Global Average Temperature
The raw temperature data consists of many temperature readings, on land and on sea, taken over many years. What is of interest is not the individual temperature reading, but the change in the average temperature of the Earths surface. One of the challenges of scientists is to use these temperature readings to figure out how the global average temperature is changing. This process is continually being monitored, improved and subject to scientific scrutiny. The analysis calculates a difference in temperature from some baseline average. This difference in temperature is called the anomaly. In what follows the base line is the surface averaged temperature, averaged over the 20th century. What is plotted is the difference between the global average temperature and the baseline temperature. If you would like to get more information on how the data is analyzed, here is a good place to start.
Below is a plot of the monthly average surface temperature anomalies of the Earth (land and ocean).
I downloaded the data from https://www.ncdc.noaa.gov/cag and plotted the results in Excel. If you are familiar with Excel, go and do it yourself! It is visually clear that the temperature has risen since at least 1960, and perhaps as early as 1910. There is a lot of up and down in this graph since the anomaly fluctuates on an annual basis. So I took the data and computed the annual average for each year, as well as the largest and smallest value for each year (easy to do in Excel). The plot of this analysis is below.
There is still some up and down motion of the average, but the upward trend is clearly visible. There seems to have been relatively quiet period between 2002 and 2009, but if you look at this period in the context of the entire graph the trend is clearly visible.
Is the data reliable?
Many people have examined the details of the data and some questions were and answered. The scientists that work with this data want it as accurate as possible, and will use new methods to improve the accuracy. That is why the analysis of the data is occasionally revised.
A better question would be “Is the data accurate and reliable enough to show that there is an increase in the surface averaged temperature anomaly?”
A random error would simply make the observed data more “noisy” with larger fluctuations. This would not destroy the trend, unless the noise was so great that the entire trend was within the noise, this would be a very large error indeed. To date, I am not aware of anyone, not even the skeptics, that have been able to point to such a large error.
A systematic error (not random) would have to change with time to pull down the trend. Why would all the thermometers slowly drift to higher temperatures? This seems very unlikely and I know of no such large systematic errors?
Yes, the data is reliable and accurate enough to show that the average surface temperature of the Earth is increasing.
What the temperature data does not show by itself.
The temperature data shows a trend, the Earth is warming. The data, by itself, does not tell us why the Earth is warming. That requires a bit more science and examining more data. The data and science can determine the mechanisms involved in global warming (green house gas emissions and the like). But the ultimate explanation for why the Earth is warming, is our insatiable desire to own more stuff and to travel larger distances faster (cars). The human element requires that we look inward to discover why we put our own desires ahead of planetary needs. That is the realm of theology, philosophy and psychology. Atmospheric science will not answer these questions, but they do need answers.