To answer this question, it's important to clarify that symmetry in the context of statistical distributions usually refers to the shape of the curve in relation to some central measure.

The options you've provided are:

• Mean: The mean is the central tendency of a distribution, and many symmetrical curves, like the normal distribution, are symmetrical about the mean. This makes the mean a logical answer in many cases.
• Variance: Variance measures the spread of a distribution, but it isn't a point or axis around which the curve can be symmetric. It's a scalar value, not a measure of symmetry.
• Standard deviation: The standard deviation is also a measure of spread and, like variance, doesn't act as a point of symmetry.
• Area: The area under a curve is always positive and is a representation of total probability or total quantity, but it’s not typically used to define symmetry.

So, the mean is typically the point of symmetry for many distributions, especially the normal distribution, which is symmetric around the mean.

Answer: a. Mean

Would you like further explanation or details on this? Here are a few related questions:

1. What is the significance of the mean in a normal distribution?
2. How do you calculate the variance and standard deviation of a dataset?
3. Can a distribution be symmetric around something other than the mean?
4. Why does the normal distribution have symmetry?
5. What is the relationship between the mean, median, and mode in symmetric distributions?

Tip: In symmetric distributions, the mean, median, and mode all coincide at the center of the distribution!