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Algebra 2
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2.2 + Review HW
1.
Given the data set : 41, 55, 48, 44 find the standard deviation “by hand.” Be sure to show your work.
2.
The mean diameter of a Purdy Goode Compact Disc is 12.0 cm, with a standard deviation of 0.012 cm. No CDs
can be shipped that are more than two standard deviations from the mean. What type of CD’s would not be
allowed to ship?
3.
The students in four classes recorded their resting
pulse rates in beats per minute. The class means
and standard deviations are given at the right.
4.
Class
Mean
First Period
Second Period
Fifth Period
Sixth Period
79.4
74.6
78.2
80.2
a.
Which class has students with pulse rates
most alike? How can you tell?
b.
Can you tell which class has the students with the fastest pulse rates? Why or why not?
Standard
Deviation
3.2
5.6
4.1
7.6
Your group built a catapult and launched tennis balls 20 times, trying to keep all the conditions the same for
each launch. The mean distance traveled was 23.5 m, with a standard deviation of 4.7 m. Would you be
surprised if the next launch was 35 m? Justify your answer using the standard deviation to support your answer.
5.
Members of the school mathematics club sold packages of hot chocolate mix to
raise funds for their club activities. The number of packages sold by individual member
are given at the right. (You may use a yellow calculator on this problem).
65
147
158
69
62
76
82
77
88
68
a.
Find the median and the interquartile range for this data set.
b.
Find the mean and the standard deviation.
c.
Draw a box and whisker plot for this data. Be sure to label any outliers.
d.
If you were to remove the outliers from the data set which do you think will be more affected:
e.
i.
The mean or the median? Justify your answer.
ii.
The Standard deviation or the IQR? Justify your answer.
100
94
62
80
71
67
92
85
63
73
44
79
71
75
74
Remove the outliers and recalculate your data from parts a and b. See if what you said in part d is true or not.
Review – Box and Whisker plots
The box-and-whisker plot below shows the distribution of tests scores in Mrs. Uebelhoer’s Algebra
2
class.
6. Determine the median of the box-and-whisker plot.
7. What percentage of students scored between 90 and 100?
8. What percentage of students scored between 70 and 90?
Joe interviewed the cross country team at his high school to find out how many miles per week they
run. The following list is the data Joe collected.
15, 25, 33, 47, 52, 35, 8, 55, 42, 29, 45, 54, 41, 37, 48, 56, 45, 40
9. Determine the 5-number summary of this data.
10. Make a box-and-whisker plot for the data set.
11. How many miles do the bottom 75% of runners run per week?
12. Use the 1.5 IQR rule to determine if there are outliers. Make sure you know what numbers represent the
fences too!
13. If there are outliers in Jim’s Data:
a.
How would the center (mean, median, mode), spread (IQR, standard deviation), and shape (symmetry),
change if there were not outliers?
If there are not outliers in Jim’s Data:
b.
How would the center (mean, median, mode), spread (IQR, standard deviation), and shape (symmetry),
change if there were outliers?
The parallel box-and-whisker plot below shows average monthly rainfall for Miami and New
Orleans.
14. a. Which city shows a greater range
in average monthly rainfall?
b. Explain how the parallel box-and-whisker
plot makes it easy to compare the ranges.
15. In Miami, what percentage of rainfall was between 60 and 216 millimeters?
16. In New Orleans, what percentage of rainfall was between 61 and 130 millimeters?
17.
For each of the box and whisker plots below tell if they are symmetrical, skewed left or skewed right. I have
included a description of the different kinds of skewedness for you.

If the distribution is normal, there are few exceptionally large or small values. The mean will be
about the same as the median, and the box plot will look symmetric.

If the distribution is skewed to the right most values are 'small', but there are a few exceptionally large
ones. Those exceptional values will impact the mean and pull it to the right, so that the mean will be
greater than the median. The box plot will look as if the box was shifted to the left so that the right tail
will be longer, and the median will be closer to the left line of the box in the box plot.

If the distribution is skewed to the left, most values are 'large', but there are a few exceptionally small
ones. Those exceptional values will impact the mean and pull it to the left, so that the mean will be less
than the median. The box plot will look as if the box was shifted to the right so that the left tail will be
longer, and the median will be closer to the right line of the box in the box plot.
As a quick way to remember skewedness:



longer tail on the left means skewed to the left means mean on the left of median (smaller)
longer tail on the right means skewed to the right means mean on the right of median (larger)
tails equally long means normal means mean about equal to median
18.
For each of the box and whisker plots below tell if they are symmetrical, skewed left or skewed right.
19. The box-and-whisker plot shows the number of hours students in Holly’s class spent volunteering last summer.
Which of the following would be the most accurate measures of central tendency for the data?
Volunteer Hours
44
46
48
50
52
54
56
58
60
62
64
66
68
a. the mean or mode
c. the mode or range
b. the mean or median
d. the median or range
Mrs. Hagan measured the height, in inches, of all the girls in her PE class. She recorded her results
in the following list.
63, 60, 67, 62, 58, 63, 68, 59, 62, 65, 56, 63, 59, 62, 58
20. Determine the 5-number summary and make a box-and-whisker plot for the data set.
21. Between what heights are the middle 50% of the girls in Mrs. Hagan’s PE class?
22. Use the 1.5 IQR rule to determine if there are outliers. Make sure you know what numbers represent the
fences too!
23. If there are outliers:
a.
How would the center (mean, median, mode), spread (range, standard deviation), and shape (symmetry),
change if there were not outliers?
If there are not outliers:
b.
How would the center (mean, median, mode), spread (range, standard deviation), and shape (symmetry),
change if there were outliers?