# Why must average only be used with normal distribution?

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'm not sure the answer to your question. It may have been unclear on the spot feedback and not what they really meant. I know several reasons why the interviewer would not like that answer though. Think of a low frequency wave. You will audibly only hear one note, but averaging small time interval samples would give you values that increased and then decreased. This would lead you to believe that visually something should be going on, but in reality there is nothing audibly going on.
– Matt
Commented Apr 10, 2014 at 21:53

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:

1. Scale the shape based on the volume
2. Alter the color based on the frequency composition

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.

• the sample was for music Commented Apr 10, 2014 at 18:51
• @Celeritas Sorry, what I mean was what aspect of the music were you supposed to be capturing for this "visual"?
– user76844
Commented Apr 10, 2014 at 19:12