Is this data skewed or symmetrical?

Question

So I have a piece of data, however, I am having a disagreement with others whether it is symmetric or skewed.

The mean of the data is 430, and the median is 433.

The data would be skewed if the mean > median, or mean < median. However the data would be symmetric if mean ≈ median.

Because the data is looks symmetrical, is it skewed due to the difference in mean and median, or would the two values be considered close enough for the data to be at least “approximately symmetrical?

Attached is a sketch of the data I am working with.

histogram

Answer 1

The data itself is definitely skewed, by the definition you give, albeit only slightly.

However if you introduce the idea that the data graphed is only a sample from a larger population, and ask whether the sample indicates the population as a whole is skewed, this is a different question.

The size of any sample is divisible by the smallest difference in height between two bars.

The fact the bars are of common heights suggests this is probably a small sample size and is sufficiently close to a normal distribution size for such a small sample that the hypothesis the parent population is not skewed, is a reasonable hypothesis.

However the very slight discrepancy in heights between the bars to the left and right of the centre would indicate this is a very large sample size. For such a large sample, the hypothesis that the population is skewed is not skewed is much weaker because large samples more closely approximate their parent populations.