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Information about Introduction to Statistics

A brief introduction to statistics.

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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

Learn the methods of gathering data and drawing conclusions from the best in this UC Berkeley Introduction to Statistics Course.

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