Explanation

Skewness in statistics is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. In other words, skewness tells us to what degree the distribution is non-symmetric about its mean.

Key Points:

• If the distribution of data is perfectly symmetric, the skewness will be zero
• If the distribution is not symmetric, then the skewness will not be zero
• Positive skewness: longer or fatter tail on the right side than on the left side
• Negative skewness: longer or fatter tail on the left side than on the right side

Why Other Options Are Incorrect:

• Choice A: Incorrect because skewness does not measure the degree of symmetry about the mean - it measures the degree of asymmetry
• Choice B: Incorrect because skewness does not measure nonsymmetry about the median - it specifically refers to nonsymmetry about the mean
• Choice D: Incorrect because the spread of a random variable around its mean is measured by variance or standard deviation, not skewness

Skewness is an important concept in statistics as it can provide insights into the underlying data generating process and potential outliers or anomalies in the data.