NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
Name
6•6
Date
1. A group of students were asked how many states they have visited in their lifetime. Below is a dot plot of
their responses.
a.
How many observations are in this data set?
b.
In a few sentences, summarize this distribution in terms of shape, center, and variability.
c.
Based on the dot plot above and without doing any calculations, circle the best response below, and
then explain your reasoning.
A. I expect the mean to be larger than the median.
B. I expect the median to be larger than the mean.
C. The mean and median should be similar.
Explain:
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
d.
To summarize the variability of this distribution, would you recommend reporting the interquartile
range or the mean absolute deviation? Explain your choice.
e.
Suppose everyone in the original data set visits one new state over summer vacation. Without doing
any calculations, describe how the following values would change (i.e., larger by, smaller by, no
change—be specific).
Mean:
Median:
Mean Absolute Deviation:
Interquartile Range:
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
2. Diabetes is a disease that occurs in both young and old people. The histogram and box plot below display
the ages at which 548 people with diabetes first found out that they had this disease.
The American Diabetes Association has identified two types of diabetes:


a.
Type 1 diabetes is when the body does not produce insulin. Type 1 diabetes is usually first found
in children and young adults (less than 20 years of age).
Type 2 diabetes is when the body does not produce enough insulin and the cells do not respond
to insulin. Type 2 diabetes is usually first found in older adults (50 years of age or older).
Explain how the histogram shows the two types of diabetes.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
b.
Estimate the percentage of these 548 people who found out they had the disease before age 20.
Explain how you made your estimate.
c.
Suggest a statistical question that the box plot of the age data would allow you to answer more
quickly than the histogram would.
d.
The interquartile range for these data is reported to be 24. Write a sentence interpreting this value
in the context of this study.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
3. The following table lists the diameters (in miles) of the original nine planets.
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
a.
Diameter
(in miles)
3,030
7,520
7,926
4,217
88,838
74,896
31,762
30,774
1,428
Calculate the five-number summary (minimum, lower quartile, median, upper quartile, and
maximum) of the planet diameters. Be sure to include measurement units with each value.
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
b.
Calculate the interquartile range (IQR) for the planet diameters.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
c.
Draw a box plot of the planet diameters.
d.
Would you classify the distribution of planet diameters as roughly symmetric or skewed? Explain.
e.
Pluto was recently reclassified as a dwarf plant because it is too small to clear other objects out of its
path. The mean diameter with all nine planets is 27,821 miles, and the MAD is 25,552 miles. Use
this information to argue whether or not Pluto is substantially smaller than the remaining eight
planets.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
A Progression Toward Mastery
Assessment
Task Item
1
a
6.SP.B.5a
b
6.SP.A.2
c
6.SP.B.5d
STEP 1
Missing or incorrect
answer and little
evidence of
reasoning or
application of
mathematics to
solve the problem.
STEP 2
Missing or incorrect
answer but
evidence of some
reasoning or
application of
mathematics to
solve the problem.
STEP 3
A correct answer
with some
evidence of
reasoning or
application of
mathematics to
solve the problem
OR an incorrect
answer with
substantial
evidence of solid
reasoning or
application of
mathematics to
solve the problem.
STEP 4
A correct answer
supported by
substantial
evidence of solid
reasoning or
application of
mathematics to
solve the problem.
Student does not use
information in the dot
plot.
Student counts 15
unique outcomes for the
number of states.
Student counts 33 or 35
dots.
Student correctly counts
34 dots.
Student does not use
information in the dot
plot.
Student provides
descriptions that are not
consistent with the
graph.
Student only addresses
two of the main
components of shape,
center, and variability.
Student gives a
complete description of
each component. For
example, “The
distribution is skewed
indicating many
students visiting around
5 states, but another
cluster indicates some
students visiting around
12 states. Almost all of
the students have
visited fewer than 15
states, but one outlier
has visited more than
35.”
Student only circles an
incorrect response and
does not provide
justification.
