Chapter 11

Displaying Distributions with Graphs

Turning Quantitative Data Into Information

Shape of the data

Center of the data

Spread of the data (Variability)

Weight DataSTAT 051 Class Survey -- Spring, 1997 – University of Vermont

Weight Data: Frequency TableWeight Group Frequency

100-120 7 120-140 12 140-160 7 160-180 9 180-200 12 200-220 4 220-240 1 240-260 0 260-280 1

* Left endpoint is included in the group, right endpoint is not.

Weight Data: Histogram

0

2

4

6

8

10

12

14

Frequency

100 120 140 160 180 200 220 240 260 280Weight

* Left endpoint is included in the group, right endpoint is not.

Shape of the Data Symmetric

– bell shaped– other symmetric shapes

Asymmetric– skewed to the right– skewed to the left

Unimodal, bimodal, multimodal

Symmetric DistributionsBell-Shaped

Symmetric Distributions Mound-Shaped

Symmetric Distributions Uniform

Asymmetric Distributions Skewed to the Left

Asymmetric Distributions Skewed to the Right

Outliers

Extreme values, far from the rest of the data.

May occur naturally May occur due to error in recording May occur due to error in measuring Observational unit may be fundamentally

different

Number of Books Read for Pleasure

0123456789

10

00 7 14 21 28 35 42 49 56 63 70 77 84 91 98Number of Books