In a technical job interview I was asked a question that I couldn't quite make sense of. The interviewer was talking about sampling a sound file to make a visual effect (such as a graph that moved to the sound). The question was how should the sample from the sound wave be taken. I said average over a time interval (such as 0.1 seconds) and he said that's a bad idea as average can only be used over a normal distribution.
It's been a while since I've studied statistics and would like a simple explination
First: what does normal distribution have to do with anything?
Second: the average can be computed as long as the two numbers can be added and divided by two so I don't know why he used the words "can't use it". What is wrong when using the average when something is not normally distributed?
I't sounds like the interviewer wanted you to come up with some way to modulate a shape to the sound, such as with the numerous Media Player visuals. I would think that you'd want to modulate in two different ways:
I'm not a sound person, but the interviewer's response to your answer seems very loaded with unexplianed assumptions. For example, if he were thinking that the median volume over an interval should be used, then if your data are not symmetric (as in a normal distribution), then a time-average would likely be skewed. But he didn't say that.
You are correct that you can take a valid average for any data set. Whether or not the average means anything depends on the underlying process generating the data. For example, the Cauchy distribution does not have a mean, so taking an average of it will not tell you anything interinsic about the population. It will with a normal distribution.
Did he say what you were trying to sample? Some sort of aggregation appears necessary, if only because our human senses have an inherent limitation in how fast they can resolve discrete sensations.