🇮🇳Statistics_India🇮🇳

Types of Exams in India

for UPSC & GPSC Mains

Time Management is a must be given priority for success.. P. Gyanvatsal Swami

Some Facts of National Account Release Quarterly Extimates of 2024-25
1. Real GDP has been estimated to grow by 5.4% in Q2 of FY 2024-25 over the growth rate of 8.1% in Q2 of FY 2023-24

2. Real GVA has grown by 5.6% in Q2 of FY 2024-25.

3. Agriculture and Allied sector has bounced back by registering a growth rate of 3.5% in Q2 of FY 2024-25

4. Tertiary sector has observed a growth rate of 7.1% in Q2 of FY 2024-25

5. Real GDP or GDP at Constant Prices in Q2 of 2024-25 is estimated at ₹44.10 lakh crore.

6. Nominal GDP or GDP at Current Prices in Q2 of 2024-25 is estimated at ₹76.60 lakh crore

7. Real GVA in Q2 of 2024-25 is estimated at ₹40.58 lakh crore & Nominal GVA in Q2 of 2024-25 is estimated at ₹69.54 lakh crore

8. Real GDP or GDP at Constant Prices in April-September of 2024-25 (H1 2024-25) is estimated at ₹87.74 lakh crore.

9. Quarterly Estimates of GDP are indicator-based and compiled using the benchmark-indicator method

10. The sector-wise estimates have been compiled using indicators/data sources viz. (i) Index of Industrial Production (IIP), (ii) Financial performance of Listed Companies in the Private Corporate
sector based on available quarterly financial results of these companies for Q2 of 2024-25, (iii) Production Targets and First Advance Estimates of Crop Production for 2024-25, (iv) Production
Targets and summer season production estimates of Major Livestock products for 2024-25; (v) Fish Production, (vi) Production/Consumption of Cement and Steel, (vii) Net Tonne Kilometres and Passenger Kilometres for Railways, (viii) Passenger and Cargo traffic handled by Civil Aviation, (ix) Cargo traffic handled at Major and Minor Sea Ports, (x) Sales of Commercial Vehicles, (xi)
Bank Deposits and Credits, (xii) Accounts of Central and State Governments, etc., available for Q2 of 2024-25.

11. The First Advance Estimates of FY 2024-25 Annual GDP will be released on 7.01.2025. The release of quarterly GDP estimates for October-December of 2024-25 (Q3 2024-25) will be on 28.02.2025.

https://mospi.gov.in/sites/default/files/press_release/NAD_PR_29112024.pdf

When sampling without replacement, the probability of selecting an item changes after each draw because the total population size decreases. To manage this complexity, certain techniques can be applied:

1. Reweighting Probabilities (Horvitz-Thompson Estimator)

Explanation: Adjust the probability of selection dynamically using weights that account for previously selected items.

Example: If you are drawing 3 items from a group of 5, where the initial probabilities of selection are proportional to some value (e.g., weights), after drawing the first item, recompute probabilities for the remaining 4 items.


2. Systematic Sampling

Explanation: Use a predefined rule or interval for selection, reducing the need to update probabilities dynamically.

Example: For a population sorted by weights, pick every nth item.


3. Sequential Sampling Algorithms

Explanation: Use algorithms such as the Weighted Reservoir Sampling that efficiently handle changes in probability after each draw.

Example: If you want to sample 2 items from a population of 10 with different probabilities, dynamically adjust weights after each selection while ensuring previously drawn items aren’t re-selected.


4. Monte Carlo Simulations

Explanation: Simulate the process multiple times to average out the expected values, accounting for the changing probabilities.

Example: Simulate drawing cards from a deck without replacement repeatedly and calculate average outcomes to estimate expectations.


By implementing these techniques, the complexity of changing expectations can be effectively managed in sampling scenarios.

GST

Census of India

UPSC/ GPSC - Constitution of India

Research Security should be a national priority

GST Collection 1.82 Lakh Crore

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🔴Bayesian Statistics and Data Analysis

Bayesian data analysis is a crucial concept in the field of data science, but it can be challenging to understand its significance. In this short post, I will explain Bayesian modeling. Let's dive in!

Why Bayesian Data Analysis?
Bayesian modeling is a powerful tool in statistics and data science, particularly in situations where traditional approaches fall short. Unlike traditional methods, Bayesian modeling avoids arbitrary assumptions and provides distributions of possible values instead of just point estimates.

Bayes' Theorem:
Bayesian modeling is based on Bayes’ theorem, which provides a mathematical formula for updating the probability of a hypothesis as more evidence or information becomes available. This allows us to revise existing predictions or theories in light of new evidence, which is known as Bayesian inference.

Simplification of Bayes’ Theorem:
Since X (data) is not dependent on θ (the model) and can be challenging to calculate, Bayes’ theorem is often simplified to P(θ|X) ∝ P(X|θ) × P(θ), meaning the posterior distribution is proportional to the likelihood times the prior.

From Bayesian Theorem to Bayesian Modeling:
Bayes’ Theorem provides a process for constructing a Bayesian model. Combining key ingredients, such as the likelihood and prior distributions, produces posterior distributions.

Calculating the Posterior Distribution:
There are two main methods for calculating the posterior distribution: direct calculation using complex equations and simulation methods, such as Markov Chain Monte Carlo (MCMC), which create samples from the posterior distribution to summarize information about parameters. Many software programs, such as PyMC, Brms, and Stan, use sampling methods like MCMC.

Advantages of Bayesian:
The Bayesian approach allows for direct inclusion of prior knowledge, transparency in modeling steps, and provides broad information about the problem, including risks, uncertainty, and variability.

Business Cases: Bayesian modeling is beneficial for businesses that require knowledge of uncertainty, such as demand forecasting, pricing strategy optimization, customer analysis, credit scoring, and financial modeling. Bayesian modeling provides not only a point estimate but also the risk or confidence of the prediction

The news article highlights Chief Economic Advisor V. Anantha Nageswaran's views on India's economic slowdown, as the July-September GDP growth slumped to 5.4%, its lowest in nearly two years. He emphasized the need for deregulation, expanding state capacity, and improving hiring and compensation policies in the private sector to stimulate growth. Nageswaran pointed to the self-generated slowdown in select industries due to tepid wage growth and limited purchasing power. He advocated for doubling down on deregulation, enhancing state capacity for public investment, and focusing on regulatory reforms to sustain long-term growth. While acknowledging challenges, he noted resilience in the economy, driven by manufacturing, construction, and recovery in profits post-COVID. He also stressed the importance of empowering local governments and the private sector for broader economic development.

