Data About Us
Looking Back Answers
1. Possible answers: Do you have any
pets? How many pets do you have?
word answers that name pets go
with What is your favorite kind of
pet? Possible explanation: This is
because the words describe types
of pets and the numbers describe
amounts of pets.
b. The word answers that name pets
are categorical data.
c. The numbers are numerical data.
d. (See Figures 1 and 2.)
2. Do you have any pets? is categorical.
How many pets do you have? is
numerical.
3. Possible answer: the heads of
households in the United States
4. Possible answers: pet breeders,
veterinarians, pet-store owners
5. a. The numbers go with the question
How many pets do you have? The
Figure 1
Figure 2
Number of Pets
Favorite Pets
1
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Data About Us
Looking Back Answers
(continued)
9. Brilliant Candle: mean 58 minutes;
MAD = 2.4 minutes
Firelight Candle: mean 58 minutes;
MAD ~ 5.067 minutes
Shimmering Candle: mean 58 minutes;
MAD ~ 4.933 minutes
To find the mean, add all the data
values together, then divide that sum by
the number of data values. In this case,
there were 15 trials, so the number of
data values is 15. To find the MAD, find
the difference of each data value and
the mean. Add these differences up,
then divide that sum by the number of
data values.
6. Possible answer: Frequency tables
and bar graphs can be used to display
categorical data. These types of graphs
only have one axis with numbers (the
frequency, or counts). This numbered
axis does not show the numerical
data values, but it instead shows the
occurrences of data values. The other
axis can have labels that are word
values rather than numerical values.
7. Line plots, dot plots, frequency tables,
bar graphs, ordered-value bar graphs,
histograms, and box-and-whisker plots
can be used to display numerical data.
All of these graph types allow for axes to
be labeled with a number line. So all of
them can handle numerical data.
8. Brilliant Candle: median 58 minutes;
IQR = 4 minutes
Firelight Candle: median 59 minutes;
IQR = 13 minutes
Shimmering Candle: median 59 minutes;
IQR = 9 minutes
Possible explanation: You find the
median by listing all data values in
order from least to greatest (or greatest
to least). Then, find the data value with
the middle position; the median has this
value. If there are two data values that
occupy the middle position, then find the
mean of those two data values. To find
the IQR, find Quartile 1 and Quartile 3.
You can find Quartile 1 by finding the
median of the data values less than the
whole data set’s median. You can find
Quartile 3 by finding the median of the
data values greater than the whole data
set’s median. The IQR is the difference of
Quartile 3 and Quartile 1.
10. Brilliant Candle is represented by Dot
Plot A, Histogram E, and Box Plot H;
Firelight Candle is represented by Dot
Plot C, Histogram F, and Box Plot G.
Note that Labsheet: Looking Back—
9 Graphs contains the dot plot,
histogram, and box plot for Shimmering
Candle as well. Shimmering Candle is
represented by Dot Plot B, Histogram D,
and Box Plot I.
11. The means for the three types of
candles are the same: 58 minutes. The
medians for two of the three candles are
59 minutes and, for the third (Brilliant),
58 minutes. There is not really any
difference in terms of magnitude of
values for any of the three types of
candles. However, Brilliant Candle,
based on its IQR and MAD, burns much
more consistently than the other two
types of candles. The consistency of
Brilliant Candle indicates that those
candles may burn the longest. The
Shimmering Candles and Firelight
Candles show more variability, since
they have greater MADs and IQRs.
2
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Data About Us
Looking Back Answers
(continued)
So, there are candles of that type that
may burn longer, but there are also
candles of that type that may burn for
a much shorter amount of time. Note
that Firelight Candle is slightly more
inconsistent than Shimmering Candle.
Firelight Candle has a slightly greater
MAD and a slightly greater IQR.
3
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