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2
Rauan Kaldybaev
Surprising statistical patterns on MIT OpenCourseWare's YouTube channel
Rauan Kaldybaev
Posted
21 days ago
376 Views
|
1 Reply
|
2 Total Likes
Follow this post
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Statistical patterns on MIT OpenCourseWare’s YouTube channel
The current essay analyzes the number likes, dislikes, and views at MIT OpenCourseWare’s YouTube channel, where some of MIT’s courses are published. The essay looks at 95 courses. An interesting pattern is that some lectures typically have significantly more likes and views than the other lectures in the same course. In the course 22.01: Introduction to Nuclear Engineering and Ionizing Radiation, for example, the most popular lecture has 185 times more views than the median! And the number of views of the
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L
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s
Extract data from YouTube channel
Here is the code that extracts the data from the YouTube channel:
I
n
[
]
:
=
y
t
D
a
t
a
=
{
#
[
[
1
]
]
,
g
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V
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o
D
a
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a
/
@
g
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t
V
i
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s
[
#
[
[
2
]
]
]
}
&
/
@
c
o
u
r
s
e
L
i
s
t
;
I
n
[
]
:
=
y
t
D
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t
a
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[
]
=
{
{
1
5
.
S
0
8
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{
{
2
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9
6
,
5
6
0
,
1
5
}
,
{
6
0
2
5
,
1
3
2
,
2
}
,
{
5
4
0
5
,
9
8
,
1
}
,
{
2
8
3
9
,
4
5
,
0
}
,
{
5
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{
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{
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{
1
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3
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3
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}
,
{
2
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1
,
3
9
,
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{
1
4
4
2
,
2
7
,
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,
{
2
5
0
5
,
4
5
,
1
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,
{
1
1
1
7
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,
⋯
9
3
⋯
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{
1
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.
0
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{
4
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2
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3
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,
{
1
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{
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1
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,
{
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,
{
4
3
3
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1
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,
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4
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1
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,
⋯
1
6
⋯
,
{
4
1
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2
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6
5
8
,
4
}
,
{
1
7
5
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5
,
1
4
,
9
}
,
{
1
7
1
6
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5
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3
3
,
1
6
}
,
{
3
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2
8
0
,
6
2
1
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}
,
{
4
3
9
8
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,
5
8
3
,
1
5
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,
{
2
6
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2
6
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7
5
6
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2
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}
,
{
2
7
0
8
9
,
4
2
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,
{
1
0
8
9
8
9
,
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0
1
,
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,
{
1
5
4
2
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8
,
8
0
9
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}
,
{
1
4
3
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3
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}
}
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}
l
a
r
g
e
o
u
t
p
u
t
s
h
o
w
l
e
s
s
s
h
o
w
m
o
r
e
s
h
o
w
a
l
l
s
e
t
s
i
z
e
l
i
m
i
t
.
.
.
And since it takes forever to run, I’ve recorded the output it produces and copied it into the notebook like that, so that the code would not have to be executed every time:
y
t
D
a
t
a
=
Y
o
u
T
u
b
e
d
a
t
a
;
It must be noted that the data above was gathered in January 2021, so by the time you read the essay, the actual numbers might change. ytData is a list of the form
{..., {name, {lec1, lec2, ... }}, ...}
, where
name
is the name of a course and
lec1
represents the first lecture in the course.
lec1
is of the form
{views, likes, dislikes}
.
The student-layman model and Zipf’s law
Introducing the model
The first thing that we notice when looking at the number of views for the lectures in a given course is that the numbers are highly uneven. Here, for example, is the data for the course 6.172:
I
n
[
]
:
=
L
i
s
t
P
l
o
t
[
R
e
v
e
r
s
e
S
o
r
t
@
y
t
D
a
t
a
[
[
1
1
,
2
,
A
l
l
,
1
]
]
,
P
l
o
t
R
a
n
g
e
A
l
l
]
O
u
t
[
]
=
Here, the vertical axis is the number of views and the horizontal axis is the lecture’s rank, with the most popular lecture being first, the second most popular lecture being second, and so on. The first lecture has 12.5 times more views than the median. And for the course 22.01, the ratio of the number of views of the most popular lecture to the median number of views is 185! It turns out that the number of times a lecture is viewed is very accurately described by a power law
N
≈
+
k
-
γ
n
for some constants
,
k
,
γ
. For the course 6.172, for example, the law is
N
≈
-
2
.
