Name:______ANSWER KEY______________________
Honors Pre-Algebra
Date:_________________________________________
Unit 1 Assessment Review
1a.) Create a stem and leaf plot for the numbers below, then answer the corresponding questions:
23, 45, 66, 25, 61, 34, 36, 32, 43, 25
2
3
4
5
6
3 5 5
2 4 6
3 5
1b.) What is the mode of the data set?____25____
1 6
1c.) What is the median of the data set?____35____
1d.) What is the difference between the median and the mode?___10___
1e.) What is the mean of the data set? ___39___
Key: 4 2 = 42
2.
Create a data set that consists of 5 numbers and has the following properties:
Median: 15
Mode: 13
Mean: 15
__13___
3.
1f.) What is the difference between the mean and the median? ___4___
___13___
___15___
___16___
___18___
The distance, in feet, of each throw Hunter made in the discus is listed below:
108
113
124
130
145
196
What is Hunter’s median throw? __136___
What is Hunter’s mean throw?
__127___
Hunter threw the discus twice more. The mean of his throws stayed the same, but the median increased by 2 feet.
What were Hunter’s two throws?
____128___
___144____
4. Use the box-and-whisker plots below to answer the following questions:
a.) What is the difference between the interquartile ranges of the two box-and-whisker plots?___2____
b.) What is the difference between the ranges of the two box-and-whisker plots? ___2____
c.) What is the difference between the Medians of the two box-and-whisker plots? ___2____
d.) Which box-and- whisker plot has more variability? How do you know? Explain your answer
thoroughly and use specific data points to justify your answer.
The box-and-whisker plot with more variability is the one on the bottom, closest to the number line. Variability refers to how
far the numbers in a data set are from one another, or how much variety there is among the numbers. Therefore, the data
set that has the greater range and greater interquartile range is the one that has the most variability. The range of the
bottom box-and-whisker plot is 11, as opposed to only 9 for the top box-and-whisker plot. Furthermore, the interquartile
range of the bottom plot is 6, which is also 2 greater than that of the top box-and-whisker plot.
e.) Is there a lot of overlap between the two box-and-whisker plots (yes/no)?__yes__
Explain why you chose that answer.
There is a lot of overlap among the two box-and-whisker plots because the top box-and-whisker plot fits almost entirely
within the bottom box-and-whisker plot. Only the maximum (upper extreme) of the top box-and-whisker plot does not lie
within the range of the bottom box-and-whisker plot. This would indicate that the numbers in both data sets would be
similar, and therefore, have a significant amount of overlap.
If a dot plot was made to show all of the data from both box-and-whisker plots, would it look like one
data set or two data sets? ___one____
Explain how you know.
If a dot plot was created to show every number in both data sets of the box-and-whisker plots above, it would be difficult to
determine which dots went with which data set, because there is a lot of overlap between the two sets of numbers. Therefore,
the combined dot plot would appear as though it is only showing one set of data.
5.
A back-to-back stem-and-leaf plot shows how students did on the first two French tests taken in 7th grade.
Find the difference in the mean of each test (2 points).
Test 1
79 – 76 = 3
____3_____
Find the difference in the median of each test (2 points).
80 – 75 = 5
_____5_____
4
7 3 2
8 5 5
8 6
8
4
2
5
2
Test 2
8
6
0
2
3
2
4
5
6
7
8
9
7
1
0
3
0
9
4
3
3
1
8
6 6 7
4 7 9
4 8
10 0
Key: 4 8 2: 84, 82
6.
72 seventh grade students took a Math exam. The results of the exam are displayed in the histogram below.
#
of
S
t
u
d
e
n
t
s
24
20
16
12
8
4
40-49 50-59 60-69 70-79 80-89 90-100
Score Ranges
𝟏
a.) What fraction of students received between an 80-89%? _____𝟑_____
b.) Which interval has the highest frequency?____ 80-89%_____
c.) What percent of students received lower than an 80%?____50%______
d.) Based on these results, how many students out of the next 300 would you expect to score a 90% or higher?
__50 students__
e.) Based on these results, how many students out of the next 600 would you expect to score at least a 60%, but
lower than an 80%?
__250 students __
f.) Based on these results, how many students out of the next 600 would you expect to score lower than a 60%?
__50 students __
7.
Create a box-and-whisker plot for the following data set, and list all of the important data points on the blanks below:
78 74 88 84 82 76 82 88 77 70 71 77 82
Minimum:___70___
70 71 74 76 77 77 78 82 82 82 84 86 88
Maximum:__ 88___
75
83
Median:___ 78___
Lower Quartile:___ 75___
Upper Quartile:___ 83___
Interquartile Range: ___8____
70
72
74
76
78
80
82
84
86
88
8.
Find the mean and the mean absolute deviation of the data set below:
94
4
94
4
92
2
84
6
87
3
83
7
96
6
90
0
85
5
95
5
Mean:___90____
Mean Absolute Deviation:___ 4.2____
9.
Find the mean and the mean absolute deviation of the data set below:
71
3
74
0
73
1
77
3
77
3
76
2
73
1
71
3
Mean:___ 74____
Mean Absolute Deviation:___ 2____
10. Does the data set in Problem 8 or in Problem 9 have MORE variability? Give TWO reasons why you know this to be
true.
