1Data
Facts and figures from which conclusions can be drawn
2Data Set
The data that are collected for a particular study
3Variable
any characteristic of an element
4Quantitative Variables
The possible measurements of the values of a variable are numbers that represent quantities
Ex: Age
5Qualitative (Categorical) Variables
Labels or names used to identify an attribute of each element
Ex: Names
6Cross Sectional Data
Data collected at. the same time or approximately the same time
7Time Series Data
Data collected over different time periods
8Population
A set of all elements about which we draw conclusions
9Sample
A. subset of all the elements in a population
10Probability Sampling
Sampling where we know the change that each element in the population will be included in the sequence
11convience sampling
sampling where we select elements because they are convenient to sample
not a probability sample
12voluntary response sampling
samples in which participants self-select
-frequently used by radio and television
-over represent people with strong opinions
13judgements sampling
samples in which a person who is extremely knowledgable about the population selects population elements he or she feels are most representative
14nominative variable
a qualitative variable for which there is no meaningful ordering
15ordinal variable
A qualitative variable for which there is a meaningful ordering or ranking of the categories.
Ex: teaching effectiveness
16interval variable
All of the characteristics of ordinal (meaningful ranking) plus... measurements are on a numerical scale with an arbitrary zero point and can only meaningfully compare values by the interval between them
Ex: Temperature
17ratio variable
interval plus Measurements are on a numerical scale with a meaningful zero point such as anything related to money
Ex: Earnings
18stratified random sampling
divide population into non-overlapping groups (strata) then select a random sample from each strata
19multistage cluster sampling
divide population into clusters and then randomly select clusters to sample
20systematic sampling
list population
21dichotomous questions
-clearly stated
-easy to answer
-easy to analyze
-limited information
22multiple choice questions
-allow more than two responses
-usually analyzed with averages
23open-ended questions
-most honest and complete information
-cannot be readily summarized
24phone surveys
-inexpensive
-low response rate
25mail surveys
-inexpensive
-low response rate (20-30%)
-requires multiple mailings
26web surveys
-cheaper still
-same problems as mail surveys
27personal interviews
-more expensive
-more control
-higher response rates
28relative frequency
summarizes a proportion of items in each class
29relative frequency for a class formula
(number of frequency of the class)/n
multiply by 100 to obtain percent frequency
30bar chart
A vertical or horizontal rectangle represents the frequency for each category
31pie chart
A circle divided into slices where the size of each slice represents its relative frequency or percent frequency
32histogram
a picture of the frequency distribution
33How to find frequency distribution (steps)
1. Find the number of classes
2. Find the class length
3. Form non overlapping classes of equal width
4. Tally and count
5. Graph the histogram
34class length fomula
(max-min)/# of classes
35frequency polygon
-Plot a point above each class midpoint at a height equal to the frequency of the class
-Useful when comparing two or more distributions
36cumulative distribution
-Another way to summarize a distribution is to construct a cumulative distribution
-To do this
37ogive
A graph of a cumulative distribution
38stem-and-leaf displays
-purpose is to see the over all pattern of the data
39how to construct a stem and leaf display
1.Decide what units will be used
2.Each leaf must be a single digit and stem values will consist of appropriate leading digits.
3.Place the stem values
4.Enter the leaf values. (each leaf should be single digit
can be any power of 10)
5.Rearrange the leaves in increasing order.
· Can split the stems as needed
40original data value formula
(stem and leaf)* leaf unit
41contingency table
classifies data on two dimensions
-rows classify according to one dimension
-columns classify according to a second dimension
42scatter plot
used to study relationships between two variables
43population parameter
a number calculated from all the population measurements that describes some aspect of the population
44sample statistic
a number calculated using the sample measurements that describes some aspect of the sample
45mean
the arithmetic average of a distribution
46median
the middle score in a distribution
47mode
The value that occurs most frequently in a given data set.
48relationship between mean, median, mode
Median < mean = curve skewed to right
Median > mean = curve skewed to the left
All equal = symmetrical curve
49range
Largest measurement minus the smallest measurement
50variance
The average of the squared deviations of all the population measurements from the population mean
51population variance formula
((x_1-μ)^2+(x_2-μ)^2+⋯+(x_N-μ)^2)/N
52Sample Variance Formula
((x_1-x ̅ )^2+(x_2-x ̅ )^2+⋯+(x_(n-1)-x ̅ )^2)/(n-1)
53standard deviation
The square root of the population variance
54population standard deviation
σ=√(σ^2 )
55sample standard deviation
s=√(s^2 )
56empirical rule
If a population has mean μ and standard deviation σ and is described by a normal curve
57Chebyshev's Theorem
Let μ and σ be a population's mean and standard deviation
58z-score forrmula
z=(x-mean)/standard deviation
59coefficient of variation
Size of the SD related to size of the mean
60coefficient of variation formula
(standard deviation/mean)X100%
61percentile
a value such that p percent of the measurements fall at. or below the value and (100-p) percent of the measurements fall at or above the value
62important percentiles
-The first quartile Q1 is the 25th percentile
-The second quartile (median) is the 50th percentile
-The third quartile Q3 is the 75th percentile
-The interquartile range IQR is Q3 - Q1
63how to calculate percentiles
1. arrange the measurements in increasing order
2. calculate the index i=(p/100)n where p is the percentile to find
3. (a) if i is not an integer
645 number summary
minimum
65a. 5.375 ((8+7+5+2+9+2+5+5)/8)
b. 5
c. 5 ((5+5)/2)
sample data: 8
66A) Mode
the measurement in a sample or a population that occurs most frequently is the _______?
