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Business Intelligence Analytics Market Size, Share, Trends, Growth, Outlook, and Insights Report, 2023- Industry Forecasts by Type, Application, Segments, Countries, and Companies, 2021- 2030

November 2023 | 180 pages | ID: BDD18F381162EN
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The Business Intelligence Analytics market is a large and high-potential growth industry. In 2023, the market is poised to register positive year-on-year growth over 2022. Further, the Business Intelligence Analytics market size maintains a super-linear growth trajectory, registering continuous expansion from 2023 to 2030.

As we enter the late half of 2023, the Business Intelligence Analytics industry is poised for significant growth and transformation. The “Business Intelligence Analytics Market Size, Share, Trends, Growth, Outlook, and Insights Report, 2023- Data Forecasts by Type, Application, Segments, Countries, and Companies, 2018- 2030” report details the definition and advantages of Business Intelligence Analytics.

Overview of the Business Intelligence Analytics Industry in 2023

The accelerating development of the industry is driven by a widening application base, R&D investment in new product development, competitive strategies focusing on expanding into niche segments, and potential growth prospects for Business Intelligence Analytics Companies in developing countries.

The Business Intelligence Analytics Insights Report provides key market size and share outlook, short-term and long-term trends, potential opportunities, analytical models, current market conditions, scenario analysis, post-COVID analysis, competitive landscape, company profiles, and market news and developments.

Business Intelligence Analytics Market Size, Share, and Trend Analysis

The global Business Intelligence Analytics market plays a major role in the global electronics and semiconductors industry. The report provides a comprehensive and in-depth analysis of different segments across the industry.

Further, potential types, applications, products, and other Business Intelligence Analytics segments are analyzed in the market study.
  • Business Intelligence Analytics Market Statistics- Current status of the Business Intelligence Analytics industry and the key statistics for 2023 are provided in detail.
  • Strategic Analysis of Business Intelligence Analytics Industry- Competitive analysis, vendor landscape, SWOT profiles, and product profiles are included.
  • Market Trends and Insights- The Business Intelligence Analytics Insights report provides a detailed examination of key market trends, drivers, and their impact on demand. Further, the increasing importance of Business Intelligence Analytics across industries is discussed.
  • Market Developments- Mergers, acquisitions, product launches, capacity expansion plans, and other developments announced by leading Business Intelligence Analytics companies are included in the study.
  • Business Intelligence Analytics Market Opportunities- Potential growth opportunities and quantitative comparison of different segments to provide an assessment of diverse opportunities in the industry.
  • Regional analysis- Further, a geographical analysis of the Business Intelligence Analytics industry, highlighting key markets and their growth prospects is included. The market size across six regions including North America, Asia Pacific, Europe, South America, the Middle East, and Africa is forecast to 2030.
Analytical Frameworks

The Business Intelligence Analytics insights report uses multiple analytical frameworks for analyzing the global Business Intelligence Analytics industry. The tools include- Industry SWOT, Porter’s Five Forces Analysis, PESTLE analysis, scenario analysis, and others.

Industry SWOT- The report identifies the key strengths, weaknesses, opportunities, and threats facing the global markets in 2023 and beyond.

Scenario analysis- 4 scenarios for the long-term future based on the global economy are analyzed.

Porter’s Five Forces Analysis- The report quantifies Porter’s five forces analysis to assess the market attractiveness using the weighted average of the Bargaining power of buyers, Bargaining power of suppliers, Threat of substitutes, Threat of new entrants, and intensity of competitive rivalry.

PESTLE Analysis- Six segments of the general environment surrounding the Business Intelligence Analytics industry including political, economic, social, technological, environmental, and legal factors are briefed.

Future Business Intelligence Analytics Growth Outlook and Opportunities

The chapter provides a detailed analysis of market size, growth rate, revenue trends, and volume analysis over the historical period from 2018 up to 2022. Projection of the future growth prospects and opportunities in the Business Intelligence Analytics industry along with insights into each of the potential market segments is included in the study. Further, the evaluation of factors driving market growth across markets is provided. In addition, the latest technological advancements and an analysis of the impact of these advancements on the performance, reliability, and efficiency of products are included.