Diabetes rates:

1. 🇵🇰Pakistan: 30.8%
2. 🇰🇼Kuwait: 24.9%
8. 🇪🇬Egypt: 20.9%
10. 🇶🇦Qatar: 19.5%
12. 🇲🇾Malaysia: 19%
14. 🇸🇦Saudi Arabia: 18.7%
17. 🇲🇽Mexico: 16.9%
26. 🇹🇷Turkey: 14.5%
27. 🇧🇩Bangladesh: 14.2%
48. 🇱🇰Sri Lanka: 11.3%
53. 🇿🇦South Africa: 10.8%
54. 🇮🇶Iraq: 10.7%
55. 🇺🇸United States: 10.7%
56. 🇮🇩Indonesia: 10.6%
57. 🇨🇳China: 10.6%
60. 🇪🇸Spain: 10.3%
63. 🇹🇭Thailand: 9.7%
64. 🇮🇳India: 9.6%
71. 🇮🇷Iran: 9.1%
74. 🇵🇹Portugal: 9.1%
78. 🇧🇷Brazil: 8.8%
83. 🇳🇵Nepal: 8.7%
86. 🇰🇵North Korea: 8.6%
96. 🇨🇦Canada: 7.7%
107. 🇵🇭Philippines: 7.1%
113. 🇰🇷South Korea: 6.8%
116. 🇯🇵Japan: 6.6%
127. 🇦🇺Australia: 6.4%
129. 🇮🇹Italy: 6.4%
132. 🇬🇧United Kingdom: 6.3%
135. 🇳🇿New Zealand: 6.2%
139. 🇻🇳Vietnam: 6.1%
153. 🇷🇺Russia: 5.6%
162. 🇦🇷Argentina: 5.4%
165. 🇫🇷France: 5.3%
169. 🇪🇹Ethiopia: 5%
183. 🇰🇪Kenya: 4%
186. 🇳🇬Nigeria: 3.6%

% of people age 20-79 who have type 1 or type 2 diabetes

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Application of Mc Nemar Test...

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Vacancy Announcement
BHARUCH DISTRICT

District planning office,Bharuch invites applications for the following contractual positions:

1.Senior Project Associate (SPA)

Salary: ₹27,500/- per month

TOTAL Vacancy SPA = 1

Eligibility Criteria:
(1)Candidates must possess at least a Postgraduate degree in Economics, Mathematics, Finance, or Statistics, or a Master’s degree in Management.

(2)we are not allow updown, so He /she must resident in Bharuch or ankleshwar

(3) He/ she able to do gujarati typeing, know excel work ( formula) , PPT work for meetings and others

How to Apply:
Interested candidates are encouraged to send their resume via: WhatsApp: 7016471985 strictily dont call directly

For further details, contact:
Mr. Mitul Dafda
Research Officer,
District planning office,Bharuch

MCQ Series

Sampling Methods

Application of Chi square test..

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Share Statistical AnalysisHandbook.pdf

Hasmukh Patel :
આરોગ્ય વિભાગની કુલ 2800 જગ્યાઓ માટેની અરજી આવતીકાલે બપોરે કલાક એક વાગ્યાથી ઓજસતી કરી શકાશે. અરજી કરવાની છેલ્લી તારીખ 10 ડિસેમ્બર 2024 રહેશે. આમાંથી એક પણ જગ્યા ખાલી ન રહે તે માટે ગુજરાતના ડોક્ટરોને તથા તબીબી વિદ્યાશાખામાં છેલ્લા વર્ષમાં ભણતા વિદ્યાર્થીઓને અરજી કરવા વિનંતી.
•••••
Join @gpscgj • @gpsctg
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⏰ November 20, 2024 at 05:16PM
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The Ministry of Statistics and Programme Implementation extends its heartfelt congratulations to Prof. Neena Gupta, Professor at the Indian Statistical Institute, Kolkata, on being awarded the Infosys Prize 2024. Prof. Gupta’s pioneering work in the field of algebraic geometry, notably her solution to the long-standing Zariski Cancellation Problem, has made a significant impact. Her exceptional contributions to mathematics have brought global recognition to India.

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Hypothesis testing is a key statistical method that allows us to draw conclusions about populations based on sample data. Choosing the right test is essential for obtaining accurate and reliable results.

When the appropriate hypothesis test is selected, it ensures sound conclusions and supports data-driven decision-making. Different tests, such as t-tests, ANOVA, and chi-squared tests, are designed to address various data types and research questions, providing both flexibility and precision.

However, using the wrong test can lead to misleading outcomes and incorrect conclusions, which can undermine the credibility of your analysis. Additionally, neglecting important assumptions, such as normality or equal variances, can compromise the validity of the test results.

Here are some important hypothesis tests:

🔹 T-test: Used to compare the means of two groups.
🔹 Z-test: Used to determine if there is a significant difference between sample and population means when the population variance is known.
🔹 ANOVA (Analysis of Variance): Used to compare means across three or more groups.
🔹 Chi-Squared Test: Used for categorical data to assess how likely the observed distribution is, given the expected distribution.

#statistical #DataScientists #DataAnalytics

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RBI Monetary Policy

👆3 new members appointed in RBI's Monetary Policy Committee The Government of India has reconstituted the Monetary Policy Committee of the Reserve Bank of India and appointed three new members - Prof. Ram Singh, Saugata Bhattacharya and Dr. Nagesh Kumar.

Monetary policy is a set of tools used by a nation's central bank to control the overall money supply and promote economic growth and employ strategies such as revising interest rates and changing bank reserve requirements.

🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
Objectives of Monetary Policy
🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸

The main objective of monetary policy is to maintain price stability while keeping in mind economic growth, because price stability is an essential condition for sustainable development.
High inflation in an economy means an increase in the prices of essential commodities. This is an indicator that inflation is rising rapidly.
The most important tool in monetary policy to reduce inflation is the repo rate. If the Reserve Bank wants to increase the supply of money and liquidity in the market, it reduces the bank rate.

