Data101_2022W1_Test1soln
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University of British Columbia *
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Course
101
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
7
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DATA 101
Test 1
Oct 13, 2022
INSTRUCTOR:
Lengyi Han
/
Yas Yamin
Irving K. Barber School
of Arts and Sciences
UBC, Okanagan Campus
This exam has 11 questions, for a total of 40 points. The 8th question is optional for 2 bonus
marks.
READ THE QUESTIONS CAREFULLY
In order to get full credit you must SHOW YOUR WORK
Answer the questions in the spaces provided on the question sheets.
Any calculator is allowed. No textbook, laptops, cell phones, or other electronic devices are
permitted.
SURNAME, GIVEN NAME (print).
STUDENT NUMBER
Signature:
Question
Points
Score
1
2
2
10
3
2
4
2
5
3
6
3
7
7
8
1
9
4
10
4
11
2
Total:
40
This exam has 7 pages including this cover page
DATA 101
Test 1 (continued)
1. Circle the correct answers for the following two questions
(a)
1
Which command will generate 25 random numbers between 0 and 5 from the uniform
distribution?
i. runif (25,0,5)
ii. runif [0,5,25]
iii. runif 25, 0, 5
iv. runif [25,0,5]
v. runif (0,5,25)
Solution:
i
(b)
1
I would like to simulate the result of tossing a pair of 6-sided dice. To do this, I can use
the following command:
i. sample(1:6, size = 2, replace = TRUE)
ii. sample(1:2, size = 6, replace = TRUE)
iii. sample(1:2, size = 6, replace = FALSE)
iv. sample(1:6, size = 2, replace = FALSE)
Solution:
ii
2. What would you expect the R output to be in response to the following commands:
(a)
1
15
%%
6
(b)
2
seq
(
2
,
6
,
2
)
^
(
3
:
1
)
(c)
1
10
^
50
+
17
-
10
^
50
Page 2 of 7
DATA 101
Test 1 (continued)
(d)
1
10
^
50
-
10
^
50
-
17
(e)
1
rep
(
1
:
4
,
1
:
4
)
(f)
2
y
<-
factor
(
c
(
1
,
3
,
1
,
1
,
1
,
3
))
levels
(y)
<-
c
(
"A"
,
"H"
)
y[
c
(
6
,
1
,
2
,
3
)]
(g)
1
y
<-
c
(
3
,
6
,
1
,
2
,
0
,
5
,
2
)
y[y
>
3
]
(h)
1
1
:
3
*
2
-
1
:
(
3
*
2
)
Page 3 of 7
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DATA 101
Test 1 (continued)
Solution:
## [1] 3
## [1]
8 16
6
## [1] 0
## [1] -17
##
[1] 1 2 2 3 3 3 4 4 4 4
## [1] H A H A
## Levels: A H
## [1] 6 5
## [1]
1
2
3 -2 -1
0
3.
2
The surface area, SA, of a sphere of radius
r
is given by
SA = 4
πr
2
.
Write the lines of R code which could be used to calculate the approximate surface area of
Earth, assuming a radius of 6378 km. The code should result in the assignment of the surface
area value to an object named
AreaEarth
.
Solution:
r
<-
6378
AreaEarth
<-
4
*
pi
*
r
^
2
4.
2
Convert the following binary number to its decimal representation: 10
.
11
2
Solution:
4.75
5. Convert the following decimal numbers to their binary representations.
(a)
1
23
(b)
2
1.625
Solution:
10111
2
1
.
101
2
Page 4 of 7
DATA 101
Test 1 (continued)
6.
(a)
2
Use the
rep
and
seq
functions to create the following vector
##
[1]
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
2
4
6
8 10
assigning it to an object called
x
.
(b)
1
Write down the R code to calculate the pairwise minima of the two vectors:
x
[1] 12 16 18 18 22
y
[1] 11 15 19 23 27
Solution:
rep
(
seq
(
2
,
10
,
2
),
5
)
pmin
(x,y)
7. In this question, you will follow the steps below to write R code to determine which is the
largest of (
∑
100
j
=1
√
j
)
2
and (
∑
100
j
=1
j
3
)
1
/
3
. Specifically, write the R code to
(a)
1
create a vector called
numbers
that contains the integers from 1 through 100.
