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Semester 2: STATISTICS FOR ECONOMICS-II
Index Numbers, Unweighted/Weighted Methods, Aggregate and Relative Index Numbers, Chain and Fixed Based Index, Test of Adequacy, WPI, CPI, Cost of Living Index
Index Numbers
Introduction to Index Numbers
Index numbers are statistical measures that represent relative changes in a variable or a group of variables over time.
Unweighted and Weighted Methods
Unweighted index numbers treat all items equally. Weighted index numbers assign different weights to items based on their importance or contribution.
Aggregate and Relative Index Numbers
Aggregate index numbers measure total changes in a set, while relative index numbers compare the change of one item or set relative to another.
Chain and Fixed Based Index
Fixed base index uses a specific base year for comparison, whereas chain index numbers link different periods to measure changes continuously.
Test of Adequacy
Involves evaluating the reliability of index numbers through various criteria such as consistency and relevance.
Wholesale Price Index (WPI)
WPI measures changes in the price of goods at the wholesale level over time, reflecting inflation and supply chain shifts.
Consumer Price Index (CPI)
CPI tracks changes in the prices of a basket of consumer goods and services, serving as a key indicator of inflation.
Cost of Living Index
This index assesses the relative cost of living over time, factoring in necessary expenses like housing, food, and healthcare.
Time Series Analysis, Definition, Measurement Methods, Uses of Time Series
Time Series Analysis
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Time series analysis involves statistical techniques to analyze time-ordered data points. It is used to identify trends, seasonal patterns, and other characteristics in data recorded over time.
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Common methods for measuring time series include: 1. Moving Averages - Smooths data by averaging values over a specific time period. 2. Exponential Smoothing - Gives more weight to recent data. 3. Decomposition - Breaks down data into trend, seasonal, and residual components.
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Time series analysis is widely used in various fields: 1. Economics - For forecasting GDP, inflation rates, and stock prices. 2. Finance - For analyzing market trends and investment risks. 3. Environmental Science - For studying climate change patterns. 4. Operations Management - For inventory control and demand forecasting.
Theory of Probability, Key Concepts, Theorems, Addition, Multiplication, Bayes, Random Variables, Distributions: Binomial, Poisson, Normal
Theory of Probability
Introduction to Probability
Probability is a measure of the likelihood that an event will occur. It quantifies uncertainty and ranges from 0 (impossible event) to 1 (certain event). In probability theory, it is crucial to understand sample spaces, events, and outcomes.
Key Concepts in Probability
Key concepts include sample space, events (simple and compound), complementary events, and mutually exclusive events. Understanding these concepts is vital for solving probability problems.
Probability Theorems
Several fundamental theorems underpin probability theory, including the Law of Total Probability and Bayes' Theorem, which provides a way to update probabilities based on new evidence.
Addition Theorem of Probability
The Addition Theorem states that the probability of either event A or event B occurring is the sum of their probabilities minus the probability of both occurring. This is used for mutually exclusive and non-mutually exclusive events.
Multiplication Theorem of Probability
The Multiplication Theorem states that the probability of both events A and B occurring is the product of their individual probabilities when A and B are independent.
Bayes' Theorem
Bayes' Theorem relates the conditional and marginal probabilities of random events. It is essential for making inferences based on prior knowledge and updating probabilities.
Random Variables
A random variable is a numerical outcome of a random event. There are two types: discrete random variables (which take on countable outcomes) and continuous random variables (which can take on an infinite number of values within a range).
Probability Distributions
Probability distributions describe how probabilities are distributed over the values of the random variable. Common distributions include the Binomial, Poisson, and Normal distributions.
Binomial Distribution
The Binomial distribution models the number of successes in a fixed number of trials, with two outcomes (success or failure) and a constant probability of success.
Poisson Distribution
The Poisson distribution models the number of events occurring in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event.
Normal Distribution
The Normal distribution is a continuous probability distribution defined by its bell-shaped curve. It is characterized by its mean and standard deviation and is essential in statistics due to the Central Limit Theorem.
Sampling, Census and Sample Methods, Sampling Errors, Methods of Sampling, Merits, Limitations
Sampling, Census and Sample Methods, Sampling Errors, Methods of Sampling, Merits, Limitations
Sampling
Sampling refers to the process of selecting a subset of individuals from a population to estimate characteristics of the whole population. It is used to gather information more efficiently than surveying the entire population.
Census
A census is the collection of data from every member of a population. Unlike sampling, which involves selecting a few members, a census aims to collect exhaustive data and is conducted periodically.
Sample Methods
Sample methods include various techniques to gather data from a subset of the population. Common methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling.
Sampling Errors
Sampling errors arise from the process of selection and can lead to differences between the sample and the true population values. Two types of errors include random sampling errors and systematic errors.
Methods of Sampling
1. Simple Random Sampling: Each member has an equal chance of being selected. 2. Stratified Sampling: Population is divided into strata and samples are taken from each. 3. Cluster Sampling: Entire clusters are sampled instead of individuals. 4. Systematic Sampling: Every nth member is selected.
Merits of Sampling
1. Cost-effective: Sampling reduces costs associated with data collection. 2. Time-saving: Less time required compared to a full census. 3. Feasibility: Easier to manage and analyze smaller data sets.
Limitations of Sampling
1. Sampling bias: Risk of not representing the population accurately. 2. Margin of error: Potential variability in results. 3. Incomplete data: Possible lack of information from certain segments of the population.
Testing of Hypothesis, Null and Alternative Hypothesis, Type I and Type II Errors, t Test, Chi Square, F Test, ANOVA
Testing of Hypothesis
Definition
Testing of hypothesis is a statistical method that uses sample data to evaluate a hypothesis about a population parameter.
Null and Alternative Hypothesis
The null hypothesis represents a statement of no effect or no difference. The alternative hypothesis expresses what we aim to support.
Formulating Hypotheses
Hypotheses should be clear and testable. The null hypothesis is usually denoted as H0 and the alternative as H1 or Ha.
Type I and Type II Errors
A Type I error occurs when the null hypothesis is rejected when it is actually true. A Type II error occurs when the null hypothesis is not rejected when it is false.
t Test
A t test is used to determine if there is a significant difference between the means of two groups.
Chi Square Test
The Chi Square test is used to determine if there is a significant association between two categorical variables.
F Test
An F test is used to compare variances between two or more groups to determine if they come from populations with the same variance.
ANOVA
ANOVA, or Analysis of Variance, is a statistical method used to compare means among three or more groups.