If the money supply and liquidity in the market needs to be reduced, then it increases the repo rate. The central bank usually increases the repo rate when inflation increases and reduces it when inflation decreases.
We can say that monetary policy is a kind of weapon, on the basis of which the supply of money in the market is controlled. Monetary policy decides at what rate the Reserve Bank will lend money to banks and at what rate it will take back money from those banks.

What is meant by "Official Statistics"?

✓✓ What are Normal Goods?

Normal goods are a type of goods whose demand shows a direct relationship with a consumer’s income. It means that the demand for normal goods increases with an increase in the consumer’s income or expansion of the economy (which generally will increase the income of the population).

Normal goods demonstrate a higher income elasticity of demand than inferior goods. The former shows an elasticity between zero to one, while the latter shows a negative income elasticity of demand.

✓✓ Normal Goods and Consumer Behavior

Demand for normal goods is determined by patterns in the behavior of consumers. Larger income leads to changes in the consumers’ behavior. As income increases, consumers may be able to afford goods that were not previously available to them.

In such a case, the demand for the goods increases due to their attractiveness to consumers. It may be explained by the higher quality of the goods, higher functionality, or more prestigious socio-economic value (think about many luxury goods).

Economists use income elasticity of demand to measure the extent to which the demand for a product reacts to a change in consumer income or purchasing power. It is calculated by dividing the change in product quantity demanded by the change in income. Income elasticity of demand is often used to differentiate between a normal, inferior, and luxury good, as well as forecast sales during periods of increasing or declining incomes.

✓✓ Examples of Normal Goods

1. Clothes

Clothes can fall under normal and inferior goods depending on their type and quality. As income rises, people tend to spend more on clothing at luxury clothing stores.

Consumers may also opt for designer clothing located in high-end markets when there is an increase in income. However, when the consumers’ income declines, people will still buy clothes but at retail outlets and consignment stores rather than luxury clothing stores.

2. Organic food

As the world moves to healthy eating, people will tend to spend more on organic foods if they receive an increase in income. Organic foods are grown more naturally compared to non-organic foods, and people are inclined to spend more on the former from a health, quality, and taste perspective. However, with declining incomes, people revert to non-organic foods, which cost less due to their mass production and fewer defects.

3. Electronics

Electronics are categorized as normal goods because people tend to spend more on electronic items, such as laptops, tablets, fitness trackers, and gaming systems whenever there is an increase in purchasing power.

Most electronics stores may stock different brands of specific electronic items, some of which may be inferior depending on consumer preferences and tastes. Most buyers tend to associate more with major brands such as Apple, Samsung, etc. when buying phones and TVs, and consider off-brand electronics as inferior goods.

#education
#economics
#economy

Cluster sampling is a statistical method used to collect data by dividing a population into smaller groups, or "clusters," and then randomly selecting some of these clusters for analysis. This approach can be particularly useful when studying large populations.

If used correctly, cluster sampling offers several benefits:

✔️ Cost-effective: Reduces the cost and time needed for data collection by focusing on a few clusters instead of the entire population.
✔️ Practical for large populations: Easier to manage and execute, especially when the population is spread over a wide area.
✔️ Representative results: Can provide reliable data when clusters are well-defined and adequately represent the whole population.

However, there are potential drawbacks if not implemented properly:

❌ Risk of bias: If clusters are not randomly selected or are too similar, the results may not accurately represent the entire population.
❌ Data variability: Differences between clusters can introduce variability, affecting the reliability of conclusions.
❌ Complex analysis: Analyzing data from cluster sampling can be more complicated due to the need to account for intra-cluster correlations.

Cluster sampling is different from other sampling methods in several ways:

1️⃣ Simple Random Sampling: This method selects individuals randomly from the entire population. While it can be very accurate, it is often impractical for large populations due to time and cost constraints.
2️⃣ Stratified Sampling: This method divides the population into different subgroups or "strata" based on specific characteristics (e.g., age, income) and randomly samples from each stratum. It ensures each subgroup is represented but can be more complex to implement.
3️⃣ Systematic Sampling: This method involves selecting every nth individual from a list of the population. It is easier to implement than random sampling but can introduce bias if there is a hidden pattern in the list.

To apply cluster sampling in practice using R and Python:

🔹 R: Use the survey package to create and analyze survey data, allowing for the design-based analysis of cluster samples.
🔹 Python: Utilize the statsmodels library, which offers functions to manage complex survey designs, including cluster sampling.
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Statistical tests
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The three probability axioms
Axiom 1
P(A) ≥ 0
For any event A, the probability of A is non-negative.

Axiom 2
P(S) = 1
The probability of the sample space S (the set of all possible outcomes) is 1.

Axiom 3
For any countable collection of mutually exclusive events ,the probability of their union is the sum of their individual probabilities.
If A ∩ B=∅ (empty set)
Then
P(A ∪ B) = P(A) + P(B)

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What do you mean by "Health Statistics "?

Vacancy Announcement

Gujarat Social Infrastructure Development Society (GSIDS), Sector 18, Gandhinagar, invites applications for the following contractual positions:

1. Senior Project Associate cum Consultant (SPAC)

Salary: ₹38,000/- per month



2. Senior Project Associate (SPA)

Salary: ₹27,500/- per month


TOTAL Vacancy (SPAC+ SPA) =5

Eligibility Criteria:
Candidates must possess at least a Postgraduate degree in Economics, Mathematics, Finance, or Statistics, or a Master’s degree in Management.

How to Apply:
Interested candidates are encouraged to send their resume via:

WhatsApp: 6353008752
Email: [email protected]
For further details, contact:

👆🏻

Nonparametric statistical methods offer powerful tools for analyzing data without making strict assumptions about the data's distribution. These methods are versatile and can be applied to various types of data, providing robust results even when traditional parametric methods fall short.

✔️ Flexibility: Nonparametric methods can handle data that doesn't fit normal distributions, making them ideal for real-world situations.
✔️ Robustness: They reduce the risk of errors by not relying on assumptions about data distribution.
✔️ Applicability: Useful in small sample sizes where parametric methods may fail.

❌ Limited Power: Nonparametric methods may have less statistical power compared to parametric tests, especially with larger sample sizes.
❌ Complexity: They can be more complex to interpret and require careful consideration of the method chosen.
❌ Computation: Nonparametric tests can be computationally intensive, particularly with large data sets.

