Describing
Distributions
SHAPES
Unimodal
Multimodal
Bimodal
Uniform
SHAPES (cont’d)
GENERAL SHAPES of DATA
Unimodal
• test scores
Multimodal
• favorite numbers
Bimodal
• height (M & F)
Uniform
• # pencils
manufactured each
day at factory
MEASURES OF CENTER
MEDIAN
• middle number
of all data values
when ordered
ascending or
descending
• NOT affected by
value of data
• Divides
histogram into
equal areas
MEAN
• arithmetic
average
• IS affected by
value of data
• the “balancing
point” of the
histogram
MODE
• data value
repeated most
• seen as humps
in a histogram
CALCULATING THE MEAN
Pronounced “y-bar”
𝑡𝑜𝑡𝑎𝑙
𝑦
𝑦=
=
𝑛
𝑛
WHICH CENTER WHERE?
Nominal – categorical data with no rank (i.e. sex, race, hair color)
Ordinal – categorical data with ranking (i.e. level of education, economic status)
Interval – quantitative data
MEASURES OF SPREAD
RANGE
• = max – min
• good to
mention for
many
distributions
IQR
• = Q3 – Q1
• use with
skewed
distribution
• sometimes
good to
mention with
symmetric
distribution
STANDARD
DEVIATION
• use with
symmetric
distribution
CALCULATING STANDARD DEVIATION
Variance:
2
𝑦)
(𝑦
−
2
𝑠 =
𝑛−1
Standard Deviation:
𝑠=
2
𝑦)
(𝑦 −
𝑛−1
Pg. 84 - Summary