Shapes of distributions: Key vocabulary terms S-012

ObsScore Here is a set of scores. Let’s make a graph. Here is a set of scores. Let’s make a graph.

ObsScore A dot represents the score for the first student.

ObsScore

ObsScore

ObsScore We can see where the scores start to pile up. We get a picture of the distribution of the scores. We can see where the scores start to pile up. We get a picture of the distribution of the scores.

ObsScore When we have a large number of scores, it is convenient to draw a smooth curve to depict the distribution. Drawing a curve is just a quick way to show the shape of the distribution. It is really just showing us where the individual scores fall. The smooth curve may sometimes be a bit too simple – it can obscure some details. Not every distribution can be described by a smooth curve. Drawing a curve is just a quick way to show the shape of the distribution. It is really just showing us where the individual scores fall. The smooth curve may sometimes be a bit too simple – it can obscure some details. Not every distribution can be described by a smooth curve.

Normal, bell-shaped Symmetric Mean=median=mode Normal, bell-shaped Symmetric Mean=median=mode Mound-shaped Symmetric Uni-modal Approximately normal Mound-shaped Symmetric Uni-modal Approximately normal Skewed to the right Positively skewed Not symmetric (Asymmetric) Mean > Median * Top 50% more spread out then bottom 50% Skewed to the right Positively skewed Not symmetric (Asymmetric) Mean > Median * Top 50% more spread out then bottom 50% Skewed to the left Negatively skewed Not symmetric (Asymmetric) Mean < Median* Bottom50% more spread out than top 50% Skewed to the left Negatively skewed Not symmetric (Asymmetric) Mean < Median* Bottom50% more spread out than top 50% * Almost always true with continuous variables. Sometimes not true with discrete variables, but mostly a good rule to use.

J-shaped Bi-modal Uniform (rectangular) U-shaped

Normal curve is our reference. Kurtosis: refers to how “sharply peaked” or “flat” the distribution is. Leptokurtic – a sharper point, a higher peak around the mean. (Lepto = “thin” or “narrow”) Platykurtic – a flatter peak around the mean. (Platy = “flat”) Definitely drop some of these terms into your dinner conversation. You will dazzle your friends when you say “platykurtic.”