Transparency International tracks a Corruption Perception Index for every country in the world. In 1995, the earliest year for which the index is available, South Africa's score was 5.62 (out of 10) with a rank of 21st least corrupt country among those sampled (out of 41 countries). In 1999, South Africa's score was 5.0 (out of 10) with a rank of 34 (out of 99). In 2013, South Africa's score was 42 (out of 100) with a rank of 72 (out of 175). South Africa's corruption score thus slipped somewhat in absolute terms during President Mandela's term and continued to slide until the present day. The good news is that South Africa surpasses the median compared to other countries. It's worth noting that Transparency's scoring methodology has changed since the inauguration of the index and many more countries are now part of the survey.
The Heritage Foundation tracks an Index of Economic Freedom for every country in the world. I used the "explore the data" option to find South Africa's figures for 1995, the earliest year available. The country's overall score that year was 60.7 (out of 100), with no ranking available. Their score in 1999 was 63.3 and in 2013 it is 61.8. That's a slight improvement overall since the end of apartheid. South Africa today ranks 74th out of 177 countries, clearly beating the median and putting it in Heritage's "Moderately Free" category.
The World Bank tracks a Logistics Performance Index, one of my favorite measures of how well a country is positioned to handle trade. The earliest year for data is 2007 so we can't see any changes during Mr. Mandela's presidency. In 2007, South Africa scored 3.53 (out of 5) and ranked 24th (out of 150). In 2012, it scored 3.67 and ranked 23rd (out of 155). This statistic alone tells us little about whether Mr. Mandela made the country's infrastructure more robust but South Africa clearly ranks quite high.
The OECD maintains plenty of stats, including GDP, but the earliest data they have online is from 2007. GDP is a very relevant measure of an economy's health. We need stats from Mr. Mandela's era. This 2006 academic paper from the University of Stellenbosch demonstrates that South Africa did experience modest improvements in economic growth since 1994. CNN reports that South Africa has experienced enormous growth in its economy and middle class, even while severe inequality remains. Consider that economic benefits were primarily available only to the white minority before the end of apartheid. The salutary economic transformation since Mr. Mandela ended apartheid is praiseworthy.
The World Bank has additional data on South Africa from its World Development Indicators. GNI per capita has risen since 1994 but life expectancy and school enrollment have fallen. The UN Statistics Division data on South Africa shows strong economic growth since 2005; labor force participation has slightly declined; telephone and Internet use have skyrocketed.
This analysis is by no means an all-encompassing consideration of Mr. Mandela's effectiveness as a leader. I would argue that his most important achievement was the turnaround of an ostracized country. He rehabilitated what the business community would call a damaged brand and made it viable. South Africa earned inclusion among the BRICS nations as a dynamic emerging economy. Mr. Mandela took great care during his presidency to assure international investors that he would not nationalize South African industries or engage in wealth redistribution, and he held true to his word. Using Big Data KPIs shows clear progress in many areas. I would hire "Madiba" to save a troubled company.