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| Sana | Obunachilarni jalb qilish | Esdaliklar | Kanallar | |
| 28 Iyun | +1 | |||
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| 25 Iyun | +5 | |||
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| 23 Iyun | +6 | |||
| 22 Iyun | 0 | |||
| 21 Iyun | 0 | |||
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| 17 Iyun | 0 | |||
| 16 Iyun | +3 | |||
| 15 Iyun | +6 | |||
| 14 Iyun | +5 | |||
| 13 Iyun | +8 | |||
| 12 Iyun | +2 | |||
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| 10 Iyun | +6 | |||
| 09 Iyun | +4 | |||
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| 07 Iyun | +3 | |||
| 06 Iyun | +3 | |||
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Kanal postlari
*Why can't correlation exceed 1? 🤔
Most people who work with data accept this without question:
−1 ≤ r ≤ +1
But *why* is that the boundary?
Why not −2 to +2?
Why not unbounded entirely?
The answer is hiding inside the denominator.
Covariance already has a built-in ceiling — a maximum magnitude it can never break through:
|Cov(X,Y)| ≤ σ_X σ_Y
This isn't a convention statisticians agreed on.
It's a provable mathematical fact.
When two variables move together, their relationship cannot be stronger than what their individual variabilities allow. σ_X σ_Y sets that limit.
Correlation simply expresses covariance as a fraction of that maximum possible magnitude.
Part 1/2
| 2 | So a correlation of 0.8 means covariance is already at 80% of the maximum it could possibly reach. A correlation of −0.5 means the same — 50% of the ceiling, in the negative direction.
Values beyond ±1 would require covariance to exceed its own maximum possible magnitude.
That's not just unlikely.
It's mathematically impossible.
The bound isn't a rule we accept.
It's a limit that math imposes.
Next up: we'll see exactly why |Cov(X,Y)| ≤ σ_X σ_Y holds true.
Hint: it comes from the Cauchy–Schwarz inequality.
Part 2/2 | 87 |
| 3 |  Celebrating 20 Years of Statistics Day!
Ministry of Statistics and Programme Implementation (MoSPI) is celebrating the 20th Statistics Day on 29 June 2026 at Dr. Ambedkar International Centre, New Delhi.
Be a part of this special occasion as we honour the invaluable contribution of statistics in nation-building and evidence-based policymaking.
Please watch the live broadcast here: https://youtube.com/live/toRvGiWq_I4?feature=share
#StatisticsDay2026 #StatisticsDay #SD2026 #MoSPI #OfficialStatistics #DataForDevelopment #GoIStats #StatisticsForNationBuilding #GovernmentOfIndia
https://t.me/statistics_india | 358 |
| 4 | NSO, MoSPI is preparing to launch Index of Services Production (ISP) in July, 2026, which shall be a new macro indicator to measure the short-term changes in the growth of the services sector.
ISP will cover the formal services sector and will be released on a monthly basis.
To assist users on ISP, a comprehensive set of booklet on Frequently Asked Questions (FAQs) has been released.
Access the FAQs at:
https://www.mospi.gov.in/uploads/latestReleases/latest_release_1782292366710_eef9114f-767b-4f72-a868-2bc185b33507_Press_Release-_FAQs_on_Index_of_Services_Production_(1).pdf
For related updates and official information, please visit MoSPI’s official website. https://www.mospi.gov.in/
#MoSPI #ISP #IndexOfServicesProduction #IndianEconomy #EconomicGrowth #DataDrivenPolicy #StatisticsIndia #ServicesSector #EconomicIndicators #IndiaGrowth #OfficialStatistics #PolicyMaking #EconomicForecasting | 511 |
| 5 |  Ministry of Statistics and Programme Implementation is pleased to convey that Prof. Arup Bose, Professor (Retd.), Indian Statistical Institute Kolkata, has been adjudged as the recipient of Sukhatme National Award in Statistics for the year 2026.
