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Correlation between Instagram followers and celebrity earnings
This IB Math Internal Assessment example examines the correlation between the number of Instagram followers and the salaries of top celebrities and fashion models. Using statistical tools such as Pearson correlation and scatter plots, the assessment explores whether a larger Instagram following translates to higher earnings. The analysis involves calculating means and standard deviations and plotting data to visually represent and confirm the positive correlation hypothesized in the study. This study highlights the impact of social media on celebrity earnings, providing a mathematical perspective on the economics of fame.
September 23, 2024
* The sample essays are for browsing purposes only and are not to be submitted as original work to avoid issues with plagiarism.
1
Relationship between Instagram Following and Salary
Student Name
Institution
Course
Professor's Name
Date
2
Relationship between Instagram Following and Salary
Research question
Is there a relationship between top celebrities' and fashion models' Salary and their Instagram
following?
Introduction
Social media growth has impacted many people's lives, especially celebrities and
fashion designers. Instagram is one of these platforms where celebrities maximize their
influence by showcasing various fashion and designs from various parts of the globe. In
December 2021, when I watched the model of the year awards, I noticed that most celebrities
who earn a lot of money have a huge following on their social accounts, such as Instagram.
Through this information, I decided to compute the correlation between celebrities' Instagram
following and SalarySalary.
Mathematical exploration
In this IA, various mathematical tools will be applied. Some of these tools include the
Pearson correlation method, which will be used to find the direction and strength of the
relationship. The scatter plot is used to represent raw data in graphical form, which also
shows the direction of the correlation (positive or negative). An uphill trend shows a positive
correlation, while a downhill trend shows a negative trend. After data collection, I will also
use the collected data to find the mean and standard deviation.
Hypothesis
3
In this exploration, I predict that there is a positive association between Instagram
following and celebrities' salaries. As Instagram following increases, the salary also
increases. The scatter graph will have a positive graph line, still confirming the positive
correlation between Instagram following and Salary.
Aim
This internal assessment aims to use mathematical tools to find the relationship
between celebrities' salary and their corresponding Instagram following. Some of the
mathematical tricks used include; Pearson correlation, scatter graph, and Chi-square methods.
Raw data
To compute the relationship between fashion models' salaries and Instagram
following, I collected data for the top 15 celebrities in the world. The data will comprise 5
models from England (Europe), the United States of America (Central America), and Brazil
(South America), as recorded in table 1 below;
Table 1: Raw data
Name
Nationality
Instagram followers
(million)
Salary
(million USD)
Gisele BĆ¼ndchen
Brazil
18.5
40.0
Adriana Lima
Brazil
13.9
11.0
Alessandra Ambrosio
Brazil
10.7
10.4
Isabeli Fontana
Brazil
1.2
4.0
Ana Beatriz Barros
Brazil
0.451
1.0
Kendall Jenner
American
21.7
40.0
Bella Hadid
American
48.9
19.0
4
Statistical Analysis
Based on the data above, I decided to use a mathematical approach to calculate the mean/
average and the standard deviation.
Mean
This is the average value of the total dataset, and it can be calculated using the following;
Given
= average/mean
= Instagram followers and SalarySalary
=Total number of models
I used the above formula to develop the following table;
Table 2: Average/mean table
Adriana Lima
American
13.9
11.0
Chrissy Teigen
American
36.8
12.0
Liu Wen
American
5.5
7.0
Cara Delevingne
England
43.4
10.73
Rosie Huntington
England
14.5
8.71
Kate Moss
England
1.3
6.72
David Gandy
England
1.0
5.37
Naomi Campbell
England
12.1
4.0
A=āx
n
A
x
N
5
It can be noted that, on average, each celebrity has 29.27million followers, and at the same
time, each celebrity earns an average of 12.667 USD.
