Statistics for Economics - Academic Notes for Class 11 CBSE Board

Course Overview

This course equips learners with essential skills in collecting, organizing, and presenting quantitative and qualitative economic information. Students will master basic statistical tools for analyzing economic data and drawing meaningful inferences about economic behavior.

Unit 1: Introduction (10 Periods)

What is Economics?

Economics is the social science that studies how individuals, businesses, governments, and nations make choices about how to allocate scarce resources to satisfy unlimited wants and needs.

Key Branches of Economics:

Microeconomics: Studies individual economic units (consumers, firms)
Macroeconomics: Studies the economy as a whole (GDP, inflation, unemployment)

Statistics in Economics

Meaning of Statistics:

Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data to make informed decisions and draw meaningful conclusions.

Scope of Statistics in Economics:

Economic planning and policy formulation
Market research and business decision making
Economic forecasting and trend analysis
Performance measurement and evaluation
Risk assessment and management

Functions of Statistics in Economics:

Descriptive Function: Summarizes and describes economic data
Comparative Function: Enables comparison across time, regions, or groups
Analytical Function: Helps analyze relationships between variables
Predictive Function: Assists in forecasting future trends

Importance of Statistics in Economics:

Policy Making: Government uses statistical data for economic policies
Business Planning: Companies use statistics for strategic decisions
Academic Research: Essential for economic research and theory testing
International Comparison: Enables comparison of economic performance
Problem Identification: Helps identify economic problems and solutions

Unit 2: Collection, Organisation and Presentation of Data (30 Periods)

Collection of Data

Sources of Data:

1. Primary Data

Definition: Data collected directly from the original source for the first time for a specific purpose.

Characteristics: Fresh, original, collected for specific purpose, more reliable but expensive and time-consuming.

2. Secondary Data

Definition: Data that has been collected by someone else for some other purpose but is being used by the researcher.

Characteristics: Already available, less expensive, quick to obtain but may not be perfectly suitable for current research.

Methods of Collecting Primary Data:

Direct Personal Investigation: Researcher collects data personally
Indirect Oral Investigation: Information collected through third parties
Information through Correspondents: Data collected through local agents
Telephonic Interviews: Data collected over phone
Questionnaires and Schedules: Structured forms for data collection

Sampling Concepts:

Population/Universe: Complete set of all possible observations or units of study.

Sample: A subset of the population selected for study.

Sampling: The process of selecting a representative subset from the population.

Types of Sampling:

Random Sampling: Every unit has equal chance of selection
Systematic Sampling: Selecting every nth unit
Stratified Sampling: Population divided into strata, then random sampling from each
Cluster Sampling: Population divided into clusters, some clusters selected randomly

Important Sources of Secondary Data:

Census of India:

Conducted every 10 years since 1872
Provides demographic, social, and economic data
Covers population, literacy, occupation, housing
Conducted by Office of Registrar General & Census Commissioner

National Sample Survey Organisation (NSSO):

Established in 1950
Conducts nationwide sample surveys
Areas covered: employment, consumer expenditure, housing, health
Publishes reports on various socio-economic indicators

Organisation of Data

Variables - Meaning and Types:

Variable: A characteristic that can take different values for different individuals or objects.

Types of Variables:

                        1. Quantitative Variables:
                        Discrete: Can take only specific values (e.g., number of children)
Continuous: Can take any value within a range (e.g., height, weight)

                    

                        2. Qualitative Variables:
                        Nominal: Categories with no natural order (e.g., gender, religion)
Ordinal: Categories with natural order (e.g., grades, satisfaction levels)

                    

Frequency Distribution:

Frequency Distribution: A table that shows how frequently each value or range of values occurs in a dataset.

Components of Frequency Distribution:

Class Interval: Range of values grouped together
Class Frequency: Number of observations in each class
Class Boundaries: Actual limits of each class
Class Width: Difference between upper and lower class boundaries
Cumulative Frequency: Running total of frequencies

Presentation of Data

1. Tabular Presentation:

Systematic arrangement of data in rows and columns for easy understanding and analysis.

