increase in dividends paid . free cash flow is defined as cash provided by operating activities less cash used in investing activities and dividends paid . free cash flow is not considered a financial measure under accounting principles generally accepted in the u.s . ( gaap ) by sec regulation g and item 10 of sec regulation s-k and may not be defined and calculated by other companies in the same manner . we believe free cash flow is important to management and investors in evaluating our financial performance and measures our ability to generate cash without additional external financings . free cash flow should be considered in addition to , rather than as a substitute for , cash provided by operating activities . the following table reconciles cash provided by operating activities ( gaap measure ) to free cash flow ( non-gaap measure ) : millions 2013 2012 2011 .
what was the average cash provided by operating activities from 2011 to 2013
2014 outlook f0b7 safety 2013 operating a safe railroad benefits our employees , our customers , our shareholders , and the communities we serve . we will continue using a multi-faceted approach to safety , utilizing technology , risk assessment , quality control , training and employee engagement , and targeted capital investments . we will continue using and expanding the deployment of total safety culture and courage to care throughout our operations , which allows us to identify and implement best practices for employee and operational safety . derailment prevention and the reduction of grade crossing incidents are also critical aspects of our safety programs . we will continue our efforts to increase detection of rail defects ; improve or close crossings ; and educate the public and law enforcement agencies about crossing safety through a combination of our own programs ( including risk assessment strategies ) , various industry programs and local community activities across our network . f0b7 network operations 2013 we believe the railroad is capable of handling growing volumes while providing high levels of customer service . our track structure is in excellent condition , and certain sections of our network have surplus line and terminal capacity . we are in a solid resource position , with sufficient supplies of locomotives , freight cars and crews to support growth . f0b7 fuel prices 2013 uncertainty about the economy makes projections of fuel prices difficult . we again could see volatile fuel prices during the year , as they are sensitive to global and u.s . domestic demand , refining capacity , geopolitical events , weather conditions and other factors . to reduce the impact of fuel price on earnings , we will continue seeking cost recovery from our customers through our fuel surcharge programs and expanding our fuel conservation efforts . f0b7 capital plan 2013 in 2014 , we plan to make total capital investments of approximately $ 3.9 billion , including expenditures for positive train control ( ptc ) , which may be revised if business conditions warrant or if new laws or regulations affect our ability to generate sufficient returns on these investments . ( see further discussion in this item 7 under liquidity and capital resources 2013 capital plan. ) f0b7 positive train control 2013 in response to a legislative mandate to implement ptc by the end of 2015 , we have invested $ 1.2 billion in capital expenditures and plan to spend an additional $ 450 million during 2014 on developing and deploying ptc . we currently estimate that ptc , in accordance with implementing rules issued by the federal rail administration ( fra ) , will cost us approximately $ 2 billion by the end of the project . this includes costs for installing the new system along our tracks , upgrading locomotives to work with the new system , and adding digital data communication equipment to integrate the various components of the system and achieve interoperability for the industry . although it is unlikely that the rail industry will meet the current mandatory 2015 deadline ( as the fra indicated in its 2012 report to congress ) , we are making a good faith effort to do so and we are working closely with regulators as we implement this new technology. .