9
·
3
1
0
+
6
.
0
6
·
4
1
0
-
0
.
8
5
3
n
:
I
n
[
]
:
=
c
o
u
r
s
e
C
K
G
M
o
d
e
l
P
l
o
t
[
1
1
]
O
u
t
[
]
=
The coefficients
,
k
,
γ
are determined using the method of least squares, in the log scale (see code at the bottom of the subsection). The model seems to be a good fit, and indeed, the value of
2
R
is 0.982. The model turns out to be accurate for all courses, as can be seen from the histogram of the values of
2
R
for the surveyed courses:
I
n
[
]
:
=
{
c
o
u
r
s
e
s
l
i
s
t
,
c
o
u
r
s
e
s
k
l
i
s
t
,
c
o
u
r
s
e
s
γ
l
i
s
t
,
c
o
u
r
s
e
s
F
V
U
l
i
s
t
}
=
T
r
a
n
s
p
o
s
e
[
c
o
u
r
s
e
C
K
G
M
o
d
e
l
F
i
t
/
@
R
a
n
g
e
[
L
e
n
g
t
h
[
y
t
D
a
t
a
]
]
]
;
I
n
[
]
:
=
H
i
s
t
o
g
r
a
m
[
1
-
c
o
u
r
s
e
s
F
V
U
l
i
s
t
,
A
x
e
s
L
a
b
e
l
{
"
2
R
"
,
"
"
}
]
O
u
t
[
]
=
I
n
[
]
:
=
M
e
d
i
a
n
[
1
-
c
o
u
r
s
e
s
F
V
U
l
i
s
t
]
O
u
t
[
]
=
0
.
9
7
3
1
1
3
The median value of
2
R
is 0.97. Isn’t this amazing how accurate the model is?
S
u
p
p
l
e
m
e
n
t
a
l
c
o
d
e
Interesting features
Things become even more interesting if we plot the histogram of the parameter
γ
in the approximate law
N
≈
+
k
-
γ
n
:
I
n
[
]
:
=
H
i
s
t
o
g
r
a
m
[
c
o
u
r
s
e
s
γ
l
i
s
t
,
A
x
e
s
L
a
b
e
l
{
"
γ
"
,
"
"
}
]
O
u
t
[
]
=
I
n
[
]
:
=
{
M
e
a
n
[
c
o
u
r
s
e
s
γ
l
i
s
t
]
,
M
e
d
i
a
n
[
c
o
u
r
s
e
s
γ
l
i
s
t
]
}
O
u
t
[
]
=
{
0
.
9
7
6
5
8
8
,
0
.
9
6
7
7
7
3
}
This is a unimodal distribution centered at 1! This is exactly what we would expect from Zipf’s law, which tells us that the number of views under the
n
-th most popular lecture in a course should be
n
times smaller than the number of views under the most popular lecture. And the distribution’s shape is similar to the bell curve, which is also quite satisfying. Also, notice that most of the times,
is much less than
k
:
I
n
[
]
:
=
H
i
s
t
o
g
r
a
m
[
c
o
u
r
s
e
s
l
i
s
t
/
c
o
u
r
s
e
s
k
l
i
s
t
,
A
x
e
s
L
a
b
e
l
{
"
/
k
"
,
"
"
}
]
O
u
t
[
]
=
Most of the times, the ratio
/
k
is between -0.05 and 0.05. Also, since the distribution looks like a symmetric zero-centered distribution with a left tail, one might suspect that the departures from 0 are caused by some sort of noise, and that the “normal” value of
is zero.
