Describing Distributions
SHAPESUnimodal Bimodal
Multimodal Uniform
GENERAL SHAPES of DATA
Unimodal• test scores
Bimodal• height (M & F)
Multimodal• favorite numbers
Uniform• # pencils
manufactured each day at factory
MEASURES OF CENTERMEDIAN
• 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
𝑦= 𝑡𝑜𝑡𝑎𝑙𝑛 =
∑ 𝑦𝑛
Pronounced “y-bar”
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 SPREADRANGE
• = max – min• good to
mention for many distributions
IQR• = Q3 – Q1• use with
skewed distribution
• sometimes good to mention with symmetric distribution
STANDARDDEVIATION
• use with symmetric distribution
CALCULATING STANDARD DEVIATION
𝑠2=∑ (𝑦− 𝑦 )2
𝑛−1
Variance:
𝑠=√∑ (𝑦− 𝑦 )2
𝑛−1
Standard Deviation:
Pg. 84 - Summary