Market Dynamics- Impact Analysis and Post-COVID Outlook of Business Intelligence Analytics Industry

Optimistic economic conditions are observed in H2-2023 across multiple scenarios. The current edition of the Business Intelligence Analytics Market Study identifies brighter views for 2023 and an increasingly optimistic global outlook over the forecast period.

However, the market is also constrained by challenges of geopolitical instability and conflicts with the Russia-Ukraine war and inflation conditions in the US and other markets, and rising interest rates continue to restrain the market growth prospects.

The four case scenarios considered for countries in the study are -
  • Sluggish economic growth, with emphasis on savings and low expenditure
  • Despite growth fluctuations, consumer confidence remains robust and gains continue for companies
  • Investments in technology deployment and productive investments
  • Stronger consumer demand and higher investments supporting solid growth
Business Intelligence Analytics Market Trends- Emerging markets present strong growth prospects

According to the World Bank, over 85% of the world’s population lives in the Asia Pacific, the Middle East and Africa (MEA), or South America. An increasing volume of companies are expanding their production and marketing bases to these countries as the consumption power of individuals continues to strengthen.

Several new market entrants are targeting niche economically attractive Business Intelligence Analytics segments when expanding into these markets. We anticipate the Business Intelligence Analytics sales growth in developing countries to continue to accelerate rapidly over the forecast period.

North America Business Intelligence Analytics Industry: Market Trends, Share, Size, Growth, Opportunity and Forecast 2023-2028

The past few quarters have been encouraging for North American Business Intelligence Analytics market suppliers. A large number of Business Intelligence Analytics companies are reporting profitability after several quarters of margin declines. Focus on increasing operational efficiency, capturing niche market opportunities, and others are widely observed. The North American Business Intelligence Analytics industry research identifies the key market trends, driving forces, and growth opportunities across 3 countries including the United States, Canada, and Mexico markets.

Europe Business Intelligence Analytics Industry: Market Trends, Share, Size, Growth, Opportunity and Forecast 2023-2028

Leading European Business Intelligence Analytics companies are focusing on customer orientation, sustainable supply chains, and economic value creation to succeed in long-term market conditions. As Asian manufacturers enter the European markets, the region’s electronics and semiconductors sector is undergoing a paradigm shift. The European Business Intelligence Analytics industry is also facing the significant impact of the Russia-Ukraine war. The insights report analyzes the Western European Business Intelligence Analytics countries including Germany, France, Spain, the United Kingdom, Italy, and other European countries including Russia, Turkey, and others.

Asia Pacific Business Intelligence Analytics Industry: Market Trends, Share, Size, Growth, Opportunity and Forecast 2023-2028

Economic growth and shifting consumer preferences are set to shape the future of the Asia Pacific Business Intelligence Analytics industry. Leading companies in China, India, Japan, South Korea, Australia, Indonesia, South East Asia, and other regions are focusing on rapid business expansion through new product launches. The Business Intelligence Analytics insights report provides the market size outlook across these countries from 2018 to 2030.

South America Business Intelligence Analytics Industry: Market Trends, Share, Size, Growth, Opportunity and Forecast 2023-2028

South American countries including Brazil, Argentina, Chile, and others continue to demonstrate robust value-creation potential through 2030. Both traditional players and new start-ups are spending more on expanding products to niche consumer segments. Increasing urbanization, infrastructure development, and improving disposable incomes are likely to drive the market outlook over the forecast period.

Middle East and Africa Business Intelligence Analytics Industry: Market Trends, Share, Size, Growth, Opportunity and Forecast 2023-2028

The Middle East and African regions have a growing population, increasing urbanization, and improving standards of living, all of which contribute to the rising Business Intelligence Analytics demand. Further, Sustainability and environmental concerns are gaining prominence in the GCC region. In Africa, vehicle sales continued an upward trend and the rapid growth in infrastructure in the African region enables Business Intelligence Analytics companies to generate significant business growth in the medium to long-term future.

Competitive Insights

The landscape of the industry is shifting, moving away from traditional competition between peers and embracing new forms of competitive interactions. There is an increasing trend among companies from building products to building businesses. Companies are investing in developing new growth opportunities with market leaders increasingly focused on building and scaling up new businesses.

