STATISTICS
(MID-CHAPTER REVIEW)
PART I: SAMPLING TECHNIQUES
population:
all individuals or items that belong to a group
being studied (the target group)
sample:
a group of individuals or items that are representative
of the population from which they are taken
Ex 1:
Each student in the MBF class is surveyed as to their favourite
snack so the cafeteria knows which snacks they should sell.
population:
sample:
Match each definition to the type of sampling technique.
Ex 2:
____ simple random sample
A. the population is divided into clusters and
every member of certain clusters respond
____ stratified random sample
B. every nth member of the population is selected
____ voluntary–response sample
C. each member of the population has an equal
chance of being selected
____ cluster sample
D. the sample contains members of the
population who have chosen to respond
____ convenience sample
E. the population is divided into subgroups and a
random sample is selected from each subgroup
in proportion to its size in the population
____ systematic sample
F. the sample contains those members of the
population from which data is easily collected
Ex 3:
Choose the best sampling technique for each survey.
a)
b)
c)
Unit 8
A bolt manufacturer wants to determine the average
length of bolt being made by a machine.
________________
The president of a company wants to know which of
two potential vice-presidents the employees prefer.
________________
A music store wants to know what type of music they
should stock for an upcoming sale.
________________
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PART II: COLLECTING AND ANALYZING DATA
primary source of data:
a person collects data for their
own use by surveying a sample
secondary source of data:
a data base or research collected
by someone else is used
ex. Internet, Statistics Canada
Ex 1:
Identify each as a primary or a secondary source of data.
a)
b)
bias:
Ex 2:
Ex 3:
Rachel has her friend Siobhan survey students at her
school about their musical preference.
________________
Monique asks students in her science class to suggest
the most important scientific discovery over the past
100 years.
________________
an intentional or unintentional distortion of the data collected in a survey
Match each description with the type of bias.
____ response bias
A. small sample size due to lack of response
____ measurement bias
B. a leading question affects the response
____ non-response bias
C. exaggerated or underestimated results
Identify the bias in each sample and suggest a way to remove it.
a)
A phone-in radio show asks callers their opinion about the city's baseball team
not making the playoffs the day after they are eliminated.
b)
To learn which team Canadians feel will win the Stanley Cup, researchers call
100 people from Ottawa.
c)
A radio talk show host asks listeners to phone in and express their opinions on a
rock band’s latest CD.
Unit 8
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PART III: DISPLAYING DATA
Ex 1:
continuous data:
data that can have any numerical value
within a finite or infinite interval
(a histogram or line graph may be used)
discrete data:
data that are distinct and can be counted
(a bar graph or circle graph may be used)
Classify each set of data as continuous or discrete.
a)
temperature measured throughout the day
________________
b)
the number of students in mathematics classes
in every high school in Ontario
________________
the volume of air in an average breath taken
by students in your science class
________________
c)
Ex 2:
Ex 3:
What type of graph would best represent the data in each case?
a)
how a school's art budget is spent
________________
b)
the time students take to eat lunch
________________
c)
the number of students in each grade
________________
d)
the change in gas price over time
________________
The histogram shows the distribution of shoe sizes of the grade 9 boys.
a)
How many boys were surveyed?
b)
How many boys have a shoe size of
10 or larger?
c)
What percent of these boys have a
shoe size of 10 or larger?
Unit 8
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PART IV: HOMEWORK QUESTIONS
1.
2.
3.
4.
Identify the population and the sample in each situation.
a)
All the dentists in the GTA are asked if they would recommend a
new toothpaste, so the manufacturer can indicate the percent of
dentists who recommend the product on the box.
b)
A new sandwich shop will open soon. The owners offer samples to people passing
by on a busy Saturday afternoon to help them decide on their final menu.
Choose the best sampling technique for each survey.
a)
Steve wants to know at which festivals his dance company would like to perform.
b)
Sherry wants to find out which Canadian actress is most popular with Ontario teens.
c)
Bruno wants to know which search engine is used most often by high school students.
Renee works as a quality control officer at a lumber yard. She selects every 200th
two-by-four that is cut and measures its dimensions.
a)
What type of sampling technique is she using?
b)
Why is it not practical to measure every two-by-four?
Identify each as a primary or a secondary source of data.
a)
b)
Ruis checks Statistics Canada to find out which Ontario provincial park is the largest.
Travis' survey indicated that almost 40% of his friends eat the same lunch every Monday.
5.
A popular television sports show asked people to phone in their pick for the NBA Most
Valuable Player. With 30 min left in the show, they announce the results to that point.
How might this announcement affect the outcome of the survey?
6.
Melissa asks five of her friends about their favourite type of movie. Four say their
favourite is comedy. She reports that 80% of teenagers prefer comedies over all other movie
types. Explain two flaws in her survey.
7.
Barney wants to know what the best-selling lunch item is in the cafeteria. He records
what he sees on the students’ trays as they leave the cafeteria during his lunch period. He
asks the cafeteria staff to keep track of the items they sell during the other lunch
periods. Which data are primary data? Which data are secondary data?
Unit 8
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8.
9.
10.
Identify the bias in each survey. Suggest how it might be removed.
a)
The student council surveys the students in the bleachers at a football game to
determine whether they feel the ticket proceeds should go to purchasing a new score
board or new calculators for the math club.
b)
A market research company mails surveys to 1000 households and 200 are returned.
c)
Shoppers at a mall are asked, “Are you against the poor decision made to close this mall
in order to build a subdivision, making the traffic in the area even more congested?”
Classify each set of data as either discrete or continuous.
a)
the number of blue cars in a parking lot
b)
the temperature outside at noon measured each day for a week
c)
the number of students taking math at OLMC
The results of a mathematics test are shown. Create a frequency table and histogram to represent
the data.
83, 54, 66, 27, 93, 91, 24, 63, 68, 71, 81, 75, 88, 54, 73,
70, 62, 48, 41, 73, 54, 77, 86, 81, 92, 67, 61, 58, 31, 89
ANSWERS:
1. a) population: all dentists in Ontario
b) population: all potential customers
sample: the dentists in the greater Toronto area
sample: people walking past the shop on Saturday
afternoon
2. a) voluntary-response sampling
b) stratified random sampling
c) convenience sampling or voluntary-response sampling
3. a) systematic sampling
b) too time consuming
4. a) secondary source
b) primary source
5. More people might call in than would have called before.
6. Her sample is too small and is made up of her friends who likely have similar tastes is movies.
7. Barney’s observations are primary data; the cafeteria staff’s observations are secondary data.
8. a) measurement bias
b) non-response bias
c) response bias
9. a) discrete
b) continuous
c) discrete
Unit 8
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