A) mode
B) mean
C) median
D) outlier
E) average
67C) median would be less than the mean
If a population distribution is skewed to the right
68C) 3
A normal population has 99.73 percent of the population measurements within ________ standard deviation(s) of the mean.
A) 1
B) 2
C) 3
D) 4
69D) whether a person has a traffic violation
Which of the following is a categorical variable?
A) air temperature
B) bank account balance
C) daily sales in a store
D) whether a person has a traffic violation
E) value of company stock
70B) convenience sampling
In ________ we select elements because they are easy to sample.
A) random sampling
B) convenience sampling
C) judgment sampling
D) probability sampling
71D) All of the other answers are correct
Which of the following is a type of question used in survey research?
A) dichotomous
B) open-ended
C) multiple-choice
D) All of the other answers are correct
72Chebyshev's Theorem Formula
(1-1/k^2)%
73Experiment
any process of observation with an uncertain outcome
Ex: Flipping a coin
74Experimental Outcomes
possible outcomes for an experiment
75Probability
A measure of the chance that an experimental outcome will occur when an experiment is carried out
76sample space
the set of all possible experimental outcomes
77classical method of assigning probabilities
For equally likely outcomes
Ex: Rolling a die
78relative frequency method of assigning probabilities
Using the long run relative frequency
79subjective of assigning probabilities
assessment based on experience
80probability model
a mathematical representation of a random phenomenon
81random variable
a numerical description of the outcome of an experiment
82probability distribution
a probability model describing a random variable
2 types: discrete and continuous
83Event
a set of sample outcomes
84probability of an event
the sum of the probabilities of the sample space outcomes
85Complement Probability Rule
the complement of an event A is the set of all sample space outcomes not in A
86Union
The ______ of A and B are elementary events that belong to either A or B or both
87Intersection
The ______ of A and B are elementary events that belong to both A and B
88If they have no sample space outcomes in common
When are A and B mutually exclusive?
89P(A|B)=P(A) which is equivalent to P(B|A)=P(B)
When are A and B independent?
90Multiply
If two events are independent
91.76
If A and B are independent events
92discrete and continuous
What are the two types of random variables?
93discrete random variable
Possible values can be counted or listed
Ex: The number of defective units in a batch of 20
94continuous random variable
may assume any numerical value in one or more intervals
Ex: The interest rate charged on a business loan
95probability distribution of a discrete random variable
a table
961. for any value x of the random variable
p(x) >=0
2. The probability of all the events in the sample space must sum to 1
971. Experiment consists of n identical trials
2. Each trial results in either "success" or "failure"
3. Probability of success
p
98Poisson Distribution
considers the number of times an event occurs over an interval of time or space
991. the probability of occurrence is the same for any intervals of equal length
2. The occurrence in any interval if independent of an occurrence in any non overlapping interval
what are the characteristics of a poisson distribution?
100the number of minutes required to run a mile
what is NOT a discrete random variable?
102poisson
the distribution whose mean is equal to its variance is the ______ distribution.
103properties of f(x):
1. f(x)>=0 for all x
2. The total area under the curve of f(x) is equal to 1
ESSENTIAL POINT: An area under a continuous probability distribution is a probability
what are the properties of a continuous random variable?
1041. there are an infinite number of normal curves
2. The highest point is over the mean (also median and mode)
3. The curve is symmetrical abut its mean
4. The tails of the curve extend to infinity in both directions
5. The area under the curve to the right of the mean equals the area under the curve to the left of the mean
what are the properties of a normal distribution
107the sampling distribution of the sample mean
the probability distribution of the population of the sample means obtainable from all possible samples of a size n from a population size N
108process of statistical inference
1. population with mean=?
2. A simple random sample of n elements is selected from the population
3. The sample data provide a value for the sample mean x-bar
4. the value of x-bar is used to make inferences about the value of the population mean
109Central Limit Theorem
The theory that
110when np ≥ 5 and n(1 − p) ≥ 5
how large of a sample size is large enough?
111A).2 (has to be between 0 and 1)
Which of the following is a valid probability value for a discrete random variable?
A) .2
B) 1.01
C) −.7
D) All of the choices are correct.
112.1112
Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Let X be a randomly selected finishing time. Find P (X > 72)
113E) np ≥ 5 and n(1 − p) ≥ 5.
The population of all sample proportions has a normal distribution if the sample size (n) is sufficiently large. The rule of thumb for ensuring that n is sufficiently large is ____________.
A) np ≥ 5.
B) n(1 − p) ≥ 5.
C) np ≤ 5.
D) n(1 − p) ≤ 5 and np ≤ 5.
E) np ≥ 5 and n(1 − p) ≥ 5.
114B) means
The Central Limit Theorem states that as the sample size increases
115D) The Central Limit Theorem
________ says that if the sample size is sufficiently large
116μx=50
A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μx?