The Business Intelligence Analytics insights report provides a competitive analysis of the industry in 2023. The business profiles of the leading 10 companies are profiled in the study along with their SWOT profile, financials, products and services, and market developments. In addition, an evaluation of the competitive landscape, including major players, market share, and strategies adopted by key manufacturers is provided in the research study. The report also identifies the most prominent challenges and potential growth barriers faced by leading companies.

Report scope
  • Data for 13 years: Historic data from 2018 to 2022 and industry forecasts from 2023 to 2030
  • 3 Parameters- Value, Volume, and Pricing Data
  • 6 Regions- Asia Pacific, Europe, North America, South America, Middle East, Africa
  • 27 Countries: United States, Canada, Mexico, Germany, France, Spain, United Kingdom, Italy, Russia, Turkey, Rest of Europe, China, India, Japan, South Korea, Australia, Indonesia, South East Asia, Saudi Arabia, United Arab Emirates, Rest of Middle East, South Africa, Egypt, Rest of Africa, Brazil, Argentina, Other South America
  • 10 Companies- Leading companies with detailed profiles
  • 5 Models- Scenario analysis, Porter’s five forces, Industry SWOT, Pricing analysis, PESTLE
  • 8 Market Dynamics- Trends, Drivers, Growth Restraints, Opportunities
Unique Additions to the current edition-
  • Impact of market developments including the Russia- Ukraine War, inflation across countries, supply-chain conditions, labor-market pressures, recession, trade, and other global factors
  • Pricing Analysis across types, applications, and countries for 2023 and industry Forecasts to 2030
  • electronics and semiconductors industry trends and market forecasts
  • Driving forces supporting the Business Intelligence Analytics sales in each of the 24 countries
  • Complimentary Excel spreadsheet and print authentication for a single-user license
Key Questions answered in this report-

1. What are the key regions in the global Business Intelligence Analytics industry?

2. Who are the major companies or key players operating in the global Business Intelligence Analytics industry?

3. What has been the impact of COVID-19 on the global Business Intelligence Analytics industry?

4. What is the projected compound annual growth rate (CAGR) of the global Business Intelligence Analytics market size for the period 2023-2028?

5. What are the key factors driving the growth of the global Business Intelligence Analytics industry?

6. How is the global Business Intelligence Analytics industry segmented based on product types?

7. What are the emerging trends and opportunities in the global Business Intelligence Analytics industry?

8. What are the challenges and obstacles faced by the global Business Intelligence Analytics market?

9. What are the competitive landscape and strategies of global Business Intelligence Analytics companies?

10. What are the innovations and advancements in product development within the global Business Intelligence Analytics industry?

11. What are the strategies adopted by key players in the global Business Intelligence Analytics market to maintain a competitive edge?

12. How is the global Business Intelligence Analytics industry expected to evolve in terms of demand and market dynamics in the coming years?
1 FOREWORD


2 EXECUTIVE SUMMARY

2.1 Key Findings, 2023
2.2 Market Overview
2.3 Market Highlights

3 REPORT GUIDE

3.1 Study Scope and Objectives
3.2 Market Segmentation
3.3 Methodology and Sources
3.4 Primary and Secondary Data Sources
3.5 Market Estimation- Data Triangulation
3.6 Forecast Methodology
3.7 Key Assumptions

4 INTRODUCTION

4.1 Market Definition and Evolution
4.2 Historical Market Size and Trends, 2018- 2022
4.3 Forecast Market Size, 2023- 2030
4.4 Industry Value Chain Analysis
4.5 Porter's Five Forces Analysis

5 MARKET ASSESSMENT

5.1 Post-COVID-19 Growth Prospects for the Business Intelligence Analytics Industry
5.2 Likely Case – Industry Forecasts
5.3 Optimistic Case- Industry Forecasts
5.4 Pessimistic Case- Industry Forecasts
5.5 Market Dynamics-
5.6 Drivers
5.7 Trends
5.8 Opportunities
5.9 Challenges