Student circles A but
does not justify the
choice or circles B or C,
but the justification is
inconsistent. For
example, “The median
should be larger
because there are some
students who have
visited a lot of states.”
Student circles A, but
the justification is
incomplete or
inconsistent. For
example, “The mean will
be larger because most
of the data are between
0 and 10.”
Student circles A and
comments on how the
skewness and/or
outliers will pull the
value of the mean to the
right of the value of the
median.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
d
6.SP.B.5d
e
6.SP.A.3
2
a
6.SP.A.2
b
6.SP.B.5a
c
6.SP.A.1
d
6.SP.A.3
3
a
6.SP.B.5
End-of-Module Assessment Task
6•6
Student does not
address the choice of
the measure of
variability.
Student makes a choice
but does not justify the
response.
Student makes a choice,
but the justification is
inconsistent (e.g., the
MAD because of the
outlier).
Student chooses the
interquartile range
because of the presence
of skewness and/or
outliers.
Student only indicates
that there is not enough
information to answer
the question.
Student only addresses
two of the four
measures.
Student answers are not
completely consistent
with the mean and
median measuring the
center and the MAD and
IQR measuring the
spread.
Student correctly
answers that the mean
and median increase by
one because everyone
shifts the same amount.
The MAD and IQR stay
the same because
everyone shifts the
same amount.
Student does not utilize
information from the
histogram.
Student discusses the
ages and the
recommendation but
does not connect to the
histogram.
Student discusses
observations below age
20 and above age 20
but does not address
the distinctness of the
two clumps of values
around age 20.
Student focuses on the
two clumps, with the
valley between the
clumps around the cited
20 years of age.
Student makes no use of
the distribution (e.g.,
Student uses the box
plot and assumes half of
the 25% below 40 years
of age are below 20
years of age.
Student uses the
histogram but makes a
minor calculation error.
The result is still
consistent with the
graph (e.g., below 20%).
Student uses the
histogram and finds
Student fails to
distinguish between the
box plot and the
histogram.
Student suggests a
feature of the box plot
but does not relate to a
statistical question. For
example, “How many
people have diabetes?”
Student suggests a
feature of the box plot,
but the statistical
question is vague or
incomplete. For
example, “Where are
most of the ages?”
Student suggests a
statistical question that
relates to the quartiles
or median. For
example, “What is the
median age at
diagnosis?”
Student only attempts
to explain how the IQR
is calculated and does so
incorrectly.
Student does not
interpret the IQR as a
measure of the spread.
For example, “Most
people are diagnosed
around 24 years.”
Student addresses the
IQR as a measure of the
spread but does not
provide an
interpretation in
context. For example,
“𝑄3 − 𝑄1.”
Student correctly
answers that the width
of the middle 50% of
the diagnosed ages is
24 years.
Student is not able to
identify information
correctly from the table.
Student does not sort
the observations before
making computations:
3,030, 77,23, 88,838,
31,268, and 1,428
miles.
Student sorts the data
but performs minor
calculation errors or
only correctly finds 3 of
the values.
Student sorts the data
correctly: 1,428,
3,623.5, 7,926, 53,329,
and 88,838 miles.
20
90
).
Module 6:
Statistics
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16+17+9+13
≈ 0.10,
548
or about 10%.
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NYS COMMON CORE MATHEMATICS CURRICULUM
b
Student calculates
𝑄3 − 𝑄2 or 𝑄2 − 𝑄1 or
reports a negative value.
Student reports correct
values from part (a), but
as a range, and does not
calculate the difference
in the values.
Student uses 𝑄3 − 𝑄1
using the values from
part (a).
Student does not
construct a graph.
Student constructs a dot
plot or histogram.
Student constructs and
scales a graph, but the
graph does not match
the values reported in
part (a).
Student correctly
constructs and scales a
graph using the values
from part (a).
Student does not justify
the choice.
Student gives a
reasonable response,
but it is not based on a
graph of the data or on
the quartiles. For
example, “A few planets
are really large, so the
data are skewed.”
