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Shapes of distributions:Key vocabulary terms
S-012
Obs Score
1 15
2 16
3 13
4 15
5 17
6 12
7 14
8 15
9 15
10 16
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15
Here is a set of scores.Let’s make a graph.
Obs Score
1 15
2 16
3 13
4 15
5 17
6 12
7 14
8 15
9 15
10 16
. .
. .
. .
15
A dot represents the score for the first student.
Obs Score
1 15
2 16
3 13
4 15
5 17
6 12
7 14
8 15
9 15
10 16
. .
. .
. .
15
Obs Score
1 15
2 16
3 13
4 15
5 17
6 12
7 14
8 15
9 15
10 16
. .
. .
. .
15
Obs Score
1 15
2 16
3 13
4 15
5 17
6 12
7 14
8 15
9 15
10 16
. .
. .
. .
15
• We can see where the scores start to pile up.
• We get a picture of the distribution of the scores.
Obs Score
1 15
2 16
3 13
4 15
5 17
6 12
7 14
8 15
9 15
10 16
. .
. .
. .
15
• 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.
Normal, bell-shaped• Symmetric• Mean=median=mode
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 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.”
