Which statement is true about skewed distributions?

Which statement is true about skewed distributions?

• A. They are symmetrical.
• B. They have tails on both sides of equal length.
• C. They are not symmetrical and have a long tail on one side.
• D. The mode, median and mean are always equal.

Answer: (C)

Skewed distributions are not symmetrical and have a long tail on one side. This distinguishing feature sets them apart from symmetrical distributions, which have tails that are roughly equal on both sides. The long tail means extreme values pull the mean in the direction of the tail, so the order of the measures of central tendency isn’t the same on both sides: in a positively skewed distribution, the mean tends to be greater than the median, which is greater than the mode; in a negatively skewed distribution, the mean is less than the median, which is less than the mode. That’s why the statement about a long tail and lack of symmetry is true, while descriptions of symmetry or all three measures being equal apply to symmetric distributions, not skewed ones.

Skewed distributions are not symmetrical and have a long tail on one side. This distinguishing feature sets them apart from symmetrical distributions, which have tails that are roughly equal on both sides. The long tail means extreme values pull the mean in the direction of the tail, so the order of the measures of central tendency isn’t the same on both sides: in a positively skewed distribution, the mean tends to be greater than the median, which is greater than the mode; in a negatively skewed distribution, the mean is less than the median, which is less than the mode. That’s why the statement about a long tail and lack of symmetry is true, while descriptions of symmetry or all three measures being equal apply to symmetric distributions, not skewed ones.