Key Nonparametric Methods:
1️⃣ Mann-Whitney U Test: Used to compare differences between two independent groups.
2️⃣ Wilcoxon Signed-Rank Test: Applied to compare two related samples or repeated measurements on a single sample.
3️⃣ Kruskal-Wallis Test: An extension of the Mann-Whitney U Test for comparing more than two independent groups.
4️⃣ Spearman's Rank Correlation: Measures the strength and direction of association between two ranked variables.
5️⃣ Chi-Square Test: Used to examine the association between categorical variables.

Applying Nonparametric Methods:
🔹 R: Use the wilcox.test() function for the Wilcoxon test and kruskal.test() for the Kruskal-Wallis test. The ggplot2 package can help visualize results effectively.
🔹 Python: Leverage the scipy.stats module for tests like the Mann-Whitney U and Kruskal-Wallis. Visualize data with matplotlib or seaborn.

1379128_DA-74-202425 (1).pdf

ડેપ્યુટી ડાયરેક્ટર ક્લાસ ૧

આપેલ જાહેરાત માં શૈક્ષણિક લાયકાત અને અનુભવ

અર્થશાસ્ત્ર, આંકડાશાસ્ત્ર અને ગણિતમાં અનુ સ્નાતક ની પદવી ધરાવતા ઉમેદવારને સંશોધન મદદનીશ અને તેની સમકક્ષનો પાંચ વર્ષનો અનુભવ માગેલ છે.

અથવા

જ્યારે અર્થશાસ્ત્ર, આંકડાશાસ્ત્ર અને ગણિતમાં પીએચડી ની પદવી ધરાવતા ઉમેદવારને સંશોધન મદદનીશની અને તેની સમકક્ષ નો બે વર્ષનો અનુભવની જરૂરિયાત રહે છે.

#HERE_ARE_SOME_IMPORTANT_CONCEPTS_IN_STATISTICS:

#Descriptive_Statistics: Summarizes data using measures such as mean, median, mode, variance, and standard deviation.

#Inferential_Statistics: Allows conclusions to be drawn about a population based on sample data, using techniques like hypothesis testing and confidence intervals.

#Probability_Distributions: Functions that describe the likelihood of different outcomes. Common types include normal, binomial, and Poisson distributions.

#Hypothesis_Testing: A method for testing a claim or hypothesis about a population parameter, involving null and alternative hypotheses, p-values, and significance levels.

#Regression_Analysis: Techniques for modeling the relationship between a dependent variable and one or more independent variables, including linear and logistic regression.

#Correlation: Measures the strength and direction of the relationship between two variables, often quantified using Pearson’s correlation coefficient.

#Sampling_Methods: Techniques for selecting individuals from a population to obtain a representative sample, including random, stratified, and cluster sampling.

#Central_Limit_Theorem: States that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

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Estimation of Sample Size with Continous Data

Intv-ISS-Exam-24-Engl-111124.pdf
Indian Statistical Service 2024
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Editorial on today's News Paper

Q. Variance of a constant 'x' is

0
x/2
x
1

Answer 👆🏻

Q. Find the median of the call received on 7 consecutive days 11,13, 17, 13, 23,25,19

13
23
25
17

Answer 👆🏻

Q.If K is the Mean of Poisson distribution, then the variance is given by

1. K/2
2. K
3. K2
4. K1/2

The Difference Between 𝑑, 𝛿, Δ and ∂ in Physics and Mathematics :

- 𝑑 (d): Represents an infinitesimal change or derivative, introduced by Leibniz in calculus.

- ∂ (partial derivative): Used for rates of change with respect to one variable, introduced by Jacobi.

- Δ (Delta): Represents a finite change or difference, first used by Johann Bernoulli.

- 𝛿 (delta): Used for small changes or the Dirac delta function, popularized by Lord Kelvin.

Temporal and spatial data

Temporal and spatial data are two distinct types of data, differing in their focus and characteristics:

Temporal Data

- Focus: Time dimension
- Represents: Events or phenomena evolving over time
- Examples:
- Sensor readings (temperature, pressure)
- Transactional data (sales, logs)
- Time series data (stock prices, weather)

- Characteristics:
- Ordered in time
- May exhibit trends, seasonality, autocorrelation
- Analyzed using time series analysis, forecasting

Spatial Data

- Focus: Geographic or spatial dimension
- Represents: Events or phenomena in physical space
- Examples:
- Geographic Information Systems (GIS) data
- Location-based data (GPS, coordinates)
- Remote sensing data (satellite imagery)

- Characteristics:
- Linked to specific locations or areas
- May exhibit spatial autocorrelation, patterns
- Analyzed using spatial analysis, GIS

Key differences:

1. Dimension: Temporal (time) vs. Spatial (space)
2. Focus: Evolution over time vs. Geographic relationships
3. Analysis: Time series, forecasting vs. Spatial analysis, GIS

Types of Spatial Data

1. Point data (e.g., locations)
2. Line data (e.g., roads, boundaries)
3. Polygon data (e.g., areas, shapes)
4. Raster data (e.g., satellite imagery)

Spatial Data Analysis Techniques
1. Spatial autocorrelation analysis
2. Geographic information systems (GIS)
3. Geostatistics (e.g., kriging)
4. Spatial regression analysis

Temporal-Spatial Data
- Combines temporal and spatial dimensions
- Examples:
- Time-stamped location data (GPS tracks)
- Spatially referenced time series data (weather stations)

Today's newspaper clips - CPI Inflation

Economic growth 💹

Eye on Viksit Bharat -MoSPI

Mospi India

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Terminology & symbols & Formula statsterms2.pdf

The 134th Meeting of the National Statistical Commission was held today in KL Bhavan, New Delhi. The meeting was chaired by Professor R.L. Karandikar, Chairman, NSC and was attended by NSC Members - Professor A. Ganesh Kumar, Professor Debasis Kundu and Shri Asit Kumar Sadhu.

Dr. BVR Subrahmanyam, CEO, NITI Aayog, Dr. Saurabh Garg, Secretary, MoSPI, Dr. O.P. Mall, Executive Director, Reserve Bank of India, and Shri Antony Cyriac, Senior Economic Advisor from the Office of Chief Economic Advisor also attended the meeting.

In the meeting, the Commission was apprised of the status of the exercises related to Base Year Revision of GDP, Consumer Price Index and the Index of Industrial Production, the 8th Economic Census and Data Innovation Lab.

