Confused how quantization would reduce number of y values, please help me understand!

[woozybydefault]

So I'm taking a beginners course in Computer Science in Khan Academy because I'm basically computer illiterate - one of those iPad kids that never leaves their browser or understands how computers work in general. I'm understanding most of my lesson, but can't grok this specific bit saying that "if there is space to represent thousands of y-values, then we can use a very small quantization interval. If there is limited space, we can use a large interval."

Are they saying that using a smaller quantization interval would increase the number of y values that the computer would need to store? I don't see how that would work; in the example they showed, there's 12 y-values regardless of the quantization interval. As far as I can tell, the quantization interval just affects how precise your rounding off is, like how using a quantization interval of 25 would round 24.439022283203116 to 25, while using a quantization interval of 20 would round 24.439022283203116 to 20. I can see how quantization would be useful in rounding numbers with very long strings of decimal numbers since that would save space, but I don't see how it would affect the number of y values in total - there's still 12 y-values, no matter how accurately you round them. And I reading this lesson wrong? Is the lesson misspeaking somehow? Am I just stupid? Pls help this is too weirdly specific for me to google and I don't know anybody tech-minded enough to explain this to me.

 

 

 

 

 

 

[swansont]

29 minutes ago, woozybydefault said:

there's 12 y-values regardless of the quantization

You can’t store all of those unique values if your discretization doesn’t allow it. The example shows 12 x values, but only 6 unique y values (though 9 are possible*, some data points have the same y value)

It’s possible that there are 12 unique y values in the raw measurement, but only 6 are recorded.

 

*100, 75, 50 25, 0, -25, -50, -75, -100

[woozybydefault]

Ahh, now it makes sense! Thank you swansont!