6 BUSINESS INTELLIGENCE ANALYTICS MARKET SIZE FORECASTS- TYPES, PRODUCTS, AND APPLICATIONS

6.1 Global Business Intelligence Analytics Growth Outlook by Type, $ Million, 2018- 2022, 2023- 2030
6.2 Global Business Intelligence Analytics Growth Outlook by Product, $ Million, 2018- 2022, 2023- 2030
6.3 Global Business Intelligence Analytics Growth Outlook by Application, $ Million, 2018- 2022, 2023- 2030

7 NORTH AMERICA BUSINESS INTELLIGENCE ANALYTICS MARKET SIZE FORECASTS- TYPES, PRODUCTS, AND APPLICATIONS

7.1 North America Business Intelligence Analytics Industry Current Market Conditions, 2023
7.2 North America Business Intelligence Analytics Market Trends and Opportunities
7.3 North America Business Intelligence Analytics Growth Outlook by Type
7.4 North America Business Intelligence Analytics Growth Outlook by Product
7.5 North America Business Intelligence Analytics Growth Outlook by Application
7.6 North America Business Intelligence Analytics Market Size Outlook by Country
7.7 United States Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
7.8 Canada Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
7.9 Mexico Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030

8 EUROPE BUSINESS INTELLIGENCE ANALYTICS MARKET SIZE FORECASTS- TYPES, PRODUCTS, AND APPLICATIONS

8.1 Europe Business Intelligence Analytics Industry Current Market Conditions, 2023
8.2 Europe Business Intelligence Analytics Market Trends and Opportunities
8.3 Europe Business Intelligence Analytics Growth Outlook by Type
8.4 Europe Business Intelligence Analytics Growth Outlook by Product
8.5 Europe Business Intelligence Analytics Growth Outlook by Application
8.6 Europe Business Intelligence Analytics Market Size Outlook by Country
8.7 Germany Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
8.8 France Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
8.9 United Kingdom Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
8.10. Italy Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
8.11 Spain Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
8.12 Rest of Europe Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030

9 ASIA PACIFIC BUSINESS INTELLIGENCE ANALYTICS MARKET SIZE FORECASTS- TYPES, PRODUCTS, AND APPLICATIONS

9.1 Asia Pacific Business Intelligence Analytics Industry Current Market Conditions, 2023
9.2 Asia Pacific Business Intelligence Analytics Market Trends and Opportunities
9.3 Asia Pacific Business Intelligence Analytics Growth Outlook by Type
9.4 Asia Pacific Business Intelligence Analytics Growth Outlook by Product
9.5 Asia Pacific Business Intelligence Analytics Growth Outlook by Application
9.6 Asia Pacific Business Intelligence Analytics Growth Outlook by Country
9.7 China Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
9.8 Japan Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
9.9 India Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
9.10. Australia Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
9.11 South Korea Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
9.12 South East Asia Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
9.13 Rest of Asia Pacific Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030

10 SOUTH AMERICA BUSINESS INTELLIGENCE ANALYTICS MARKET SIZE FORECASTS- TYPES, PRODUCTS, AND APPLICATIONS

10.1 South America Business Intelligence Analytics Industry Current Market Conditions, 2023
10.2 South America Business Intelligence Analytics Market Trends and Opportunities
10.3 South America Business Intelligence Analytics Growth Outlook by Type
10.4 South America Business Intelligence Analytics Growth Outlook by Product
10.5 South America Business Intelligence Analytics Growth Outlook by Application
10.6 South America Business Intelligence Analytics Growth Outlook by Country
10.7 Brazil Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
10.8 Argentina Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
10.9 Rest of South America Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030

11 MIDDLE EAST AND AFRICA BUSINESS INTELLIGENCE ANALYTICS MARKET SIZE FORECASTS- TYPES, PRODUCTS, AND APPLICATIONS

11.1 Middle East and Africa Business Intelligence Analytics Industry Current Market Conditions, 2023
11.2 Middle East and Africa Business Intelligence Analytics Market Trends and Opportunities
11.3 Middle East and Africa Business Intelligence Analytics Growth Outlook by Type
11.4 Middle East and Africa Business Intelligence Analytics Growth Outlook by Product
11.5 Middle East and Africa Business Intelligence Analytics Growth Outlook by Application
11.6 Middle East and Africa Business Intelligence Analytics Growth Outlook by Country
11.7 Saudi Arabia Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
11.8 United Arab Emirates Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
11.9 South Africa Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
11.10. Rest of Middle East Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030
11.11 Rest of Africa Business Intelligence Analytics Market Size Outlook, $ Million, 2018 to 2030