Presentations were also made on the Data User Conferences and the Conference of Central and State Statistical Organizations (CoCSSO) organised by MoSPI.

NSC was also briefed about the restructuring of Survey Verticals from process based to product based that has been undertaken by MoSPI.

#datafordevelopment #easeofdata

અગત્યના સંકેતો 💯

1) + = સરવાળો
2) - = બાદબાકી
3) × = ગુણાકાર
4) ÷ = ભાગ
5)% = ટકા
6) ∵ = ત્યારથી
7) તેથી = તેથી
8) ∆ = ત્રિકોણ
9) Ω = ઓમ
10) ∞ = અનંત
11) π = પાઇ
12) ω = ઓમેગા
13) ° = ડિગ્રી
14) ⊥ = લંબ
15) θ = થેટા
16) Φ = ફાઇ
17) β = બીટા
18) = = બરાબર
19) ≠ = બરાબર નથી
20) √ = વર્ગમૂળ
21)? = પ્રશ્ન વાચક
22) α = આલ્ફા
23) ∥ = સમાંતર
24) ~ = સમાન છે
25): = ગુણોત્તર
26) :: = પ્રમાણ
27) ^ = વધુ
28) ! = પરિબળ
29) એફ = ફંક્શન
30) @ =
31); = જેમ
32) / = દીઠ
33) () = નાના કૌંસ
34) {} = માધ્યમ કૌંસ
35) [] = મોટું કૌંસ
36)> = કરતા વધારે
37) <= કરતા નાનું
38) ≈ = આશરે
39) ³√ = ક્યુબ રુટ
40) τ = ટau
41) ≌ = સર્વગસમ
42) ∀ = બધા માટે
43) ∃ = અસ્તિત્વમાં છે
44) ∄ = અસ્તિત્વમાં નથી
45) ∠ = કોણ
46) ∑ = સિગ્મા
47) Ψ = સાંઇ
48) δ = ડેલ્ટા
49) λ = લેમ્બડા
50) ∦ = સમાંતર નથી
51) ≁ = સમાન નથી
52) d / dx = વિભેદક
53) ∩ = સમૂહનો સામાન્ય
54) ∪ = જોડાણ
55) iff = ફક્ત અને માત્ર જો
56) ∈ = સભ્ય છે!
57) ∉ = સભ્ય નથી
58) Def = વ્યાખ્યા
59) μ = મ્યુ
60) ∫ = અભિન્ન
61) ⊂ = સબસેટ છે
62) ⇒ = સૂચવે છે
63) હું l = મોડ્યુલસ
64) '= મિનિટ
65) "= સેકંડ

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#Permutation and #Combination

#mathematics
#statistics

Inferencial Statistics

National Statistics Office, Ministry of Statistics and Programme Implementation will now release the Consumer Price Index (CPI) and Index of Industrial Production (IIP) at 4:00 PM (instead of 5:30 PM) on the 12th of each month.
The new release time aligns with the closing hours of major financial markets in India, ensuring that CPI data dissemination does not interfere with active trading. This adjustment also adheres to MoSPI's commitment to transparency and accessibility in data dissemination.
The next release of CPI and IIP for October 2024, will be available on November 12, 2024, at 4:00 PM. For more details, follow the link below:
https://pib.gov.in/PressReleasePage.aspx?PRID=2070932

Profit & loss Formula

BODMAS & Example

Global Hunger Index (GHI) 2024
🍵

According to the Global Hunger Index (GHI) 2024, India is ranked 105th out of 127 countries, indicating a state of "severe" hunger.

India's GHI score this year is 27.3.

According to the report, child malnutrition is a major challenge in India, with the child wasting rate (i.e. underweight children) at 18.7%, the highest in the world.

In addition, the child stunting rate is 35.5%, under-5 mortality rate is 2.9%, and malnutrition rate is 13.7%.

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𝗕𝗲𝗿𝗻𝗼𝘂𝗹𝗹𝗶'𝘀 𝗜𝗻𝗲𝗾𝘂𝗮𝗹𝗶𝘁𝘆

Jacob Bernoulli first published the inequality in his treatise Positiones Arithmeticae de Seriebus Infinitis, where he made frequent use of the inequality.

Demographics Dividend

Data Centre @statistics_india

#Census #2026@statistics_india

#𝐃𝐞𝐬𝐜𝐫𝐢𝐩𝐭𝐢𝐯𝐞_𝐬𝐭𝐚𝐭𝐢𝐬𝐭𝐢𝐜𝐬 are used to summarize and describe the main features of a dataset. They can be categorized into several types:

𝟏. 𝐌𝐞𝐚𝐬𝐮𝐫𝐞𝐬 𝐨𝐟 𝐂𝐞𝐧𝐭𝐫𝐚𝐥 𝐓𝐞𝐧𝐝𝐞𝐧𝐜𝐲:
Mean:The average of the data.
Median: The middle value when data is ordered.
Mode: The most frequently occurring value.

𝟐. 𝐌𝐞𝐚𝐬𝐮𝐫𝐞𝐬 𝐨𝐟 𝐃𝐢𝐬𝐩𝐞𝐫𝐬𝐢𝐨𝐧:
Range: The difference between the highest and lowest values.
Variance: The average of the squared differences from the mean.
Standard Deviation: The square root of the variance, indicating how much data varies from the mean.

𝟑. 𝐌𝐞𝐚𝐬𝐮𝐫𝐞𝐬 𝐨𝐟 𝐏𝐨𝐬𝐢𝐭𝐢𝐨𝐧:
Percentiles: Values that divide the data into 100 equal parts.
Quartiles: Values that divide the data into four equal parts (Q1, Q2, Q3).

𝟒. 𝐅𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧𝐬:
Tabulation of data showing the number of occurrences of each value.

𝟓. 𝐆𝐫𝐚𝐩𝐡𝐬 𝐚𝐧𝐝 𝐂𝐡𝐚𝐫𝐭𝐬:
Histograms: Bar charts showing frequency distributions.
Box plots: Visual representation of the median, quartiles, and outliers.
Bar charts and pie charts: Useful for categorical data.

