Transcript Describe a Distribution Using a Histogram

Five-Minute Check (over Lesson 11–1)
CCSS
Then/Now
New Vocabulary
Key Concept: Symmetric and Skewed Distributions
Example 1: Real-World Example: Describe a Distribution
Using a Histogram
Key Concept: Box-and-Whisker Plots as Distributions
Example 2: Describe a Distribution Using a Box-andWhisker Plot
Example 3: Compare Data Using Histograms
Example 4: Compare Data Using Box-and-Whisker Plots
Over Lesson 11–1
Determine whether the situation calls for a survey, an
experiment, or an observational study. Explain your
reasoning.
MOVIES A production studio played a movie for a test
audience and watched their reactions.
A. Survey; members of the sample are observed and
asked their opinions.
B. Experiment; members of the sample are observed
and affected by the study.
C. Observational study; members of the sample are
observed and unaffected by the study.
D. Experiment; members of the sample are treated
and affected by the study.
Over Lesson 11–1
Determine whether the situation calls for a survey, an
experiment, or an observational study. Explain your
reasoning.
AUTHORS At a library, every 10th person is asked
some questions about their favorite author.
A. Survey; members of the sample are observed and
unaffected by the study.
B. Survey; members of the sample are asked for their
opinions.
C. Observational study; members of the sample are
observed and unaffected by the study.
D. Experiment; members of the sample are treated and
affected by the study.
Over Lesson 11–1
Determine whether the survey question is biased or
unbiased. If biased, explain your reasoning.
Shouldn’t Megan Fox win the Best Actress award
this year?
A. Biased; the question is confusing and wordy.
B. Biased; the question causes a strong reaction.
C. Biased; the question encourages a certain
response.
D. unbiased
Over Lesson 11–1
Determine whether the survey question is biased or
unbiased. If biased, explain your reasoning.
How many siblings do you have?
A. Biased; the question is confusing and wordy.
B. Biased; the question causes a strong reaction.
C. Biased; the question encourages a certain
response.
D. unbiased
Over Lesson 11–1
MANAGERS A manager of a company wants to
determine if her employees would prefer to work
four 10-hour days as opposed to five 8-hour days
each week. State the objective of the survey,
suggest a population, and write two unbiased
survey questions.
Over Lesson 11–1
A.
objective: to determine the work preferences of the employees;
population: all employees; sample survey questions: Are you
satisfied with working five 8-hour days each week? Would you
be willing to try to work four 10-hour days?
B.
objective: to determine the work preferences of the employees;
population: the employees who responded to the survey;
sample survey questions: Are you satisfied with working five 8hour days each week? Would you be willing to try to work four
10-hour days?
C.
objective: to determine the work preferences of the employees;
population: the employees who want to work four 10-hour days;
sample survey questions: Are you satisfied with working five 8hour days each week? Would you be willing to try to work four
10-hour days?
D.
objective: to determine the work preferences of the employees;
population: the sample; sample survey questions: Are you
satisfied with working five 8-hour days each week? Would
you be willing to try to work four 10-hour days?
Content Standards
S.IC.1 Understand statistics as a process for
making inferences about population
parameters based on a random sample from
that population.
Mathematical Practices
1 Make sense of problems and persevere in
solving them.
You calculated measures of central tendency
and variation.
• Use the shapes of distributions to select
appropriate statistics.
• Use the shapes of distributions to compare
data.
• distribution
• negatively skewed distribution
• symmetric distribution
• positively skewed distribution
Describe a Distribution Using a
Histogram
PRESENTATIONS Ms. Shroyer’s students each
gave a presentation as part of their class project.
The length of each presentation is shown in the
table.
A. Use a graphing calculator to create a histogram.
Then describe the shape of the distribution.
Describe a Distribution Using a
Histogram
First, press
and enter each data
value. Then, press
[STAT PLOT]
and choose „. Finally, adjust the window to the
dimensions shown.
Answer: The majority of the data are on the right side of
the distribution, so the distribution is negatively
skewed.
Describe a Distribution Using a
Histogram
PRESENTATIONS Ms. Shroyer’s students each
gave a presentation as part of their class project.
The length of each presentation is shown in the
table.
B. Describe the center and spread of the data
using either the mean and standard deviation or the
five-number summary. Justify your choice.
Describe a Distribution Using a
Histogram
The distribution is skewed, so use the five-number
summary to describe the center and spread. Press
and scroll down to view
the five-number summary. The range is 7 to 23
minutes. The median is 17 minutes, and half of the
times are between 13 and 19.5 minutes.
Answer: The range is 7 to 23 minutes. The median is
17 minutes, and half of the times are between
13 and 19.5 minutes.
PRICING Eddie looked up prices for
floor speakers for his basement. The
prices are shown in the table. Describe
the center and spread of the data
using either the mean and standard
deviation or the five-number summary.
Justify your choice.
A.
mean: 134.75, standard deviation: 30.3; skewed
distribution
B.
median: 137, range: 70 to 195, half of the data between
117.5 and 149.5; skewed distribution
C.
mean: 134.75, standard deviation: 30.3; symmetric
distribution
D.
median: 137, range: 70 to 195, half of the data between
117.5 and 149.5; symmetric distribution
Describe a Distribution Using a Box-andWhisker Plot
A. WAGES The hourly wages for a random sample
of employees of a restaurant are shown in the table.