12 COMPETITIVE LANDSCAPE

12.1 Competitive Scenario
12.2 Key Players
12.3 Company Profiles of Leading 10 Companies
12.4 Company Snapshot
12.5 Business Description of Leading Business Intelligence Analytics Companies
12.6 Business Intelligence Analytics Companies- Products and Services
12.7 Business Intelligence Analytics Companies- SWOT Analysis
12.8 Financial Profile

13 APPENDIX

13.1 List of Charts and Tables
13.2 Sources and Methodology
13.3 Conclusion and Future Remarks

12. TABLES AND CHARTS

Table 1: Global Business Intelligence Analytics Statistics, 2023
Exhibit 2: Research Methodology
Exhibit 3: Forecast Methodology
Table 4: Global Business Intelligence Analytics Market Size Forecast, 2021- 2030
Exhibit 5: Global Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 6: Global Business Intelligence Analytics Outlook by Type, $ Million, 2021- 2030
Table 7: Global Business Intelligence Analytics Outlook by Product, $ Million, 2021- 2030
Table 8: Global Business Intelligence Analytics Outlook by Application, $ Million, 2021- 2030
Exhibit 9: Porter’s Framework
Exhibit 10: SWOT Profile
Exhibit 11: Growth Outlook Scenario Analysis
Table 12: North America Business Intelligence Analytics Outlook by Type, 2021-2030
Table 13: North America Business Intelligence Analytics Outlook by Application, 2021-2030
Table 14: North America Business Intelligence Analytics Outlook by Product, 2021-2030
Table 15: North America Business Intelligence Analytics Outlook by Country, 2021-2030
Table 16: Europe Business Intelligence Analytics Outlook by Type, 2021-2030
Table 17: Europe Business Intelligence Analytics Outlook by Application, 2021-2030
Table 18: Europe Business Intelligence Analytics Outlook by Product, 2021-2030
Table 19: Europe Business Intelligence Analytics Outlook by Country, 2021-2030
Table 20: Asia Pacific Business Intelligence Analytics Outlook by Type, 2021-2030
Table 21: Asia Pacific Business Intelligence Analytics Outlook by Application, 2021-2030
Table 22: Asia Pacific Business Intelligence Analytics Outlook by Product, 2021-2030
Table 23: Asia Pacific Business Intelligence Analytics Outlook by Country, 2021-2030
Table 24: North America Business Intelligence Analytics Outlook by Type, 2021-2030
Table 25: South America Business Intelligence Analytics Outlook by Application, 2021-2030
Table 26: South America Business Intelligence Analytics Outlook by Product, 2021-2030
Table 27: South America Business Intelligence Analytics Outlook by Country, 2021-2030
Table 28: Middle East and Africa Business Intelligence Analytics Outlook by Type, 2021-2030
Table 29: Middle East and Africa Business Intelligence Analytics Outlook by Application, 2021-2030
Table 30: Middle East and Africa Business Intelligence Analytics Outlook by Product, 2021-2030
Table 31: Middle East and Africa Business Intelligence Analytics Outlook by Country, 2021-2030
Table 32: United States Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 33: United States Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 34: Canada Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 35: Canada Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 36: Mexico Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 37: Mexico Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 38: Germany Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 39: Germany Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 40: France Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 41: France Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 42: United Kingdom Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 43: United Kingdom Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 44: Spain Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 45: Spain Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 46: Italy Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 47: Italy Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 48: China Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 49: China Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 50: India Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 51: India Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 52: Japan Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 53: Japan Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 54: South Korea Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 55: South Korea Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 56: South East Asia Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 57: South East Asia Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 58: Australia Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 59: Australia Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 60: Brazil Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 61: Brazil Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 62: Argentina Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 63: Argentina Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 64: Saudi Arabia Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 65: Saudi Arabia Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 66: United Arab Emirates Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 67: United Arab Emirates Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 68: South Africa Business Intelligence Analytics Outlook, $ Million, 2021- 2030
Exhibit 69: South Africa Business Intelligence Analytics Outlook, year-on-year, %, 2021- 2030
Table 70: Market Entropy


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