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24 UNIT 1 Exploring One-Variable Data

Describing Shape

When you describe the shape of a dotplot or another graph of quantitative
data, focus on the main features. Look for clear peaks, not for minor ups and
downs in the graph. Look for clusters of values and obvious gaps. Decide if
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the distribution is roughly symmetric, skewed to the left, or skewed to the
right.

DEFINITION Roughly symmetric, Skewed to the left, Skewed to the right
A distribution is roughly symmetric if the right side of the graph (containing the half
of the observations with the largest values) is approximately a mirror image of the
left side.

Roughly symmetric

A distribution is skewed to the left if the left side of the graph is much longer than
the right side.

Skewed to the left

A distribution is skewed to the right if the right side of the graph is much longer
than the left side.

Skewed to the right

We could also describe a distribution with a long tail to the left as “skewed
toward negative values” or “negatively skewed,” and a distribution with a long
right tail as “positively skewed.” For ease, we sometimes say “left-skewed”
to the instead of “skewed to the left” and “right-skewed” instead of “skewed to the
left! caution right.” The direction of skewness is toward the long tail, not in the direction
where most observations are clustered. The drawing is a cute but corny way
to help you keep this straight. To avoid danger, Mr. Starnes skis on the gentler
slope — in the direction of the skewness.

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