(b)
2
create two new vectors, called
numsqrt
and
numcube
which contain the square roots and
cubes of the numbers in
numbers
, respectively.
(c)
2
find the sums of the 2 vectors obtained in the previous part. Then calculate the second
power of the first sum and the cube root of the second sum.
(d)
2
determine which of the two quantities obtained in the previous part is the largest?
Solution:
numbers
<-
1
:
100
numsqrt
<-
sqrt
(numbers)
numcube
<-
numbers
^
3
sum
(numsqrt)
^
2
;
sum
(numcube)
^
(
1
/
3
)
## [1] 450862.489
## [1] 294.347884
max
(
sum
(numsqrt)
^
2
,
sum
(numcube)
^
(
1
/
3
))
## [1] 450862.489
Page 5 of 7
DATA 101
Test 1 (continued)
8.
1
The music preferences for a class of 50 university students are contained in a vector called
music
, displayed below. Fill in the blank in the R code (below) which would produce output
showing the numbers of students favoring each type of music.
##
[1] "alternative" "country"
"alternative" "alternative" "country"
##
[6] "rock"
"hip-hop"
"alternative" "hip-hop"
"rock"
## [11] "rock"
"country"
"country"
"rock"
"alternative"
## [16] "alternative" "alternative" "country"
"rock"
"rock"
## [21] "rock"
"hip-hop"
"alternative" "rock"
"country"
## [26] "country"
"rock"
"alternative" "alternative" "country"
## [31] "alternative" "alternative" "alternative" "rock"
"hip-hop"
## [36] "alternative" "alternative" "alternative" "country"
"country"
## [41] "rock"
"rock"
"alternative" "rock"
"country"
## [46] "alternative" "alternative" "alternative" "rock"
"alternative"
__________
(music)
Solution:
table
(music)
9. Consider the following vector in R:
x
<-
c
(
1
,
7
,
NA
,
2
,
4
,
3
,
NA
,
5
,
NA
,
6
)
(a)
1
Write an R command which returns the positions of the missing values in x.
(b)
1
Write an R command which returns the number of non-missing values in x.
(c)
2
Write an R program which replaces the missing values in x with the mean of the non-
missing values in x.
Solution:
#a
which
(
is.na
(x))
## [1] 3 7 9
#b
x[
!
is.na
(x)]
## [1] 1 7 2 4 3 5 6
#or
x[
-
which
(
is.na
(x))]
## [1] 1 7 2 4 3 5 6
#c
x[
which
(
is.na
(x))]
<-
mean
(x[
!
is.na
(x)])
x
##
[1] 1 7 4 2 4 3 4 5 4 6
Page 6 of 7
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DATA 101
Test 1 (continued)
10. Suppose the data frame
my.df
has been entered into an R workspace, and its contents are as
follows.
##
name height owncar occupation
## 1
Ann
170
TRUE
engineer
## 2
Bob
180
TRUE
lawyer
## 3 Carl
175
FALSE
engineer
## 4 Dave
170
FALSE
lawyer
## 5 Emma
172
TRUE
engineer
## 6 Fran
167
TRUE
lawyer
## 7 Gary
174
FALSE
engineer
What is printed to the screen when the following commands are executed?
(a)
1
my.df[
3
,
2
]
Solution:
## [1] 175
(b)
1
subset
(my.df, occupation
==
"lawyer"
)
$
name
Solution:
## [1] "Bob"
"Dave" "Fran"
(c)
1
subset
(my.df, (occupation
==
"lawyer"
)
&
(height
>
179
))
Solution:
##
name height owncar occupation
## 2
Bob
180
TRUE
lawyer
(d)
1
my.df
$
height[my.df
$
owncar]
Solution:
## [1] 170 180 172 167
11.
2
What would you expect the R output to be in response to the following commands:
x
<-
"The"
y
<-
"End"
paste
(
paste
(x, y),
"!"
,
sep
=
":-)"
)
Solution:
## [1] "The End:-)!"
Page 7 of 7