Describing distributions
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Describing Distributions. SHAPES. Bimodal. Unimodal. Multimodal. Uniform. GENERAL SHAPES of DATA. Bimodal height (M & F). Unimodal t est scores. Multimodal f avorite numbers. Uniform # pencils manufactured each day at factory. MEASURES OF CENTER. MODE data value repeated most

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Shapes
SHAPES

Bimodal

Unimodal

Multimodal

Uniform


General shapes of data
GENERAL SHAPES of DATA

Bimodal

  • height(M & F)

Unimodal

  • test scores

Multimodal

  • favorite numbers

Uniform

  • # pencils manufactured each day at factory


Measures of center
MEASURES OF CENTER

MODE

  • data value repeated most

  • seen as humps in a histogram

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


Calculating the mean
CALCULATING THE MEAN

Pronounced “y-bar”


Which center where
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
MEASURES OF SPREAD

STANDARDDEVIATION

  • use with symmetric distribution

RANGE

  • = max – min

  • good to mention for many distributions

IQR

  • = Q3 – Q1

  • use with skewed distribution

  • sometimes good to mention with symmetric distribution


Calculating standard deviation
CALCULATING STANDARD DEVIATION

Variance:

Standard Deviation:



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