Student refers to the
box plot and/or
quartiles but draws an
inconsistent conclusion
(e.g., describes the
correct box plot as
symmetric or judges the
distance between the
quartiles as similar
because the values are
so large).
Student uses the box
plot and judges the
relative widths of the
segments to answer the
question.
Student only uses the
context and does not
use the mean and MAD
values.
Student compares
Pluto’s diameter to the
mean without
considering the MAD.
Student answers
generically but does not
relate to Pluto’s value
explicitly. For example,
“Not all observations
will fall within one MAD
from the mean.”
Student uses the
difference between the
mean and the MAD to
determine that Pluto’s
diameter is just over one
MAD away from the
mean; thus, Pluto is not
much smaller.
6.SP.B.4
d
6.SP.A.2
e
6.SP.B.5
6•6
Student does not
perform a calculation.
6.SP.B.5c
c
End-of-Module Assessment Task
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
Name
6•6
Date
1. A group of students were asked how many states they have visited in their lifetime. Below is a dot plot of
their responses.
a.
How many observations are in this data set?
b.
In a few sentences, summarize this distribution in terms of shape, center, and variability.
c.
Based on the dot plot above and without doing any calculations, circle the best response below, and
then explain your reasoning.
A. I expect the mean to be larger than the median.
B. I expect the median to be larger than the mean.
C. The mean and median should be similar.
Explain:
Module 6:
Statistics
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This file derived from G6-M6-TE-1.3.0-10.2015
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
d.
To summarize the variability of this distribution, would you recommend reporting the interquartile
range or the mean absolute deviation? Explain your choice.
e.
Suppose everyone in the original data set visits one new state over summer vacation. Without doing
any calculations, describe how the following values would change (i.e., larger by, smaller by, no
change—be specific).
Mean:
Median:
Mean Absolute Deviation:
Interquartile Range:
Module 6:
Statistics
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This file derived from G6-M6-TE-1.3.0-10.2015
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
2. Diabetes is a disease that occurs in both young and old people. The histogram and box plot below display
the ages at which 548 people with diabetes first found out that they had this disease.
The American Diabetes Association has identified two types of diabetes:


a.
Type 1 diabetes is when the body does not produce insulin. Type 1 diabetes is usually first found
in children and young adults (less than 20 years of age).
Type 2 diabetes is when the body does not produce enough insulin and the cells do not respond
to insulin. Type 2 diabetes is usually first found in older adults (50 years of age or older).
Explain how the histogram shows the two types of diabetes.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
b.
Estimate the percentage of these 548 people who found out they had the disease before age 20.
Explain how you made your estimate.
c.
Suggest a statistical question that the box plot of the age data would allow you to answer more
quickly than the histogram would.
d.
The interquartile range for these data is reported to be 24. Write a sentence interpreting this value
in the context of this study.
Module 6:
Statistics
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This file derived from G6-M6-TE-1.3.0-10.2015
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
3. The following table lists the diameters (in miles) of the original nine planets.
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
a.
Diameter
(in miles)
3,030
7,520
7,926
4,217
88,838
74,896
31,762
30,774
1,428
Calculate the five-number summary (minimum, lower quartile, median, upper quartile, and
maximum) of the planet diameters. Be sure to include measurement units with each value.
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
b.
Calculate the interquartile range (IQR) for the planet diameters.
Module 6:
Statistics
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NYS COMMON CORE MATHEMATICS CURRICULUM
End-of-Module Assessment Task
6•6
c.
Draw a box plot of the planet diameters.
d.
Would you classify the distribution of planet diameters as roughly symmetric or skewed? Explain.
e.
Pluto was recently reclassified as a dwarf plant because it is too small to clear other objects out of its
path. The mean diameter with all nine planets is 27,821 miles, and the MAD is 25,552 miles. Use
this information to argue whether or not Pluto is substantially smaller than the remaining eight
planets.
Module 6:
Statistics
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This file derived from G6-M6-TE-1.3.0-10.2015
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This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.