The award is being conferred on Prof. Arup Bose in recognition of his pioneering and sustained contributions to Statistical Theory, Probability, Random Matrix Theory, High-Dimensional Data Analysis, Resampling Methods, and Time Series Analysis, which have profoundly influenced modern statistical research and practice. The award will be conferred on 29th June 2026, as part of 'National Statistics Day Celebration -2026' in New Delhi.
#NationalStatisticsDay2026 #Sukhatme
#Statistics #DataScience
#IndianStatisticalInstitute #MoSPI #OfficialStatistics #DataAnalytics #StatisticalResearch #IndiaStatistics
http://t.me/statistics_india | 460 |
| 6 | ➡️ Features of National Income:
1. Measured in Money Terms: National income is calculated in terms of monetary value.
2. Includes Final Goods and Services: It includes only final goods and services to avoid double counting.
3. Measured Over a Period: It is generally calculated for one year.
4. Includes Factor Incomes: It consists of wages, rent, interest, and profits earned by factors of production.
5. Represents Economic Performance: It reflects the overall economic condition of a country.
➡️ Components of National Income:
1. Wages and Salaries: Income earned by labor.
2. Rent: Income earned from land and property.
3. Interest: Income earned from capital.
4. Profit: Income earned by entrepreneurs.
5. Mixed Income: Income of self-employed individuals.
➡️ Importance of National Income
▪️Helps measure economic growth.
▪️Provides information for government planning and policymaking.
▪️Helps compare economic performance between countries.
▪️Shows changes in people's income and living standards.
▪️Assists in understanding the structure of an economy.
National Income is a key indicator of a country's economic progress. It represents the total income earned from the production of goods and services and helps governments, economists, and policymakers evaluate economic performance and design appropriate development strategies.
Part 2/2 | 724 |
| 7 | Follow the Statistics_india channel on WhatsApp:
https://wa.me/channel/0029Vadop5ZBfxoF9Lq8h015
Kindly Note:
Telegram may face interruptions for the next few days for on 22 June Neet Exam as per some government guidelines.
To ensure you don't miss any important updates, please join our WhatsApp group.
આગામી થોડા દિવસો માટે સરકારશ્રી ની ગાઇડલાઇન મુજબ નીટ પરીક્ષા સંદર્ભે ટેલિગ્રામ સેવા પર restrictions છે.
સરકારી સેવાની તૈયારી માટે વોટ્સએપ ગ્રુપમાં જોડાઈ શકો છો. | 508 |
| 8 |  +1🇮🇳GDP (Gross Domestic Product)
🎯GDP is the total monetary value of all final goods and services produced within a country’s border during a specific period, usually a year or a quarter.
📍GDP = C + I + G + (X-M)
📚Importance
1.measure the size if economy
2. Track economic Growth
3. Compare economic Perfomence within Countries
4. Help to make a government policy
🗓️Types of GDP
1. Nominal (Compare to Previous Year)
2. Real GDP (Compare to Base Year )
#gdp #nationalaccounts #india #statistics_india
https://t.me/statistics_india | 1 326 |
| 9 | 🔆 CURRENT AFFAIRS – 16 JUNE 2026
🔆 ECONOMY
📍 India Launches Producer Price Index (PPI)
✅ India released its first Producer Price Index (PPI)
✅ Base Year: 2022–23
✅ WPI to be phased out over the next 5 years
✅ Measures producer-level prices for goods and services
✅ Aligns with global practices and IMF recommendations
✅ Output PPI Inflation (May 2026): 9.4%
✅ WPI Inflation (May 2026): 9.68%
🔆 STATES
📍 Assam Gets Four New GI Tags
✅ GI Tags awarded to:
✅ Bah Silpa (Bamboo Craft)
✅ Karbi Anglong Handloom
✅ Bihu Pepa
