Meaning of Skewness: Symmetric and Skewed Distributions

In your earlier chapters on Statistics you learned to summarise a frequency distribution using measures of central tendency (mean, median, mode) and measures of dispersion (range, quartile deviation, mean deviation, standard deviation). These measures tell you where the data is centred and how spread out it is, but they say nothing about the shape of the distribution — specifically, whether the data trails off equally on both sides of the centre or leans more toward one side. This chapter, part of the Gujarat Std 11 Statistics (GSHSEB Commerce) syllabus, studies exactly this third property: skewness.

A frequency distribution is said to be symmetric when the values are distributed evenly around the centre — the left half of the frequency curve is a mirror image of the right half. In a perfectly symmetric distribution:

and the two tails of the distribution are equal in length. A distribution is skewed (asymmetrical) when this mirror-image property fails — one tail of the distribution is longer or fatter than the other, so the bulk of observations is pushed toward one end while a few extreme values stretch the opposite tail. Skewness measures the degree and direction of this lack of symmetry.

Two distributions can have identical mean, identical standard deviation, and still look completely different once you plot them — one may be a neat symmetric bell, the other may be badly lopsided. This is exactly why skewness is treated as a distinct, third characteristic of a distribution, alongside central tendency and dispersion.