Statistics
Assignment 1
Example Problems
Types of Data
• Question: Determine whether the given value is
a statistic or a parameter.
– In a study of all 1904 seniors at college, it is found that
25% own a television.
• Answer: Know your definitions!
– A statistic is a numerical measurement describing
some characteristic of a sample
– A parameter is a numerical measurement describing
some characteristic of a population
Types of Data
• Question: Determine whether the given value
is a statistic or a parameter.
– In a study of all 1904 seniors at college, it is found
that 25% own a television.
• Answer: A parameter is a numerical
measurement describing some characteristic
of a population
Types of Data
• Question: Determine whether the value given
below is from a discrete or continuous data set.
– The volume of cola in a can is 10.4 oz.
• Answer: Know your definitions!
– Discrete data result when the number of possible
values is either a finite number or a “countable”
number (e.g. 0, 1, 2, …)
– Continuous data result from infinitely many possible
values that correspond to some continuous scale that
covers a range of values without gaps, interruptions,
or jumps.
Types of Data
• Question: Determine whether the value given
below is from a discrete or continuous data set.
– The volume of cola in a can is 10.4 oz.
• Answer: Continuous data result from infinitely
many possible values that correspond to some
continuous scale that covers a range of values
without gaps, interruptions, or jumps.
Types of Data
• Objective: Identify sample and population;
determine whether a sample is a representative
of a population
• Question:
– Some people responded to this request: “Dial 1-900PRO-LIFE to participate in a telephone poll on
abortion. ($4.95 per minute. Average call: 3 minutes.
You must be 17 years old.)”
– Identify the sample and population as well as
determine whether the sample is likely to be
representative of the population
Types of Data
• Question:
– Some people responded to this request: “Dial 1900-PRO-LIFE to participate in a telephone poll on
abortion. ($4.95 per minute. Average call: 3
minutes. You must be 17 years old.)”
• Answer: The sample would be all the
individuals that actually responded.
Types of Data
• Question:
– Some people responded to this request: “Dial 1900-PRO-LIFE to participate in a telephone poll on
abortion. ($4.95 per minute. Average call: 3
minutes. You must be 17 years old.)”
• Answer: The population would be all
individuals who are at least 17 years of age.
Types of Data
• Question:
– Some people responded to this request: “Dial 1900-PRO-LIFE to participate in a telephone poll on
abortion. ($4.95 per minute. Average call: 3
minutes. You must be 17 years old.)”
• Answer: No, the sample is not likely to be
representative of the population because
those with strong opinions about abortion are
more likely to respond.
Collecting Sample Data
• Objective: Identify types of sampling used.
• Question: Identify which type of sampling is
used: random, systematic, convenience,
stratified, or cluster.
– To determine her heart rate, Britney divides up her
day into three parts: morning, afternoon, and
evening. She then measures her heart rate at 4
randomly selected times during each part of the day.
– Which type of sampling is used?
Collecting Sample Data
• To determine her heart rate, Britney divides up her day into
three parts: morning, afternoon, and evening. She then
measures her heart rate at 4 randomly selected times
during each part of the day. Which type of sampling is
used?
• Answer: Well I know I can rule out Random (equal chance
of being selected), Convenience (easy to obtain) and
Systematic (every kth element) because she “divides up her
day into parts”. So the question is “Is this Stratified or
Cluster”?
– Remember that Stratified sampling the subgroups have the
same characteristics. Cluster sampling the subgroups are just
“divided”. What is common is doing the same thing in each sub
group (measuring heart rate), and thus would be Stratified.