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An overview of describing distributions, focusing on their shape, measure of center, and measures of spread. Topics include symmetric, skewed left and right, unimodal, bimodal, multimodal, uniform distributions, outliers, gaps, median, mean, and five number summary. Learn how to calculate measures of center and spread, and understand the differences between mean and median.
What you will learn
Typology: Schemes and Mind Maps
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Shape
Skewed
Left
of
the
data
is
on
the
right
side
but
tails
out
to
the
left
Skewed
Right
of
the
data
is
on
the
left
side
but
tails
out
to
the
right
Unimodal
major
mode
where
the
data
is
collected
around
Bimodal
major
modes
Multimodal
modes
Uniform
is
flat
and
featureless
Also
mention
any
unusual
features
Outliers
away
from
the
main
distribution.
Can
be
some
of
the
most
informative
and
interesting
Gaps
between
clumps
of
data
1
2 ,^
,...,
n
x
x
x
1
1
=
=
n
i^
n
i
i
i
`
The
mean
is
affected
by
outliers
and
the
median
is
resistant
to
outliers Ex.
`
When
the
data
is
symmetric
with
no
major
outliers
use
the
mean
`
When
the
data
is
skewed
or
has
major
outliers
use
the
median
Numeric
description
of
the
distribution
st
Quartile
1
number
of
the
bottom
half
of
the
data
rd
Quartile
3
number
of
the
top
half
of
the
data
Put
data
in
order
2
2
3
4
5
5
6
6
7
7
7
7
7
8
9
9
9
10
11
12
14
16
19
27
35
Min
=
2
Q
= 1
Med
=
7
Q
3 =^
Max
=
35
Range
between
the
highest
and
lowest
values
Range
Max
Interquartile
Range
between
the
percentile
and
percentile
Range
of
the
middle
of
the
data
3
1
Standard
Deviation
is
a
number
that
describes
how
much
data
vary
or
spread
out.
Uses
difference
of
each
data
value
from
the
mean.
(
) 2
1
=
โ
n
i
i
x
x
s
n
The
higher
the
number
the
more
the
data
is
spread
out.
Can
never
be
negative
If
s
all
the
values
in
the
data
set
are
equal.
The
square
of
the
standard
deviation
is
call
the
variance.
(s
2
var)
Two
machines
are
set
to
cut
a
piece
of
metal
that
should
weigh
15
grams.
A
random
sample
of
50
pieces
from
each
machine
is
taken
and
the
weights
are
measured.
Both
are
centered
at
15
grams.
s 1
=
g
s 2
=
g
If
you
use
the
mean,
use
st. dev.
If
you
use
the
median,
use
the
20.434.
20.031.
x s medIQR
= =
= =
With
Upper
Outlier
Without
Upper
Outlier
19.842.
20.031.
x s medIQR
= =
= =