Standard deviation
Instagram following
(million)
Salary
(million USD)
18.5
40.0
13.9
11.0
10.7
10.4
1.2
4.0
0.451
1.0
217
40.0
48.9
19.0
13.9
11.0
36.8
12.0
5.5
7.0
43.4
10.73
14.5
8.71
1.3
6.72
1.0
5.37
12.1
4.0
439.151
āx=
190.93
āx=
A.m(instagram)followers =439.151
15 = 29.27million
A.m(salar y)=190.93
15 =$12.667ī¢million
6
The formula to calculate the standard deviation is given below;
(McGrath et al., 2020)
Where;
= S.D
N= number of celebrities
= individual value (Instagram followers and SalarySalary)
Applying the above formula, I developed the following table;
Table 3: Standard deviation table
Ļ=ā(x1āĪ¼)2
N
Ļ
x1
Instagram
(million)
Salary
(million USD)
18.5
115.9929
40
744.1984
13.9
236.2369
11
2.9584
10.7
344.8449
10.4
5.3824
1.2
787.9249
4
76.0384
0.451
830.534761
1
137.3584
217
35242.5529
40
744.1984
48.9
385.3369
19
39.4384
13.9
236.2369
11
2.9584
36.8
56.7009
12
0.5184
5.5
565.0129
7
32.7184
43.4
199.6569
10.73
3.9601
14.5
218.1529
8.71
16.0801
ā(x1āĪ¼)2
ā(x1āĪ¼)2
7
Chi-square
This is a method that is used to find the level at which variables depend on each other.
The formula to calculate Chi-square;
(Connelly, 2019)
Given that;
=hypothetical value
Prior to computing the correlation coefficient, it is imperative to state both the alternative and
null hypotheses, as shown below;
H0 =Salary is independent of the Instagram following (Āµā¤0.5)
H1= SalarySalary is dependent on the Instagram following (Āµ>0.5)
1.3
782.3209
6.72
36
1
799.1929
5.37
54.0225
12.1
294.8089
4
76.0384
41095.5074
1971.869
Ļ(instagramī¢following) = 41095.5074
15 = 52.34
(Salar y) = 1971.869
15 = 11.46
x2=ā(0i
2āEi
2)
Ei
Ei=Listedī¢value
0i
x2=Chi āsquaredī¢valueī¢
8
I applied the topic above to develop the following table;
The chi-square from the above table is 154.9436, which is> 0.5. Thus the alternative
hypothesis, which states that "Salary is dependent on the Instagram following," will be
adopted. The null hypothesis states that "Salary is independent of the Instagram following"
will be ignored.
Pearson correlation
(million)
Observed value
(O)
Expected value
(e)
18.5
40
12.728
112.9791
13.9
11
12.728
-3.2214
10.7
10.4
12.728
-4.2302
1.2
4
12.728
-11.4709
0.451
1
12.728
-12.6494
21.7
40
12.728
112.9791
48.9
19
12.728
15.63466
13.9
11
12.728
-3.2214
36.8
12
12.728
-1.41436
5.5
7
12.728
-8.87822
43.4
10.73
12.728
-3.68236
14.5
8.71
12.728
-6.76759
1.3
6.72
12.728
-9.18004
1
5.37
12.728
-10.4624
12.1
4
12.728
-11.4709
154.9436
Chi-square
x2=(0i
2āEi
2)
Ei
9
The Pearson method is used to calculate the relation between dependent and
independent variables within a dataset. To compute the correlation coefficient of the above
data;
Where;
= link between salary and Instagram following
= Instagram following
Average number of Instagram followers
Model's Salary
= average model's SalarySalary
I used the above formula to develop the following table;
r=ā(xā ī¤x)(yā ī¢Č³)
[ā(xāxī¤2)(yā ī¢Č³2)]
r
X
ī¤x=
y=
Č³
followers
(x)
Salary
dx(x-x
!)