Parts of a Table:

Title: Describes the content of the table
Stub: Left-hand column showing row headings
Caption: Column headings at the top
Body: Main part containing the data
Source Note: Source of data
Footnote: Additional explanations

2. Diagrammatic Presentation:

                        Geometric Forms:
                        Bar Diagrams: Rectangular bars of equal width, length proportional to values
Pie Diagrams: Circle divided into sectors proportional to values

                    

                        Frequency Diagrams:
                        Histogram: Bars representing frequency distribution of continuous data
Frequency Polygon: Line graph connecting midpoints of histogram bars
Ogive: Graph of cumulative frequency distribution

                    

                        Arithmetic Line Graphs:
                        Time Series Graph: Shows changes in data over time
Useful for trend analysis and forecasting

                    

Unit 3: Statistical Tools and Interpretation (50 Periods)

Measures of Central Tendency

1. Arithmetic Mean

The arithmetic mean is the sum of all values divided by the number of values.

For Simple Data:

Mean (x̄) = Σx / n

For Frequency Distribution:

Mean (x̄) = Σfx / Σf

Properties of Mean:

Affected by extreme values
Sum of deviations from mean is zero
Can be calculated for quantitative data only
Used in further statistical calculations

2. Median

The median is the middle value when data is arranged in ascending or descending order.

For Odd Number of Values:

Median = ((n+1)/2)th value

For Even Number of Values:

Median = (n/2)th value + ((n/2)+1)th value / 2

Properties of Median:

Not affected by extreme values
Can be calculated for ordinal data
Divides data into two equal halves
Suitable for skewed distributions

3. Mode

The mode is the value that appears most frequently in a dataset.

Properties of Mode:

Can be calculated for all types of data
Not affected by extreme values
May not exist or may not be unique
Represents the most typical value

Correlation

Correlation measures the strength and direction of the linear relationship between two variables.

Types of Correlation:

Positive Correlation: Both variables move in the same direction
Negative Correlation: Variables move in opposite directions
Zero Correlation: No linear relationship between variables

Properties of Correlation:

Correlation coefficient ranges from -1 to +1
Correlation does not imply causation
It measures only linear relationships
Independent of origin and scale

Scatter Diagram:

A graph that plots pairs of values for two variables to show their relationship visually.

Karl Pearson's Correlation Coefficient:

r = Σ(x-x̄)(y-ȳ) / √[Σ(x-x̄)² × Σ(y-ȳ)²]

Alternative Formula:
r = [nΣxy - ΣxΣy] / √[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]

Spearman's Rank Correlation:

Used when data is in the form of ranks or when the relationship is non-linear.

For Non-Repeated Ranks:

rs = 1 - (6Σd²) / [n(n²-1)]

For Repeated Ranks:

rs = (Σx² + Σy² - Σd²) / (2√(Σx² × Σy²))

Index Numbers

Index Numbers are statistical measures that show the relative change in a variable or group of variables over time, space, or other characteristics.

Types of Index Numbers:

                        1. Wholesale Price Index (WPI):
                        Measures price changes at wholesale level
Used to measure inflation in the economy
Base year currently 2011-12
Published weekly by Ministry of Commerce

                    

                        2. Consumer Price Index (CPI):
                        Measures price changes at retail level
Reflects cost of living for consumers
Base year currently 2012
Published monthly by NSO

                    

                        3. Index of Industrial Production (IIP):
                        Measures industrial growth
Covers mining, manufacturing, electricity
Base year currently 2011-12
Published monthly by NSO

                    

Uses of Index Numbers:

Measuring inflation and deflation
Economic policy formulation
Wage and salary adjustments
International comparisons
Business forecasting and planning

Inflation and Index Numbers:

Inflation is the sustained increase in the general price level of goods and services in an economy over time.

Inflation Rate = [(Current Year Index - Base Year Index) / Base Year Index] × 100

Simple Aggregative Method:

The simplest method of constructing index numbers by taking the ratio of the sum of current year prices to the sum of base year prices.

Price Index = (Σp₁ / Σp₀) × 100

Where:
Σp₁ = Sum of current year prices
Σp₀ = Sum of base year prices

Example Problem:

Calculate the price index using simple aggregative method:

Commodity	Base Year Price	Current Year Price
Rice	20	25
Wheat	15	18
Sugar	30	40

Solution:

Σp₀ = 20 + 15 + 30 = 65

Σp₁ = 25 + 18 + 40 = 83

Price Index = (83/65) × 100 = 127.69

Interpretation: Prices have increased by 27.69% from the base year.