Interpretation
T
h
e
n
u
m
b
e
r
o
f
v
i
e
w
s
a
l
e
c
t
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h
a
s
c
a
n
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p
r
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s
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d
a
s
a
s
u
m
o
f
t
w
o
c
o
m
p
o
n
e
n
t
s
:
s
t
u
d
e
n
t
s
,
w
h
o
p
e
d
a
n
t
i
c
a
l
l
y
w
a
t
c
h
a
l
l
t
h
e
l
e
c
t
u
r
e
s
i
n
o
r
d
e
r
,
a
n
d
“
l
a
y
m
e
n
”
,
w
h
o
c
l
i
c
k
o
n
t
h
e
l
e
c
t
u
r
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s
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i
t
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r
a
c
c
i
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t
a
l
l
y
o
r
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c
a
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o
f
t
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r
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d
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a
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s
.
T
h
e
n
u
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b
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f
s
t
u
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t
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w
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c
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f
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c
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c
t
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,
w
h
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t
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u
m
b
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o
f
l
a
y
m
e
n
v
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w
s
c
h
a
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.
C
o
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p
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N
≈
+
k
-
γ
n
,
w
e
w
o
u
l
d
e
x
p
e
c
t
t
o
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e
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l
u
s
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s
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a
n
d
k
-
t
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a
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.
T
h
e
c
o
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s
t
a
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γ
c
o
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t
r
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l
s
h
o
w
q
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k
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t
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Max to median views
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2
,
7
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1
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1
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8
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2
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7
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5
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4
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}
I
n
[
]
:
=
y
t
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[
[
#
,
1
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]
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{
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5
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,
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2
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3
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}
As previously, 2.003J: Dynamics and Control I comes as the course with the most homogenous stats. The most uneven course is now 22.01: Introduction to Nuclear Engineering and Ionizing radiation. Similarly to the result we got by comparing
γ
, courses with loud names tend to have more uneven views than courses with modest names, although the exact ordering has changed quite a bit.
Total views
Let’s now assess courses’ popularity by comparing their total number of views:
I
n
[
]
:
=
C
l
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a
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l
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=
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[
[
2
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;
I
n
[
]
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=
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;
I
n
[
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:
=
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[
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{
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8
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3
3
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6
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1
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3
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2
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2
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1
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4
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6
}
The most popular course is 6.006: Introduction to Algorithms, and the next most popular one is 18.06: Linear Algebra. These courses are relevant in fields like machine learning and IT, as well as a ton of other industries - probably that’s why they are so popular. Notice that the first seven positions are taken by math and computer science as the most “industrious” fields. The first non-math and non-CS popular courses are 8.04: Quantum mechanics I and 14.01SC: Principles of Microeconomics. The three least popular courses are 4.696: A Global History of Architecture, 3.091: Introduction to Solid State Chemistry and 11.601: Introduction to Environmental Policy and Planning. These are courses with very specific target audience and a comparatively limited practical application (apart from 3.091, which strangely has so few views). It is interesting that 6.S897, a computer science course, is the fifth least popular course, as CS is the most popular major. The explanation is probably that the course is very specific: its name is Machine Learning for Health Care, which is only going to attract a few narrow specialists. All in all, it can be seen that majors relevant in industry, such as computer science and math, are the most popular, while courses with a narrow target audience and comparatively limited practical applications get the least number of views.
I
n
[
]
:
=
{
B
a
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[
[
;
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7
]
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[
[
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,
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,
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[
[
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7
;
;
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[
[
-
7
;
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5
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}
O
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[
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=
,
I
n
[
]
:
=
H
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s
t
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{
{
0
,
2
*
6
1
0
}
,
A
l
l
}
]
O
u
t
[
]
=
Likes to dislikes
Having assessed the courses’ popularity, it would now be interesting to evaluate how enjoyable they are by comparing the total number of likes to the total number of dislikes they have. The idea is that the more exciting is the course, the higher is the ratio of likes to dislikes. There are of course some issues with this metric - for example, since there are far more laymen than students, the data we get will reflect the preferences of laymen - it’s still a fairly reasonable way to measure how exciting the course’s content is. So, here is the code:
I
n
[
]
:
=
C
l
e
a
r
A
l
l
[
g
e
t
T
o
t
a
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L
i
k
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s
]
;
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t
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[
c
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D
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a
_
]
:
=
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l
@
c
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r
s
e
D
a
t
a
[
[
2
,
A
l
l
,
2
]
]
;
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l
e
a
r
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l
[
g
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]
;
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s
[
c
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e