𝐓𝐡𝐞𝐬𝐞 𝐭𝐨𝐨𝐥𝐬 𝐡𝐞𝐥𝐩 𝐢𝐧 𝐮𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠 𝐚𝐧𝐝 𝐢𝐧𝐭𝐞𝐫𝐩𝐫𝐞𝐭𝐢𝐧𝐠 𝐝𝐚𝐭𝐚 𝐛𝐲 𝐬𝐮𝐦𝐦𝐚𝐫𝐢𝐳𝐢𝐧𝐠 𝐢𝐭𝐬 𝐜𝐡𝐚𝐫𝐚𝐜𝐭𝐞𝐫𝐢𝐬𝐭𝐢𝐜𝐬 𝐞𝐟𝐟𝐞𝐜𝐭𝐢𝐯𝐞𝐥𝐲.

Understanding degrees of freedom (DoF) is crucial because it plays a vital role in determining the accuracy and reliability of various statistical tests. Essentially, DoF refers to the number of independent values or quantities that can vary in a calculation while still meeting certain constraints. In simpler terms, it represents the number of independent pieces of information available to estimate a parameter or test a hypothesis. This concept is critical because it directly shapes the statistical distributions used in tests, which in turn affects the interpretation of results.

Example:

In a simple t-test comparing the means of two groups, the degrees of freedom are determined by the sample size of each group. Specifically, the DoF is calculated as the total number of observations across both groups minus the number of groups being compared (n₁ + n₂ - 2). This value influences the shape of the t-distribution used to determine the p-value, which in turn affects whether the difference between the group means is statistically significant. Without correctly accounting for the DoF, the test could yield inaccurate conclusions.

Key Areas Where Degrees of Freedom (DoF) Matter:

✔️ ANOVA (Analysis of Variance): DoF is crucial for comparing means across multiple groups.
✔️ t-tests: Properly applying DoF ensures accurate comparisons between two groups.
✔️ Chi-square tests: DoF helps determine the significance of relationships between categorical variables.
✔️ Regression analysis: DoF is used to assess the fit and complexity of the model, preventing overfitting.

To Implement DoF Correctly in Practice:

🔹 R: Use the df argument in functions like chisq.test() and t.test() to specify the correct degrees of freedom.
🔹 Python: Leverage the scipy.stats module, particularly functions like chi2 and t, where the DoF parameter (df) must be correctly defined.

The visualization provided shows chi-square distributions for various degrees of freedom (k = 1, 2, 3, 4, 6, 9). It illustrates how the distribution shape changes with different DoF values, highlighting the importance of selecting the appropriate DoF in your analysis.

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MoSPI reaffirms its commitment to timeliness and transparency in statistical reporting. All scheduled data reports/ releases/ publications for the year 2024-25 up to the month of October 2024 have been released/published as per Advance Release Calendar (ARC) of 2024-25. For details of the reports/ releases/ publications of MoSPI, ARC can be accessed at
https://www.mospi.gov.in/announcements/advance-release-calendar-mospis-website-reg

#DataforDevelopment #easeofdata

🔰 મહત્વપૂર્ણ સૂચકાંક 2024: 🔰

▫️ગ્લોબલ જેન્ડર ગેપ ઈન્ડેક્સ – 129મો
▫️પર્યાવરણ પ્રદર્શન સૂચકાંક -176મો
▫️ગ્લોબલ એનર્જી ટ્રાન્ઝિશન ઇન્ડેક્સ – 63મો
▫️વર્લ્ડ સાયબર ક્રાઈમ – 10મી
▫️વર્લ્ડ પ્રેસ ફ્રીડમ ઈન્ડેક્સ-159મો
▫️ટ્રાવેલ એન્ડ ટુરીઝમ ડેવલપમેન્ટ ઈન્ડેક્સ-39મો
▫️વર્લ્ડ પોવર્ટી રિપોર્ટ – 126મો
▫️લોકશાહી સૂચકાંક – 41મો
▫️ભ્રષ્ટાચાર પર્સેપ્શન ઇન્ડેક્સ-93મો
▫️લિંગ સમાનતા સૂચકાંક 129મો

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Pctograms: an attractive way of presentation.

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Diwali is a reminder that no matter how dark life gets, there's always light waiting to shine through...🔅🪔💫

May this Diwali your life will shine with good health, wealth and happiness.💫🤗
*Happy Diwali to you and your family* 🪔🪔
Mehul Patel
Deputy Director, (DSO, Bharuch).
💐💐💐

#ℝ𝔼𝔾ℝ𝔼𝕊𝕊𝕀𝕆ℕ!

𝐀 𝐫𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐦𝐨𝐝𝐞𝐥 𝐢𝐬 𝐚 𝐦𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐚𝐥 𝐟𝐫𝐚𝐦𝐞𝐰𝐨𝐫𝐤 𝐮𝐬𝐞𝐝 𝐭𝐨 𝐝𝐞𝐬𝐜𝐫𝐢𝐛𝐞 𝐭𝐡𝐞 𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧𝐬𝐡𝐢𝐩 𝐛𝐞𝐭𝐰𝐞𝐞𝐧 𝐚 𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞 𝐚𝐧𝐝 𝐨𝐧𝐞 𝐨𝐫 𝐦𝐨𝐫𝐞 𝐢𝐧𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞𝐬. 𝐈𝐭 𝐞𝐬𝐭𝐢𝐦𝐚𝐭𝐞𝐬 𝐡𝐨𝐰 𝐭𝐡𝐞 𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞 𝐜𝐡𝐚𝐧𝐠𝐞𝐬 𝐚𝐬 𝐭𝐡𝐞 𝐢𝐧𝐝𝐞𝐩𝐞𝐧𝐝𝐞𝐧𝐭 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞𝐬 𝐯𝐚𝐫𝐲. 𝐂𝐨𝐦𝐦𝐨𝐧 𝐭𝐲𝐩𝐞𝐬 𝐨𝐟 𝐫𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐦𝐨𝐝𝐞𝐥𝐬 𝐢𝐧𝐜𝐥𝐮𝐝𝐞:

𝟏. 𝐋𝐢𝐧𝐞𝐚𝐫 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧: Assumes a straight-line relationship between variables.
𝟐. 𝐌𝐮𝐥𝐭𝐢𝐩𝐥𝐞 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧: Involves multiple independent variables to predict a dependent variable.
𝟑. 𝐋𝐨𝐠𝐢𝐬𝐭𝐢𝐜 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧: Used for binary outcomes, modeling the probability of a particular event occurring.
𝟒. 𝐏𝐨𝐥𝐲𝐧𝐨𝐦𝐢𝐚𝐥 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧: Fits a polynomial equation to the data, capturing non-linear relationships.

𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐦𝐨𝐝𝐞𝐥𝐬 𝐚𝐫𝐞 𝐰𝐢𝐝𝐞𝐥𝐲 𝐮𝐬𝐞𝐝 𝐟𝐨𝐫 𝐩𝐫𝐞𝐝𝐢𝐜𝐭𝐢𝐨𝐧, 𝐭𝐫𝐞𝐧𝐝 𝐚𝐧𝐚𝐥𝐲𝐬𝐢𝐬, 𝐚𝐧𝐝 𝐮𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠 𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧𝐬𝐡𝐢𝐩𝐬 𝐢𝐧 𝐯𝐚𝐫𝐢𝐨𝐮𝐬 𝐟𝐢𝐞𝐥𝐝𝐬 𝐬𝐮𝐜𝐡 𝐚𝐬 𝐟𝐢𝐧𝐚𝐧𝐜𝐞, 𝐡𝐞𝐚𝐥𝐭𝐡𝐜𝐚𝐫𝐞, 𝐚𝐧𝐝 𝐬𝐨𝐜𝐢𝐚𝐥 𝐬𝐜𝐢𝐞𝐧𝐜𝐞𝐬.

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A COMPLETE GUIDE TO INTERPRETING MULTIPLE REGRESSION ANALYSES

Interpreting the results of a multiple linear regression analysis involves understanding several key components, including the ANOVA table, coefficients table, and regression diagnostics. Here’s a detailed overview of these elements:

A. Analysis of Variance (ANOVA) Table

The ANOVA table provides insights into the overall significance of the regression model.

♂️⭐F-statistic: This value tests the null hypothesis that all regression coefficients (except the intercept) are equal to zero. A high F-statistic indicates that at least one predictor variable has a significant relationship with the dependent variable.

♂️⭐Significance F (p-value): This is the p-value associated with the F-statistic. A p-value less than 0.05 typically suggests that the model is statistically significant, meaning at least one independent variable significantly predicts the dependent variable.

♂️⭐Regression Mean Square (MS): This measures the variance explained by the regression model.

♂️⭐Residual Mean Square: This measures the variance not explained by the model. The ratio of these two mean squares (F-statistic) helps determine if the model fits better than a model with no predictors.

B. Regression Coefficients Table

The coefficients table details the individual contributions of each independent variable to the model.

♂️⭐Coefficients: Each coefficient represents the expected change in the dependent variable for a one-unit change in the corresponding independent variable, holding all other variables constant. For example, a coefficient of 0.5 for an independent variable indicates that a one-unit increase in that variable results in a 0.5 unit increase in the dependent variable.

♂️⭐Standard Error: This measures the average distance that the estimated values fall from the actual value. Smaller values indicate more precise estimates.

♂️⭐t-statistic: This tests whether each coefficient is significantly different from zero. It is calculated as the coefficient divided by its standard error.

♂️⭐p-value: Similar to Significance F, this indicates whether each individual predictor is statistically significant. A p-value below 0.05 suggests that there is strong evidence against the null hypothesis for that predictor.

C. Regression Diagnostics

Regression diagnostics assess whether the assumptions of multiple linear regression are met and help identify potential issues with the model.

Key Assumptions:

♂️⭐Linearity: The relationship between each independent variable and the dependent variable should be linear. This can be checked using scatterplots.

♂️⭐Independence: Observations should be independent of one another. This can be evaluated using tests like Durbin-Watson statistic to detect autocorrelation in residuals.

♂️⭐Homoscedasticity: The residuals should have constant variance across all levels of independent variables. A scatterplot of residuals versus predicted values should not show patterns; if it does, it indicates heteroscedasticity.

♂️⭐Normality of Residuals: The residuals should be normally distributed, which can be assessed using Q-Q plots or histograms of residuals.

♂️⭐No Multicollinearity: Independent variables should not be too highly correlated with each other. This can be checked using correlation matrices and Variance Inflation Factor (VIF). A VIF above 10 suggests multicollinearity issues.

♂️⭐Outliers and Influential Points: Outliers can disproportionately affect regression results. Diagnostic plots, such as leverage plots or Cook's distance, can help identify these points.

Interpreting multiple linear regression results requires careful examination of both statistical significance and diagnostic checks to ensure valid conclusions can be drawn from the analysis

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In 2022-23, contribution of Maharashtra was the highest in the Gross Value Added (GVA) of the Manufacturing Sector, followed by Gujarat, Tamil Nadu, Karnataka and Uttar Pradesh. The top five states contributed around 55% of the Gross Value Added (GVA) of the Manufacturing Sector during the year. For more details follow the link below:
https://www.mospi.gov.in/asi-summary-results/867
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Key manufacturing industries viz. manufacturing of Basic Metals, Chemical and Chemical Products, Coke & Refined Petroleum Products, Motor Vehicles, Trailers & Semi-Trailers and Pharmaceutical Products were the driving forces behind the impressive growth in the manufacturing sector in 2022-23. Together, they constitute 46% of the total manufacturing GVA of the country during the year. For more details follow the link below:
https://www.mospi.gov.in/asi-summary-results/867

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દિવાળીનું પર્વ આપણાં જીવનમાં આનંદ અને ઉત્સાહ લઇને આવે છે, કશુંક નવું કરવા માટે આપણે દિવાળીની રાહ જોતા હોઇએ છીએ. દિવાળીનું પર્વ અંધકારથી ઉજાસ તરફ લઇ જાય છે. આપ સૌની આશા, આંકાક્ષા, ઇચ્છાઓ, સ્વપ્નો સર્વ ફળે એવી ભગવાન શ્રી રામને પ્રાર્થના 🙏🏻

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M-o-M performance growth rate (August, 2024 viz-a-viz August, 2023) and actual performance against the Monthly Target Value are showcased below indicating Infrastructure Sector Performance in the Civil Aviation Sector, for more details visit http://www.cspm.gov.in/english/Review.htm

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📈📉📊Statistical error
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Markov chains are a fundamental concept in probability theory, modeling systems that undergo transitions from one state to another in a random process. When properly utilized, Markov chains can unlock powerful insights across various fields, from finance to genetics.

However, improper handling of Markov chains can lead to significant drawbacks.

