Unfortunately, based only on the information that the third central moment was zero, many people would in fact describe it as symmetric.I've seen many examples over the years, so I figured it shouldn't be hard to find one or two. A quick google search reveals some examples:
- This page on using a TI83 calculator has:
- "Skewness measures the departure from symmetry" (it defines skewness as the third moment measure I mentioned, so it is saying that 0 third moment implies symmetry)
- it goes on to suggest a test statistic for symmetry based on this, and concludes that discussion with "If that fraction is between −2 and 2, you can’t say whether the population is symmetric (skewness = 0) or skewed."
- This paper on brain evolution has:
- "SK, subclade skewness (- negative skew; 0, symmetric distribution; + positive skew)"
- "the system is probably passive if average subclade skew is neutral (symmetric distribution) or negative"
- This set of notes for a university* subject called "Introduction to Statistics" has the following complete howlers:
- "If the skewness is approximately zero, the histogram (distribution) for the data is symmetric and usually normal"
- "'varB' has a skewness close to zero so that its distribution should be normal and mean and median should be similar."
That last site approaches farce, and it's trying to teach statistics!. This is often what happens when people whose own area is not statistics get put in charge of teaching it. (For some reason mathematicians are among the worst offenders.)
There were more examples. The above ones are pretty standard.