Ch. 1 Exploring Data
Objective 1: To recognize the difference between
categorical and quantitative variables.
Statistics the science of conducting studies to
collect, organize, summarize, analyze, and draw
conclusions from data.
1.2 Describing Distributions with Numbers
Objective 4: To describe data using the measures of
Measures of Center
Mean: the number obtained by adding the values
and dividing the total by the amount of values.
= Denotes the sum of a set of values
1.1 Displaying Distributions with Graphs
Objective 2: To create and interpret graphs that
accurately represent data.
A graph is not in itself an end result; it is a tool
for describing, exploring, and comparing data.
Graphs show the distribution of data
2.1 Density Curves and the Normal
Objective 1: To connect the density curve to
the shape of a histogram/stem plot.
Mathematical Model: a curve for a distribution
that gives a compact picture of the overall
pattern of the data.
2.2 Standard Normal Calculations
Objective 3: To apply the standard normal
distribution to calculate percentages and data values.
Standard Normal Distribution: a normal
distribution that has a mean of 0 and a standard
deviation of 1.
z-score : the nu
3.1 Scatter Plots
Objective 1: To interpret a scatter plot for a set of
Scatter Plot: a graph of the ordered pairs (x,y) of
numbers consisting of the independent variable x and
the dependent variable y; a visual way to describe the
Objective 2: To compute the correlation coefficient
between two quantitative variables.
Correlation Coefficient: measures the strength and
direction of a linear relationship between two
Formula for the Correlation C
3.3 Least Squares Regression
Objective 3: To calculate and plot the least squares
regression line between two variables.
Least Squares Regression: A method for finding a
line that summarizes the relationship between two
Regression Line: A strai
4.2 Cautions about Correlation and Regression
Objective 4: To identify situations where causation,
common response, or confounding occur between
Correlation and regression describe only linear
The correlation coefficient an
5.1 Designing Samples
Objective 1: To identify the difference between an
observational study and an experimental study.
Observational Study: the researcher observes
individuals and measures variables of interest but
does not attempt to influence the respo
5.2 Designing Experiments
Objective 4: To identify subjects, treatments, and
variables in experiments.
Experiments can give good evidence for
Control Group: the patients that receive the placebo
Placebo Effect: a response to a placebo
6.3 General Probability Rules
Objective 5: To calculate the probability of
compound events that are joint (not mutually
Formal Addition Rule
P(A or B) = P(A) + P(B) P(A and B)
P(A B) = P(A) + P(B) P(A B)
applies when A and B are joint (not mu
7.1 Discrete and Continuous Random Variables
Objective 1: To construct a probability distribution
for a discrete random variable.
Random Variable: a variable whose values are
determined by chance.
Discrete Random Variable: has a countable
number of possib
Objective 2: To calculate probabilities for a
continuous random variable.
Continuous Random Variable: takes all
values in an interval of numbers.
Continuous Probability Distribution:
described by a density curve; the probability of
any event is the area u
7.2 Means and Variances of Random Variables
Objective 3: To calculate the mean, variance,
standard deviation, and expected value for a discrete
Mean of a Probability Distribution
also called the expected value
= x P(x)
Variance of a Pro
Discrete Probability Distributions
1. Determine whether the distribution represents a probability distribution. If it does
not, state why.
2. Construct a probability distribution for a family of four chi
1. The probability distribution table for the following scenario is shown below. Place a $10
bet on the outcome of the number 21 at the casino. The probability for winning $350 is
1/38 and the probability of losing $
Ch. 7 Worksheet
1. Assume that a time between 0 and 4 hours is randomly selected in such a way that
every possible time is equally likely. x is a continuous random variable with a
uniform distribution. Find the given probabilities.
a. less t