dy (y- Č³)
dxdy
(dx)2
(dy)2
18.5
40
-10.77
27.28
-293.806
115.9929
744.1984
13.9
11
-15.37
-1.72
26.4364
236.2369
2.9584
10.7
10.4
-18.57
-2.32
43.0824
344.8449
5.3824
1.2
4
-28.07
-8.72
244.7704
787.9249
76.0384
0.451
1
-28.819
-11.72
337.7587
830.5348
137.3584
217
40
187.73
27.28
5121.274
35242.55
744.1984
48.9
19
19.63
6.28
123.2764
385.3369
39.4384
13.9
11
-15.37
-1.72
26.4364
236.2369
2.9584
10
r =0.701
From the computation above, it is worth noting that the association coefficient is
0.701. This clarifies that there is a strong positive correlation between the variables; whereas
Instagram follows advances, the Salary also increases.
Scatter plot
The data in table 1 can be plotted in a scatter plot, as shown in figure 1 below;
36.8
12
7.53
-0.72
-5.4216
56.7009
0.5184
5.5
7
-23.77
-5.72
135.9644
565.0129
32.7184
43.4
10.73
14.13
-1.99
-28.1187
199.6569
3.9601
14.5
8.71
-14.77
-4.01
59.2277
218.1529
16.0801
1.3
6.72
-27.97
-6
167.82
782.3209
36
1
5.37
-28.27
-7.35
207.7845
799.1929
54.0225
12.1
4
-17.17
-8.72
149.7224
294.8089
76.0384
29.27673
12.72867
6316.208
41095.51
1971.869
Salary&&(million&USD)&vs&instagrm&following
Salary (million USD)
0
12,5
25
37,5
50
Instagram following
0
75
150
225
300
y&=&0,1537x&+&8,229
RĀ²&=&0,4923
11
From the graph in the figure above, it can be realized that as the number of Instagram
following escalates, the SalarySalary also increases. The graph line above indicates an
escalation trend, still confirming that there is a positive link between Instagram following and
Salary. The coefficient value from the scatter plot above is;
The coefficient value from the above computation is 0.701, indicating that there is a
positive correlation between Instagram following and Salary. The calculation concludes that
there is a positive link between the two variables and thus confirms my hypothesis, which
stated that "there is a positive correlation between celebrity earnings/salary and Instagram
following."
Conclusion
The primary objective of this internal assessment was to investigate if there is a
relationship between celebrity salary and Instagram following. Before the exploration, I
predicted that "there is a positive correlation between celebrity earnings/salary and Instagram
following." Various methodologies were used to calculate the coefficient, such as; scatter
graphs and Pearson methods. In both methods, it was evident that there is a strong positive
association/correlation between celebrities' salaries and Instagram following. As the
Instagram following increases, the celebrity's SalarySalary also increases and thus confirming
my hypothesis.
Evaluation
R2= 0.4923
R= 0.4923
R= 0.701
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The IA was great as the aim, "to use mathematical tools to find the relationship
between celebrities' salary and their corresponding Instagram following," was achieved.
However, various reasons have contributed to some errors in this exploration. There are
various social media platforms such as; Facebook, YouTube, and Tiktok platforms. In this
exploration, only the Instagram platform was used. In future exploration, the research should
also consider the relationship between salary and social media following.
13
References
Connelly, L. (2019). Chi-square test. Medsurg Nursing, 28(2), 127-127.
McGrath, S., Zhao, X., Steele, R., Thombs, B. D., Benedetti, A., & DEPRESsion Screening
Data (DEPRESSED) Collaboration. (2020). Estimating the sample mean and standard
deviation from commonly reported quantiles in meta-analysis. Statistical methods in
medical research, 29(9), 2520-2537.
September 23, 2024
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Academic level:
IB Student
Type of paper:
IB Internal Assessment
Discipline:
Math
Citation:
APA
Pages:
12 (2200 words)
Spacing:
Double
* The sample essays are for browsing purposes only and are not to be submitted as original work to avoid issues with plagiarism.
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