Transcript Peanut Butter Taster’s Choice Test

Peanut Butter Taster’s
Choice Test
Which is the better quality
Peanut Butter?
Rate Brand A and B on a
scale of 1-10 with
1 being “I really hate this”
and 10 being “I Love it.”
Peanut Butter Taster’s
Choice Test
Which is the better quality
Peanut Butter?
 Who might be interested in the
results of this study?
 What interesting questions about
peanut butter can be answered
with these data?
 What interesting questions about
peanut butter can’t be answered
with these data?
Samples and Populations
Problem 1.1
• Compute the measures of center
(mean and median) and the spread
(range) of the quality ratings for the
natural brands and the regular
brands.
• Display the same data using a double
stem-and-leaf plot and histograms.
• What were your findings?
Samples and Populations
Problem 1.1 Follow-up
• The median and mean provide two
ways to summarize data. Which is
most stable?
• What conclusions can be made if the
mean is greater that the median?
• What conclusions can be made if the
mean is less than the median?
Box-and-Whisker Plots
• DEFINITION
“A representation of the distribution of
values in a data set.”
• CONSTRUCTION
“It is constructed from the five number
summary of the data.”
Five Number Summary
•
•
•
•
Minimum Value
Maximum Value
Median
Lower Quartile – the median of the
data values below the median
• Upper Quartile – the median of the
data values above the median
Five Number Summary
Lower Quartile
Minimum
Upper Quartile
Median
Maximum
Samples and Populations
Problem 1.2
Complete
Problem 1.2
on page 9
of
Samples and Populations.
Problem 1.3
Comparing Prices
Many people consider both
quality and prices when
deciding which products or
brands to buy.
Problem 1.3 Follow Up
• About what percent of the data are in the box
of a box plot? That is, what percent are
between the upper and lower quartile?
• About what percent of the data are in the
interval from the minimum value to the upper
quartile?
• About what percent of the data are in the
interval from the lower quartile to the
maximum value?
Problem 1.5 Follow-Up
Some people are
concerned about the
sodium content of the
foods they eat. People
with heart and bloodpressure problems are
often put on low-
sodium diets.
Scatter Plot
Problem 2.1
Conducting Surveys
• Americans spend 44% of their food budget on
meals prepared away from home.
• Of all restaurant orders, 49% are for offpremises consumption.
• More than 2 million American youths, most of
them girls, participate in competitive
gymnastics.
• On Tuesday, July 30, 1996, more than 45
million American households watched
evening broadcasts of the Atlanta Olympic
Games.
Problem 2.1 Conducting Surveys
• POPULATION
“The entire collection of people or objects under
study.”
• SAMPLE
“A group of people or objects selected from a
population. You can study a large population by
collecting data from a sample. You can make
predictions or draw conclusions about the entire
population based on data from the sample.”
• REPRESENTATIVE SAMPLE
“A sample that accurately represents a population.”
Problem 2.2 Selecting a Sample
Suppose you are doing a research project on the
lives of students at your school and would like to
answer these questions.
• How many hours of sleep do students get each
night?
• How many students eat breakfast in the morning?
• How many hours of television do students watch in a
week?
• How many soft drinks do students consume in a
day?
• How many students wear braces on their teeth?
• Convenience Sampling
“choosing a sample based on
the availability of respondents.”
Terms
• Systemic Sampling
“choosing a sample by using a methodical
technique.”
• Voluntary-Response Sampling
“asking people to choose to participate.”
• Random Sampling
“giving every member of a population an
equally likely chance of being selected.”
• Biased Samples
“samples that give misleading impressions.”
• Convenience Sampling
“choosing a sample based on
the availability of respondents.”
Terms
• Systemic Sampling
“choosing a sample by using a methodical
technique.”
• Voluntary-Response Sampling
“asking people to choose to participate.”
• Random Sampling
“giving every member of a population an
equally likely chance of being selected.”
• Biased Samples
“samples that give misleading impressions.”
Random Samples
• Andy overheard the
conversation among his
toys concerning who was
his favorite toy.
• So, he decided to play
with a different toy each
day.
• How could he randomly
select a toy for each day?
Random Samples
How could he randomly select a toy for each day?
TA-4-3
Random Samples
Problem 3.2
Selecting a Random Sample
Instead of working with the entire set of
data, you can select a random sample of
students. You can look for patterns in
the data for the sample and then use your
findings to make predictions about the
populations.
What methods might you use to select a
random sample of students?
Selecting a Random Sample
Instead of working with the entire set of
data, you can select a random sample of
students. You can look for patterns in
the data for the sample and then use your
findings to make predictions about the
populations.
How many students would you need in your
sample in order to make accurate estimates of
the typical number of hours of sleep and the
typical number of movies watched for the
entire population of 100 students?
Selecting a Random Sample
You can use two spinners like these:
You can roll two 10-sided cubes like these:
Problem 4.1 Archaeological Mystery
Archaeologists study
past civilizations by
excavating ancient
settlements and
examining the artifacts
of the people who lived
there.
Archaeological Mystery
On digs in southeastern
Montana and northcentral Wyoming,
archaeologists
discovered the remains
of two Native
American settlements.
Archaeological Mystery
They unearthed a
number of arrowheads
at both sites. They
hoped to use the
arrowhead data to
estimate the time
period during which
each site was
inhabited.