The data set in Problem 8 has more variability than the data set in Problem 9. Variability refers to how far the numbers in a data set are
from one another, or how much variety there is among the numbers. Therefore, the data set that has the greater range and greater mean
absolute deviation also has the higher variability. Because the both the range (13) and the MAD (4.2) of the data in Problem 8 are more
than twice that of the range (6) and MAD (2) of the data in Problem 9, the data set in Problem 8 has more variability than the data set in
Problem 9.
11. The age at retirement of 30 randomly selected men from two different towns was collected. Fifteen of the
men were from Newtonia and 15 of the men were from Euclidia. The following statistical information was
calculated from the data.
Mean
Median
Mode
Range
Newtonia Euclidia
65
73
60
72
62
62
50
33
Based on these samples, what generalization can be made?
A. More men retire in Euclidia than in Newtonia.
B. At least half of the men in both towns will retire before they reach 60 years of age.
C. The range of retirement ages is greater in Euclidia than in Newtonia.
D. The most common age for retirement in Newtonia is the same as the most common age for retirement in Euclidia.
12. A survey was conducted on the salaries of 20 randomly selected college graduates with degrees in the
same subject area. Each person surveyed graduated within the same 5-year period. Ten of the people
surveyed attended a private university, while the other 10 people surveyed attended a public university of
roughly the same size.
Private
First Quartile $58,000
Second Quartile (Median) $71,000
Third Quartile $85,000
Public
$35,000
$42,000
$54,000
Based on the samples, what generalization can be made?
A. The interquartile range for private universities is $27,000 more than for public universities.
B. The top ten percent of both the private and public university graduates surveyed earned more than $60,000
annually.
C. The top twenty-five percent of both the private and public university graduates surveyed earned more than $50,000
annually.
D. The interquartile range for public universities is $19,000 more than for private universities.
13. Which of these is an example of a random sample?
A. The five employees who work the late shift answer questions about management.
B. Five employees out of 2,000 are chosen randomly to complete an anonymous survey.
C. The five people seated on the first row at the circus are asked their opinion about the animal acts.
D. Henry asks five of his friends to fill out a survey to find out their favorite musicians.
14. Which of these is an example of a random sample?
A. A town official surveys 50 people in a library to decide if town residents want the library expanded.
B. Harris telephones 100 randomly chosen voters to find out who they plan to vote for in the upcoming mayoral
election.
C. George surveys 15 students on the soccer team to learn whether middle school students want more money spent
on school sports.
D. Zack surveys 80 high school students who are leaving a jazz concert to determine the favorite type of music among
high school students.
15. A factory produces 12,000 computers per week. The manager of a factory finds that in a random sample of
500 computers, 2 are found to be defective. Predict the number of computers that will be defective each
week.
Defective Computers:___ 48____
16. A mint produces 150,000 souvenir coins each year. In a random sample of 400 coins, 3 are found to have a
misprint. Predict the number of coins that will have misprints in a year.
Misprinted Coins:____ 1,125_____
17. What is the probability that a fair 2-sided coin will land on heads four times in a row?
𝟏
Answer:__ 𝟏𝟔 ___
18. How many possible outcomes would there be in an experiment that requires the rolling of two 6-sided dice and
flipping two coins?
Answer:____ 144____
19. Two regular 6-sided dice are rolled and their face up numbers are added together.
a. What is the probability that the sum of the numbers is exactly seven?
𝟏
𝟔
Answer:___ ____
b. What is the probability that the sum of the numbers is greater than nine?
𝟏
Answer:___ 𝟔 ____
20. Use the spinner on the right to answer the following questions:
a. What is the probability that the spinner
will land on a number less than five?
𝟏
Answer:____ 𝟒 ____
b. What is the probability that the spinner
will land on a prime number or a multiple of 3?
𝟑
Answer:___ 𝟒 ____
21. What is the probability that I select a red card or a queen when I choose one card from a deck of 52 cards? __
𝟕
𝟏𝟑
__
22. What is the probability that I select a card that is less than five or a king when I choose one card from a deck of 52
cards?
𝟒
____ _____
𝟏𝟑
23. What is the probability that I select a card that is a spade or a face card when I choose one card from a deck of 52
cards?
𝟏𝟏
____ 𝟐𝟔 ____
24. What is the probability that when I flip a coin and roll a 6-sided die that I get heads AND THEN a multiple of 3?
𝟏
____ 𝟔 ____
25. What is the probability that when I roll a 6-sided die and flip a coin that I get a composite number and then tails?
𝟏
𝟔
____ _____
26. Find the number of possible ways to travel to and from San Diego if you can travel by car, bus, train, or airplane.
____16_____
27. The safe at a bank is protected by a lock that requires a 5-digit code in order to be unlocked.
a.) How many possible combinations are there if there are no restrictions on any of the digits? ___100,000___
b.) How many possible combinations are there if no digit can be repeated? _____30,240______
28. 75 flower seeds are planted in a garden. Sixty of them blossom into beautiful flowers. What is the experimental
probability that the next flower seed planted will blossom?
𝟒
______ 𝟓 _______
29. A bag contains 6 red marbles, 3 blue marbles, 2 green marbles, and 5 white marbles
a) You select a marble, place it back in the bag, then select another marble. What is the probability that both
marbles are green?
________
𝟏
𝟔𝟒
________
b) You select a marble, do not place it back in the bag, and then select another marble. What is the probability that
both marbles are red?
𝟏
________ 𝟖 _________
c.) You select a marble, place it back in the bag, then select another marble. What is the probability that both
marbles are white?
________
𝟐𝟓
𝟐𝟓𝟔
_________