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# Describing Distributions PowerPoint PPT Presentation

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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Describing Distributions

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## Describing Distributions

Bimodal

Unimodal

Multimodal

Uniform

### GENERAL SHAPES of DATA

Bimodal

• height(M & F)

Unimodal

• test scores

Multimodal

• favorite numbers

Uniform

• # pencils manufactured each day at factory

### 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

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 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

Variance:

Standard Deviation: