Mathematics AI SL's Sample Internal Assessment

Mathematics AI SL's Sample Internal Assessment

To what extent is there a Correlation between the number of individuals who are going out to their workplaces after Lockdown and the number of individuals who are getting infected by COVID-19?

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Word count: 1,937

Table of content

Rationale

The world has turned upside down after the spread of corona virus. We all are fighting with the virus in our own ways. To practice social distancing, the world had gone to a lockdown.

 

It has been months. No school, no outings, no vacations, no playing in parks; we are confined to our houses. The world could not be locked down for months, so with all safety measures it is trying to get back to its workings.

 

With every passing day, there is so much deaths and active corona cases. It is really disheartening. Though there is no more lockdown, we prefer staying at home. We do not go out until any need.

 

With everything getting back to normal, a news of reopening schools was surfacing for quite some time for which parents' consent was required.

 

The decision of going to school required a lot of research because that could not only cost me and my friends and family getting infected but also could cost our lives.

 

I went on to research more about the spread of the virus. I read many articles, surfed the internet and got to know many factors, precautions and many more. I could not get the answer I was looking for. However, reading several newspapers and statistical data that has been reported collecting data from a number of companies in the cities has helped to get a clear idea about the number of individuals who were bound to go out of their houses to their work places after remission of lockdown period.

 

I wanted to know to what extent there is a relation between the number of individuals going out to their workplaces after lockdown and the number of individuals getting infected by COVID – 19.

 

This IA is about the same. This research would allow my family to decide if I should attend school or should I continue with my online classes.

Aim

The main motive of this IA is to show a correlation between the number of employees and working professionals those who are getting infected by COVID-19 with respect to the number of working professionals going out right after calling off the Lockdown.  The study will show the effect of Lockdown during the COVID-19 pandemic on the rate of spreading after remission of it. It will also redirect to the fact how much it is safe for individuals to go out for work after Lockdown.

Research question

What is the relationship between the number of individuals who are going out to their workplaces after Lockdown and the number of individuals who are getting infected by COVID-19?

Introduction

COVID – 19 was one of the most infectious diseases the world has ever seen. It has spread throughout the globe within a span of 3 to 5 months. Originating from the city of Yuhan in China, it has spread to different countries including the far west – The USA. One of the most affect countries is India. From the month of March to July, complete Lockdown was called by the government to cope up with the pandemic and restrict the spread. However, lockdown was called off by the government since August and emergency services, such as, banking sector, media, etc. were allowed to start their usual operation. In this process, the infection of COVID – 19 is again taking its pace in an increasing order.

 

In this IA, data of the number of attendees of 20 companies situated in Mumbai, Delhi, and Kolkata, the three most affected cities of India, has been collected and the number of employees who got infected were noted. This collection is done for three different age groups from 25 years old to 55 years old with an interval of 10 years. This will help to analyze the spread of infection among individuals of different age groups after lockdown.

Data collection

The data collection for this correlative analysis has been done from a number of internationalized media houses and newspaper which are considered as authentic sources of information.

Sl. No.Total number of individualsNumber of individuals infected
115021
216018
315030
412012
520021
614018
716020
815040
917015
1015021
111206
121608
1315030
1416031
1512013
1615010
171407
1818017
191606
2012020

Figure 1 - Table On Number Of Individuals Getting Infected By COVID-19 Out Of The Individuals Those Were Going Out For Work Of The Age Group 25 Years To 35 Years

Sl. No.Total number of individualsNumber of individuals infected
11504
21606
31509
41203
52008
614010
71600
81500
917012
101503
1112030
121601
131505
141603
151201
161509
171404
181807
191606
201203

Figure 2 - Table On Number Of Individuals Getting Infected By COVID-19 Out Of The Individuals Those Were Going Out For Work Of The Age Group 35 Years To 45 Years

Sl. No.Total number of individualsNumber of individuals infected
115034
216036
315032
412024
520021
61403
716025
815028
917032
1015034
1112021
1216014
1315025
1416023
1512020
1615021
1714022
1818027
1916034
2012021

Figure 3 - Table On Number Of Individuals Getting Infected By COVID-19 Out Of The Individuals Those Were Going Out For Work Of The Age Group 45 Years To 55 Years

Processed data

Sl. No.Cumulative total number of individualsCumulative number of infected individuals
115021
231039
346069
458081
5780102
6920120
71080140
81230180
91400195
101550216
111670222
121830230
131980260
142140291
152260304
162410314
172550321
182730338
192890344
203010364

Figure 4 - Table On Cumulative Frequency Table For The Age Group Of 25 Years To 35 Years

Sl. No.Cumulative total number of individualsCumulative number of infected individuals
11504
231010
346019
458022
578030
692040
7108040
8123040
9140052
10155055
11167085
12183086
13198091
14214094
15226095
162410104
172550108
182730115
192890121
203010124

Figure 5 - Table On Cumulative Frequency Table For The Age Group Of 35 Years To 45 Years

Sl. No.Cumulative total number of individualsCumulative number of infected individuals
115034
231070
3460102
4580126
5780147
6920150
71080175
81230203
91400235
101550269
111670290
121830304
131980329
142140352
152260372
162410393
172550415
182730442
192890476
203010497

Figure 6 - Table On Cumulative Frequency Table For The Age Group Of 45 Years To 55 Years

Graphical analysis

Figure 7 - Cumulative Number Of Individuals Getting Infected By COVID-19 With Respect To Cumulative Individuals Those Were Going Out For Work Of The Age Group 25 Years To 35 Years

Figure 8 - Number Of Individuals Getting Infected By COVID-19 With Respect To The Individuals Those Were Going Out For Work Of The Age Group 25 Years To 35 Years

Figure 9 - Cumulative Number Of Individuals Getting Infected By COVID-19 With Respect To Cumulative Individuals Those Were Going Out For Work Of The Age Group 35 Years To 45 Years

Figure 10 - Number Of Individuals Getting Infected By COVID-19 With Respect To The Individuals Those Were Going Out For Work Of The Age Group 35 Years To 45 Years

Figure 11 - Cumulative Number Of Individuals Getting Infected By COVID-19 With Respect To Cumulative Individuals Those Were Going Out For Work Of The Age Group 45 Years To 55 Years

Figure 12 - Number Of Individuals Getting Infected By COVID-19 With Respect To The Individuals Those Were Going Out For Work Of The Age Group 45 Years To 55 Years

Calculation of R2

x

y

x2

y2

xy

15021225004413150
3103996100152112090
46069211600476131740
58081336400656146980
7801026084001040479560
92012084640014400110400
1080140116640019600151200
1230180151290032400221400
1400195196000038025273000
1550216240250046656334800
1670222278890049284370740
1830230334890052900420900
1980260392040067600514800
2140291457960084681622740
2260304510760092416687040
2410314580810098596756740
25503216502500103041818550
27303387452900114244922740
28903448352100118336994160
301036490601001324961095640
∑x = 31930∑y = 4151

∑x2 = 66084300

∑y2 = 1088363

∑xy = 8468370

Figure 13 - Table On Processed Data For Calculation Of Correlation Coefficient R2 For Group 1 (25 Years To 35 Years)

\(r = \frac{n\bigg(∑xy\bigg)-(∑x)(∑y)}{\sqrt{[n∑x^2-\bigg(∑x\bigg)^2][n∑y^2-\bigg(∑y\bigg)^2]}}\)

 

\(r = \frac{20×8468370-(31930)(4151)}{[20×66084300-(31930)^2][20×1088363-(4151)^2]}\)

 

=> r2 = 0.9894

x

y

x2

y2

xy

15042250016600
31010961001003100
460192116003618740
5802233640048412760
7803060840090023400
92040846400160036800
1080401166400160043200
1230401512900160049200
1400521960000270472800
1550552402500302585250
16708527889007225141950
18308633489007396157380
19809139204008281180180
21409445796008836201160
22609551076009025214700
2410104580810010816250640
2550108650250011664275400
2730115745290013225313950
2890121835210014641349690
3010124906010015376373240
∑x = 31930∑y = 1335

∑x= 66084300

∑y2 = 118875

∑xy = 2794140

Figure 14 - Table On Processed Data For Calculation Of Correlation Coefficient R2 For Group 2 (35 Years To 45 Years)

\(r = \frac{n\bigg(∑xy\bigg)-(∑x)(∑y)}{\sqrt{[n∑x^2-\bigg(∑x\bigg)^2][n∑y^2-\bigg(∑y\bigg)^2]}}\)

 

\(=> r = \frac{20×2794140-(31930)(1335)}{\sqrt{[20×66084300-(31930)^2][20×118875-(1335)^2]}}\)

 

=> r2 = 0.977

x

y

x2

y2

xy

150342250011565100
3107096100490021700
4601022116001040446920
5801263364001587673080
78014760840021609114660
92015084640022500138000
1080175116640030625189000
1230203151290041209249690
1400235196000055225329000
1550269240250072361416950
1670290278890084100484300
1830304334890092416556320
19803293920400108241651420
21403524579600123904753280
22603725107600138384840720
24103935808100154449947130
255041565025001722251058250
273044274529001953641206660
289047683521002265761375640
301049790601002470091495970
∑x = 31930∑y = 5381

∑x= 66084300

∑y2 = 1818533

∑xy = 10953790

Figure 15 - Table On Processed Data For Calculation Of Correlation Coefficient R2 For Group 2 (45 Years To 55 Years)

\(r = \frac{n\bigg(∑xy\bigg)-(∑x)(∑y)}{\sqrt{[n∑x^2-\bigg(∑x\bigg)^2][n∑y^2-\bigg(∑y\bigg)^2]}}\)

 

\(=> r = \frac{20×10953790-(31930)(5381)}{\sqrt{[20×66084300-(31930)^2][20×1818533-(5381)^2]}}\)

 

=> r2 = 0.9968

Calculation of pearson’s correlation coefficient

x

y

\( x-\bar x\)

\(y-\bar y\)

\((x-\bar x)(y-\bar y)\)

\((x-\bar x)^2\)

\((y-\bar y)^2\)

150211596.5207.55-1446.5-186.55269844.575
310391596.5207.55-1286.5-168.55216839.575
460691596.5207.55-1136.5-138.55157462.075
580811596.5207.55-1016.5-126.55128638.075
7801021596.5207.55-816.5-105.5586181.575
9201201596.5207.55-676.5-87.5559227.575
10801401596.5207.55-516.5-67.5534889.575
12301801596.5207.55-366.5-27.5510097.075
14001951596.5207.55-196.5-12.552466.075
15502161596.5207.55-46.58.45-392.925
16702221596.5207.5573.514.451062.075
18302301596.5207.55233.522.455242.075
19802601596.5207.55383.552.4520114.575
21402911596.5207.55543.583.4545355.075
22603041596.5207.55663.596.4563994.575
24103141596.5207.55813.5106.4586597.075
25503211596.5207.55953.5113.45108174.575
27303381596.5207.551133.5130.45147865.075
28903441596.5207.551293.5136.45176498.075
30103641596.5207.551413.5156.45221142.075

Figure 16 - Table On Processed Data Table For Calculation Of Pearson’s Correlation Coefficient In Group 1