Challenges of Markov Chains:
❌ Misinterpretation: Without a thorough understanding, results derived from Markov chains might be misleading, particularly if the memoryless property is overlooked.
❌ Data Dependency: Markov chains rely heavily on accurate and representative data. If the data set is not sufficiently robust, the chain’s predictions could be inaccurate.
❌ Complexity: For large systems, constructing a Markov chain becomes increasingly complex, often requiring sophisticated computational tools and techniques.

Benefits of Markov Chains:
✔️ Predictive Modeling: When correctly applied, Markov chains can help forecast future states in a system based on its current state, leading to more accurate predictive models.
✔️ Simplified Analysis: They break down complex systems into manageable parts, allowing for a clearer understanding of each component and its behavior.
✔️ Versatile Applications: Markov chains are highly adaptable, with applications in queueing theory, economics, and machine learning, making them a versatile tool in a data scientist's arsenal.

To implement Markov chains in practice:
🔹 R: Use the markovchain package to create and analyze discrete-time Markov chains, which simplifies transitions, state spaces, and probabilities.
🔹 Python: Utilize the pymc or hmmlearn libraries to model and infer the hidden states in sequential data.

The followings shows a simple two-state Markov process. The numbers represent the probabilities of transitioning from one state to another, illustrating the flow within the system.

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Comparing Non-Parametric to Parametric

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Birth Rate

TFR

Census 2025

Combinations and Permutations with and without repetition.

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The concept of snowball sampling...

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✅𝗧𝗢𝗣 𝟱 𝗖𝗢𝗨𝗡𝗧𝗥𝗜𝗘𝗦 𝗕𝗬 𝗙𝗢𝗥𝗘𝗫 𝗥𝗘𝗦𝗘𝗥𝗩𝗘𝗦

🌍💰 India's Forex Reserves Soar to $701 Billion! 🇮🇳 India has now become the 4th country globally to cross the $700 billion mark in foreign exchange reserves, joining the ranks of China, Japan, and Switzerland. This achievement strengthens India's financial stability and global economic standing. 💪

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𝐈𝐧𝐯𝐢𝐭𝐚𝐭𝐢𝐨𝐧 𝐭𝐨 𝐂𝐨𝐥𝐥𝐚𝐛𝐨𝐫𝐚𝐭𝐞 𝐰𝐢𝐭𝐡 𝐌𝐨𝐒𝐏𝐈'𝐬 𝐃𝐚𝐭𝐚 𝐈𝐧𝐧𝐨𝐯𝐚𝐭𝐢𝐨𝐧 𝐋𝐚𝐛

The Ministry of Statistics and Programme Implementation (MoSPI) is inviting agencies, startups, research and other institutions to contribute to innovative solutions for official statistics. Join us in developing cutting-edge methodologies and shaping the future of India's statistical system through the Data Innovation Lab.

Apply here: [eprocure.gov.in/eprocure]
To know more about DI Labs, click here: [www.mospi.gov.in]

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Probability Vs Non-Probability Sampling

P&C Equation 🔥💯👍💪😎

Mean & Standard Deviation 😁😎👍💪💯

IMF Growth Forecast: 2024

🇺🇸 US: 2.8%
🇩🇪 Germany: 0.0%
🇫🇷 France: 1.1%
🇮🇹 Italy: 0.7%
🇪🇸 Spain: 2.9%
🇬🇧 UK: 1.1%
🇯🇵 Japan: 0.3%
🇨🇦 Canada: 1.3%
🇨🇳 China: 4.8%
🇮🇳 India: 7.0%
🇷🇺 Russia: 3.6%
🇧🇷 Brazil: 3.0%
🇲🇽 Mexico: 1.5%
🇸🇦 Saudi Arabia: 1.5%
🇳🇬 Nigeria: 2.9%
🇿🇦 South Africa: 1.1%

Systematic random sampling involves selection of every Kth participant.

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Understanding the differences between the mean and median is crucial in data analysis. Although these measures of central tendency may seem similar, they can yield significantly different results when a data set contains outliers.

✔️ Properly distinguishing between the mean and median helps you choose the most appropriate measure of central tendency, depending on your data set's characteristics.

✔️ Using the median is particularly advantageous in skewed distributions, as it provides a more accurate representation of the central value by not being influenced by outliers.

✔️ Recognizing when to use the mean allows for better interpretation of normally distributed data, where each value contributes equally to the average.

❌ Failing to differentiate between the mean and median can lead to incorrect interpretations of your data, especially in the presence of outliers or skewed distributions.

❌ Misusing the mean or median could result in biased conclusions, potentially affecting decision-making processes based on flawed data insights.

In the visualization of this post, two data sets are compared using density plots. In the left plot, the mean and median are similar, indicating a symmetric distribution. Notice how outliers in the right data set significantly affect the mean, pulling it away from the central peak, while the median remains closer to the mode, providing a more accurate center of the data distribution.

🔹 R: Use the mean() and median() functions from base R, combined with visualization tools like ggplot2 to compare these measures in your data set.

🔹 Python: Utilize the mean() and median() functions from the statistics module or numpy, and visualize with libraries like matplotlib or seaborn for a clear comparison.

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Statistical inference is a powerful tool in data analysis that helps us make conclusions about a population based on a sample.

It allows us to draw meaningful insights and predictions from limited data, enabling informed decision-making even when it's impractical or impossible to study an entire population.

By leveraging statistical inference, we can assess the reliability of our estimates and quantify uncertainty in our findings.

Here’s a quick overview:

✅ Point Estimation: A point estimate gives us a single value as our best guess for a population parameter (like the mean or proportion). It’s derived from the sample data and is used to make inferences about the population.

✅ Variance Estimation: Variance estimation involves calculating how much the data in your sample varies. It’s essential for understanding the spread and reliability of your data.

✅ Standard Error and Confidence Intervals: The standard error measures the accuracy of your point estimate. Confidence intervals, which are calculated using the standard error, provide a range that would contain the true population parameter in a certain percentage of repeated samples.

✅ p-Value: The p-value helps determine the significance of your results. It tells you whether the observed data is consistent with the null hypothesis or if there’s enough evidence to reject it.

The visualization of this post shows the distribution of sample data, highlighting the sample mean with a red dashed line and illustrating the 95% confidence interval with a blue error bar. An annotation provides key statistical details, including the mean, variance, and confidence interval.

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Power of study depends on sample size, type 1 error and effect size.

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Real GDP & GVA Q1 2024-25

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