✅ Deori Handloom Products
✅ Strengthens preservation of Assam’s cultural heritage
📍 Jharkhand Receives GI Tags for 11 Traditional Products
✅ Includes Bhoya Saree, Dokra Craft, Jadopatia Painting, Kesaria Kalakand and Munda Jewellery
✅ Sohrai Painting had already received GI status earlier
✅ Promotes indigenous crafts and traditional products
🔆 NATIONAL
📍 FSSAI Cracks Down on Misleading Food Labels
✅ Notices issued to 15 food businesses
✅ Restricts misleading claims like Healthy, Natural, High Protein and Immunity Boosting
✅ Mandatory disclosure of ingredients, nutrition facts and allergens
✅ Online food platforms must display complete label information
✅ Food packaging must comply with prescribed food-grade safety standards
📍 India’s Horticulture Production Reaches Record Level
✅ Second Advance Estimates 2025–26 released by Department of Agriculture & Farmers Welfare
✅ Total horticulture production estimated at 3,777.76 lakh tonnes
✅ Growth of 1.90% over previous year
✅ Fruit production: 1,214.75 lakh tonnes
✅ Vegetable production: 2,210 lakh tonnes
✅ Major growth seen in potato, tomato, okra and peas
🔆 INTERNATIONAL
📍 UK Announces Social Media Restrictions for Children Under 16
✅ Restricts livestreaming and interaction with strangers
✅ Applies to social media and selected gaming platforms
✅ Aims to enhance online child safety
✅ Part of UK’s broader digital protection measures
📍 WEF Releases Technology Pioneers 2026 Cohort
✅ Includes 100 startups from 23 countries
✅ 9 Indian startups selected
✅ Recognises innovation in AI, Biotechnology, Climate Tech and Space Technology
✅ Total Indian companies recognised under programme reaches 28
🔆 INDIA & THE WORLD
📍 India & France Launch ATL Bridge Initiative
✅ Connects school innovation ecosystems of both countries
✅ Announced during India-France Year of Innovation 2026
✅ Based on India’s Atal Tinkering Labs (ATL) model
✅ France to establish its first School Innovation Lab
✅ Implemented through AIM and La Fondation Dassault Systèmes
📍 India & France Adopt Innovation Roadmap 2030
✅ Roadmap outlines 13 key cooperation outcomes
✅ Joint AI Working Group established
✅ Expansion of UPI usage in France
✅ Collaboration in space research, digital health and skilling
✅ High-level mechanism created to double bilateral trade in five years
🔆 AGREEMENTS & MoUs
📍 Oil India Signs Clean Energy Pact with Canada’s PTRC
✅ Collaboration on Carbon Capture, Utilisation and Storage (CCUS)
✅ Focus on Geothermal Energy and Subsurface Energy Technologies
✅ Agreement signed during Global Energy Show 2026
✅ Promotes clean energy research cooperation
🔆 AWARDS & RECOGNITIONS
📍 PM Narendra Modi Receives Slovakia’s Highest Honour
✅ Awarded Order of the White Double Cross (1st Class)
✅ Conferred by President Peter Pellegrini
✅ Highest civilian and military honour for foreign citizens
✅ Marks the first-ever visit by an Indian Prime Minister to Slovakia
#CurrentAffairs | 521 |
| 10 |  Concept of Probability v/s Likelihood
👍Likelihood is not probability.
📊In probability, the outcome is unknown.
👍In likelihood, the outcome is already sitting in front of you — and you're working backwards.
https://t.me/statistics_india | 704 |
| 11 | NSO, MoSPI is undertaking Annual Survey of Incorporated Services Sector Enterprises (ASISSE) from April 2026. It covers incorporated service sector enterprises across India to generate key data on output, capital, and employment.
Please click on the link below to access the documents related to ASISSE:
https://mospi.gov.in/Annual-Survey-of-Services-Sector-Enterprises-2026.
