Lesson 1 - 0

Summary to

Exploring Data

Chapter Objectives• Use a variety of graphical techniques to display a

distribution. These should include bar graphs, pie charts, stemplots, histograms, ogives, time plots, and Boxplots

• Interpret graphical displays in terms of the shape, center, and spread of the distribution, as well as gaps and outliers

• Use a variety of numerical techniques to describe a distribution. These should include mean, median, quartiles, five-number summary, interquartile range, standard deviation, range, and variance

• Interpret numerical measures in the context of the situation in which they occur

• Learn to identify outliers in a data set

Section Objectives

• Identify the individuals and variables in a set of data

• Classify variables as categorical or quantitative

• Identify units of measurement for a quantitative variable

Vocabulary

• Individuals – objects described by a set of data; maybe people, animals or things

• Variable – any characteristic of an individual; can take on different values for different individuals

• Categorical variable – places an individual into one of several groups or categories

• Quantitative variable – takes numerical values; for which it makes sense to find an average!

• Distribution – tells us what values the variable takes on and how often it takes these values

• Inference – using a sample of data to infer (to draw conclusions) about a larger group of data

Activity• Hiring Discrimination – It just won’t fly! on pg 5

Captains Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

Male

Female

Activity – Computer Assisted

Capt 0 1 2 3 4 5 6 7 8

M-Pct 0.000 0.001 0.020 0.106 0.265 0.333 0.208 0.059 0.006

Cum 0.000 0.001 0.021 0.127 0.392 0.725 0.933 0.992 ~1

Using Excel to help calculate the probabilities of having that number of male captains selected with the parameters given in the activity:

Cumulative probabilities don’t always add to 1 from a table due to round-off error. Almost 13% chance of this or more extreme result.

Later in the course we will cover this type of problem again in the non-AP portion of discrete random variables.

Categorical Variables

• From Mr. Starnes data collection sheet:– Gender M/F– Hair color Br/Bl/Rd/Gr– Restaurant– Birth date– Dominant hand R/L– Bathroom Y/N– Numbers (1-4) 1/2/3/4– S or Q S/Q– Heads or Tails H/T

Quantitative Variables

• From Mr. Starnes data collection sheet:– Hours of sleep 0-10– Number of siblings 0-8– Height 4’9” – 6’5”– SAT scores 400-800– Ounces of soda 0-64– Pulse 40-80– Days 0-10– Time spent 0-4– Instructor’s age 50-70

Summary and Homework

• Summary– A data set contains information on a number of

individuals– Information is often values for one or more

variables– Variables can be categorical or quantitative– Distribution of a variable describes what values it

can take on and how often

• Homework– Pg 7-8, problems 1, 3, 5, 7, 8