Use a graphing calculator to create a box-andwhisker plot. Then describe the shape of the
distribution.
Describe a Distribution Using a Box-andWhisker Plot
Enter the data as L1. Press
[STAT PLOT]
and choose fl. Adjust the window to
the dimensions shown.
Answer: The right whisker is longer than the other and
the median is to the left of the center, so the
distribution is positively skewed.
Describe a Distribution Using a Box-andWhisker Plot
B. WAGES The hourly wages
for a random sample of
employees of a restaurant are
shown in the table. Describe
the center and spread of the
data using either the mean
and standard deviation or the
five-number summary. Justify
your choice.
Answer: The distribution is skewed, so use the fivenumber summary. The range is $6.50 to
$11.25. The median is about $7.88, and half of
the data are between $7.25 and $9.00.
EXPERIENCE The number of years of playing experience for
each player on an over 30 recreational soccer team are shown
in the table. Describe the center and spread of the data using
either the mean and standard deviation or the five-number
summary. Justify your choice.
A.
mean: 4.1, standard deviation: 3.5; skewed distribution
B.
median: 3, range: 0 to 12, half of the data between 1 and 7;
skewed distribution
C.
mean: 4.1, standard deviation: 3.5; symmetric distribution
D.
median: 3, range: 0 to 12, half of the data between 1 and 7;
symmetric distribution
Compare Data Using Histograms
A. GAMES Tyler and Jordan
are working through several
brainteasers on the
computer. The time in
minutes that it took to
complete each game is
shown. Use a graphing
calculator to create a
histogram for each data set.
Then describe the shape of
each distribution.
Compare Data Using Histograms
Answer: Tyler, positively skewed; Jordan, symmetric
Compare Data Using Histograms
B. GAMES Tyler and Jordan
are working through several
brainteasers on the
computer. The time in
minutes that it took to
complete each game is
shown. Compare the
distributions using either
the means and standard
deviations or the fivenumber summaries. Justify
your choice.
Compare Data Using Histograms
Answer: Sample answer: One distribution is
symmetric and the other is skewed, so use
the five-number summaries. The median for
both sets is 4.35 but 50% of Tyler’s times
occur between 3.45 and 5.15, while 50% of
Jordan’s times occur between 3.75 and 5.4.
The smaller interquartile range for Jordan
may suggest that she was slightly more
consistent than Tyler.
GAMES Mr. Cline’s 1st and 2nd Period
classes tracked the amount of time per
week they spent on their favorite Web site.
The times in minutes are shown. Compare
the distributions using either the means
and standard deviations or the five-number
summaries. Justify your choice.
A.
2nd Period had a slightly higher median and the ranges
were almost the same. The distributions are very similar.
B.
2nd Period had a higher mean and greater deviation. 1st
Period is a little more consistent.
C.
2nd Period had a higher mean and greater deviation. 2nd
Period is a little more consistent.
D.
2nd Period had a slightly higher median and the ranges
were almost the same. 2nd Period is a little more
consistent.
Compare Data Using Box-and-Whisker Plots
A. TEMPERATURES The
daily high temperatures
over a 20-day period for
two cities are shown. Use
a graphing calculator to
create a box-and-whisker
plot for each data set.
Then describe the shape
of each distribution.
Compare Data Using Box-and-Whisker Plots
Enter the Clintonville temperatures as L1. Graph these
data as Plot1 by pressing
[STAT PLOT] ENTER
ENTER and choosing fl. Enter the Stockton
temperatures as L2. Graph these data as Plot2 by
pressing 2ND [STAT PLOT] ▼ ENTER ENTER and
choosing fl. For Xlist, enter L2. Adjust the window to
the dimensions shown.
Answer: Both distributions are symmetric.
Compare Data Using Box-and-Whisker Plots
B. TEMPERATURES The
daily high temperatures
over a 20-day period for
two cities are shown.
Compare the distributions
using either the means and
standard deviations or the
five-number summaries.
Justify your choice.
Compare Data Using Box-and-Whisker Plots
Answer: The distributions are symmetric, so use
the means and standard deviations. The
mean temperature for Clintonville is about
63.15° with standard deviation of about
5.40°. The mean temperature for
Stockton is about 63.05° with standard
deviation of about 1.76°. The average
temperatures for both cities are about the
same, but the lower standard deviation
for Stockton means that the temperatures
there are more consistently near 63° than
at Clintonville.
SUMMER CAMP The number of participants
for two sports at a summer camp for the
past 15 sessions is shown. Compare the
distributions using either the means and
standard deviations or the five-number
summaries. Justify your choice.
A.
B.
C.
D.
The mean number for baseball was
almost twice the mean for soccer. The distributions are
skewed.
The standard deviation of the number for baseball was
almost three times the standard deviation for soccer. The
distributions are symmetric.
The median number for baseball was 23 more than the
median for soccer. The distributions are skewed.
The median number for baseball was 23 more than the
median for soccer. The distributions are
symmetric.