#nso #MoSPI #asisse #ServiceSector #incorporatedenterprises #economicstatistics #OfficialStatistics #DataForDevelopment #statisticalsystem #EvidenceBasedPolicy #DataDrivenGovernance #EconomicData
https://t.me/statistics_india | 594 |
| 12 | Fiscal policy is related to: | 624 |
| 13 | NSO, MoSPI has released the Periodic Labour Force Survey (PLFS) monthly Bulletin for May 2026. According to this bulletin the Labour Force Participation Rate (LFPR) for aged (15+ years) stood at 54.4%, while the Worker Population Ratio (WPR) for aged (15+ years) was recorded at 51.4%. These figures indicate that key macroeconomic labour metrics have maintained structural stability with consistent workforce participation throughout the month.
Please click on the link to read the complete report:
https://mospi.gov.in/uploads/publications_reports/publications_reports1781518752261_5d38323b-1931-4e2b-803e-34684fb7643d_MB_May_2026-1-1.pdf
For related updates and official information, please visit MoSPI’s official website. https://mospi.gov.in
#NSO #MoSPI #WomenInWorkforce #WomenEmpowerment #FemaleLabourForceParticipation #EconomicGrowth #InclusiveDevelopment #WomenAtWork #LabourForce #EmpoweringWomen #SustainableDevelopment #IndiaGrowth #StatisticsForDevelopment #PLFS
https://t.me/statistics_india | 814 |
| 14 |  Basic of Probability (Gujarati)
📚વ્યાખ્યાઓ:
1. Classical (Laplace)
2. Axiomatic (Kolmogorov)
🏘સંભાવના ના પ્રકારો
1. Classical Probability
2. Axiomatic (Mathematical)
3. Empirical (Experimental)
📧સૂત્રો :
P(A) = m/n
or
P(A)= n(A)/n(S)
✅લક્ષણો :
Classical Probability
1. 0<= P(A) <= 1
2. P(S) = 1
3. A=🚫, then P(A) = 0
4. P(A') = 1 - P(A)
📍વાસ્તવિક જીવનના ઉદાહરણ :
1. Rolling a Die
2. Tossing a Coin
3. Height of a Person
4. Prob. of Machine Failure
🔝 મુખ્ય તફાવત : Classical v/s Axiomatic
✅પરીક્ષામાં યાદ રાખવાની સરળ રીત :
📲Quick Revision Points :
Follow us on Social Media
"Statistics_India"
💻https://youtube.com/@statistics_india/
📜https://wa.me/channel/0029Vadop5ZBfxoF9Lq8h015
🎟️https://www.instagram.com/statistics_india
📧https://t.me/statistics_india_chat
⏺️https://www.fb.com/statistics_india
🌐https://www.threads.net/@statistics_india | 3 010 |
| 15 |  Basic of Probability
📚Definitions:
1. Classical (Laplace)
2. Axiomatic (Kolmogorov)
🏘Types of Probability
1. Classical Probability
2. Axiomatic (Mathematical)
3. Empirical (Experimental)
📧Formulas:
P(A) = m/n
or
P(A)= n(A)/n(S)
✅Properties:
Classical Probability
1. 0<= P(A) <= 1
2. P(S) = 1
3. A=🚫, then P(A) = 0
4. P(A') = 1 - P(A)
📍Real Time Example:
1. Rolling a Die
2. Tossing a Coin
3. Height of a Person
4. Prob. of Machine Failure
🔝 Classical v/s Axiomatic
Tricks & Tips For Exams
Quick Revisions Points
Follow us on Social Media
"Statistics_India"
🚫 | 2 330 |
| 16 |  What is Statistics?
Statistics is the science of collecting, organizing, analyzing, interpreting and presenting data to help in making better decisions.
"Data speaks, Statistics gives it meaning"
📊Example
🔔why Importanc?
Like👍
Share 📲
Subscribe 🔔
https://t.me./statistics_india | 2 550 |
| 17 | Consistency
"When someone's hope is tied to your journey, never stop."
Consistency is not just about doing something at the same pace every day, but also not letting the work stop even when the circumstances turn completely against you, that's what consistency is all about.
It is difficult to focus on one thing when so much is happening around us... But we must do what is necessary... The decision to enter this dark tunnel was our own, and now we have to keep walking in this darkness... No matter how thorny the path may be...
Only by continuing to move forward can we reach the end of this thorny tunnel... Where we will find success, achievement and a wonderful satisfaction that our struggle was not in vain, it was worthwhile...
By walking this path, not only you are moving towards that light, but your family, friends and all the well-wishers who cheer you on are also moving forward... When you win, it is not only your victory but also theirs... Every step you take towards your goal proves that their efforts for you are not going in vain.
So you don't stop but keep moving forward... If you find it difficult to do this for yourself, then also move forward for the sake of those who believe in you wholeheartedly. | 803 |
| 18 | "જ્યારે કોઈકની આશા તમારી સફર સાથે જોડાયેલી હોય, ત્યારે ક્યારેય અટકશો નહીં."
સાતત્ય (consistency) એટલે માત્ર એક જ ગતિથી રોજ કોઈ કામ કરવું એટલું જ નથી, પણ જ્યારે પરિસ્થિતિઓ સાવ વિપરીત થઈ જાય ત્યારે પણ કામને અટકવા ન દેવું, તેનું નામ સાતત્ય છે.
જ્યારે આપણી આસપાસ ઘણું બધું ઘટી રહ્યું હોય ત્યારે કોઈ એક બાબત પર ધ્યાન કેન્દ્રિત કરવું અઘરું છે... પરંતુ જે જરૂરી છે તે આપણે કરવું જ પડશે... આ અંધારી ટનલમાં પ્રવેશવાનો નિર્ણય આપણો પોતાનો હતો, અને હવે આપણે આ અંધકારમાં પણ ચાલતા રહેવું પડશે... ભલે રસ્તો કાંટાળો કેમ ન હોય...
માત્ર આગળ વધતા રહેવું જ આપણને આ કાંટાળી ટનલના અંતિમ છેડા સુધી લઈ જઈ શકે છે... જ્યાં આપણને સફળતા, સિદ્ધિ અને એક અદ્ભુત સંતોષ જોવા મળશે કે આપણો આ સંઘર્ષ એળે નહોતો ગયો, તે સાર્થક હતો...
આ માર્ગ પર ચાલીને માત્ર તમે જ એ પ્રકાશ તરફ નથી વધી રહ્યા, પરંતુ તમારી સાથે તમારો પરિવાર, મિત્રો અને તમારો ઉત્સાહ વધારનારા તમામ શુભચિંતકો પણ આગળ વધી રહ્યા છે... જ્યારે તમે જીતો છો, ત્યારે એ માત્ર તમારી એકલાની જીત નથી હોતી પણ એ તેમની પણ જીત હોય છે... તમારા લક્ષ્ય તરફ ભરેલું તમારું દરેક પગલું એ સાબિત કરે છે કે તમારા માટે કરેલા તેમના પ્રયત્નો વ્યર્થ નથી જઈ રહ્યા.
તેથી તમે અટકશો નહીં પરંતુ આગળ વધતા રહો... જો તમને તમારા પોતાના માટે આ કરવું અઘરું લાગતું હોય, તો એવા લોકો ખાતર પણ આગળ વધો જેઓ પૂરા દિલથી તમારામાં વિશ્વાસ રાખે છે. | 515 |
| 19 | https://youtu.be/0-lFwT5EaFg
🌐CPI General Index - May 2026
Base Year 2024 = 💯
🇮🇳CPI Inflation 3.93%
🏡Rural - 3.74%
🏘Urban - 3.16%
Food Inflation - 4.78%🍟🍨🌽🍢🍡🍞🥬
🔝State - CPI Inflation
1. Telangana - 6.71%
2. Tamilnadu - 5.11%
3. Andhra Pradesh - 4.90%
4. Karnataka - 4.59%
5. Odisha - 4.54%
👍📲🔔⛳📚 | 2 337 |
| 20 | 3⃣. Which of the following best describes a parameter? | 647 |
