Not that I necessarily doubt these numbers, but by personal experience these always feel awfully low (even jobs paying to TVöD on entry level should put you above the median). Especially when going for larger enterprises I can only recommend negotiating - a lot is possible and realistic beyond the 90th percentile with even moderate experience.
Calling it awfully low is bit of stretch. I would have expected the top 10% to be higher but median not that different. I suppose HN attracts Crème de la Crème of German devs who might be earning higher because these numbers look quite alright to me. I get lot of XING jobs notification with salary ranges mentioned on it and majority of them have like 60K-80K salary ranges.
I've seen quite a few job positions in the German public sector that where trying to hire people with a CS education on a E8, which will be something around 36.000 euro per annum before taxes and social security. Although, there are extremely underpaying employers in the private sector as well. At the end of 2015 when I was a fresh graduate a company offered me 26000 (with a 42h week and 24 vacation days) for a Junior Java EE position, which even then was an offer which required a bit of chuzpah, to say the least...
For public services, entry level sw engineering with a master's degree would put you at ~52k€ (TVöD E13 I); with 1 yr of experience you would get ~+5k€; with around 3 yrs of experience you would get ~+9k€, surpassing the median salary if you have a master's degree. With a bachelor's degree you'd start at ~46k (TVöD E11 I, though E10 would be possible, too) and would need to wait a bit longer until you surpass the median.
Note that German public services generally base your base pay on your qualification (your degree), only then can your experience "shift" the base pay upwards. Also note that starting next year, they will get a 10 % salary increase...
Tl;dr public service employees earn pretty average
Actually the pay is based on the required qualification for this job. Oftentines, for software developers, they just require a bachelor's degree and will pay E11. If you apply with a higher degree, you will not be paid more..
My bad, thanks for the correction. From talking to colleagues who used to be on such contracts I understood they ended at 60k, but then probably they got some sort of experience accredited.