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