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A lot of the noise that shows up in high ISO pictures (ISO 1600 and above) is due to shooting in low-light situations where those have great dynamic range. This is common in low light situations: think pools of light by local illumination from home table lamps or street lamps and compare that with bright overall lighting in an office for example.
This is why it is frequently claimed that all you have to do is "expose properly" (i.e. not under-expose) to avoid a lot of noise. There is some truth to that, but it is not the whole story.
If you under-expose a low light, low dynamic range scene, you will get more noise. So be sure to give those enough exposure.
However, with a high dynamic range scene, you can expose the highlights hard to the right (lots of good exposure) and still have dark noisy shadows.
Beware of scenes that have inherent high dynamic range and use techniques appropriately (adding light to fill shadows, Expose to the Right, multi-exposure HDR, Zero-Noise 0+4 exposure merge, etc.)