Ch. 1 Exploring Data
Introduction
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.
Individual th
1.2 Describing Distributions with Numbers
Objective 4: To describe data using the measures of
center.
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
x
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
Distributions
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.
Density Curve
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=
x
z-score : the nu
3.1 Scatter Plots
Objective 1: To interpret a scatter plot for a set of
ordered pairs.
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
nature o
3.2 Correlation
Objective 2: To compute the correlation coefficient
between two quantitative variables.
Correlation Coefficient: measures the strength and
direction of a linear relationship between two
quantitative variables.
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
variables.
Regression Line: A strai
4.2 Cautions about Correlation and Regression
Objective 4: To identify situations where causation,
common response, or confounding occur between
two variables.
Correlation and regression describe only linear
relationships.
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
causation.
Control Group: the patients that receive the placebo
Placebo Effect: a response to a placebo
Principl
6.3 General Probability Rules
Objective 5: To calculate the probability of
compound events that are joint (not mutually
exclusive).
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
random variable.
Mean of a Probability Distribution
also called the expected value
= x P(x)
Variance of a Pro
Name _
AP Statistics
Discrete Probability Distributions
1. Determine whether the distribution represents a probability distribution. If it does
not, state why.
x
0
1
2
3
P(x)
.30
.25
.35
.20
2. Construct a probability distribution for a family of four chi
AP STATISTICS
Chapter 7
Expected Value
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 $
AP Statistics
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