables move in opposite direction. Example,  Price & Demand  Day temp. & Sales of sweater

Linear & Non-linear Correlation  Linear if unit change in one variable bring constant change in other variable. Example, X 1 2 3 4 5 Y 5 10 15 20 25

Linear & Non-linear Correlation  Non-linear if unit change in one variable doesn’t bring constant change in other variable. Example, X 1 2 3 4 5 Y 4 10 12 13 20

Partial Correlation  Study under two variables at a time keeping other variables constant. Example,  Relationship between production and seed quality keeping fertilizer constant

Multiple Correlation  Study relationship between one variable & combined effect of other variables. Example,  Relationship between production and combined effect of seed quality & fertilizer

Methods of Studying Correlation  Scatter diagram method  Karl Pearson’s method  Rank correlation method  Bivariate frequency method

Scatter diagram method  Graphical and simplest method of finding correlation between two variables  One variable is plotted on the horizontal axis and the other is plotted on the vertical axis

Interpretation of data  Perfect positive correlation

Interpretation of data  Perfect negative correlation

Interpretation of data  High degree of positive correlation

Interpretation of data  High degree of negative correlation

Interpretation of data  Low degree of positive correlation

Interpretation of data  Low degree of negative correlation

Interpretation of data  No correlation

Karl pearson’s method  Mathematical method for studying relationship between variables  Two methods of calculating  Direct method  Actual mean method

Properties of simple correlation  Symmetric  Value lies between -1 and 1  Independent of change of origin and scale  Independent of unit of measurement  Geometric mean of two regression coefficient

Interpretation of correlation coefficient Value of r Interpretation +1 Perfect positive correlation -1 Perfect negative correlation Close to +1 High degree of positive correlation Close to -1 High degree of negative correlation 0 No correlation Close to 0 Low degree of positive or negative correlation

Rank correlation method  Mathematical method for studying relationship between variables according to rank  Qualitative characteristics cannot be measured qualitatively but can be arranged in order

Merits of Rank correlation method  Easy to calculate  Simple to understand  Can be applied to any type of data (Qualitative or Quantitative)

Demerits of Rank correlation method  Actual values are not used for calculations  Not convenient method for large samples

Role of Computer Technology in Statistics  SPSS is used by students later in their career  Can be used as an amplifier  Quick computational abilities of massive figure  Can be used to produce many graphs quickly and easily

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