Candidate name: Felix Dyrek Candidate number: 001528-031

Investigation

Math Studies

Working Title:

Candidate Name: Felix Dyrek

Candidate number: 001528-031

School name: Kolegium Europejskie

School number: 001528

Assignment supervisor: Katarzyna Nosalska

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The correlation between lung cancer incidents and the mean amount of

smoked cigarettes

Candidate name: Felix Dyrek Candidate number: 001528-031

Introduction:

The aim of my investigation is to find out if there is a correlation between lung cancer incidents

in total and tobacco consumption of men and women in 6 countries.

Hypothesis:

My hypothesis assumes that the rate of lung cancer incidents is bigger in the countries with

higher tobacco consumption then in the countries with smaller tobacco consumption.

Method:

In order to be able to investigate the correlation between lung cancer incidents and tobacco

consumption I needed to collect data from the tobacco industry and various (lung) cancer

constitutions. The next step is to verify the collected data and form statistics. In order to calculate

the correlation the following mathematical methods are used:

The Pearson’s Correlation Coefficient

The X2 Test

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Candidate name: Felix Dyrek Candidate number: 001528-031

Raw Data:

Table 1 : Lung Cancer incident rates per 100000 people

Country Lung Cancer

incidents

Female Lung Cancer

incidents

Male Lung Cancer

incidents

China 93 27 66

Japan 60 13 47

Thailand 87 37 50

Sweden 35 13 22

Poland 85 21 64

UK 73 22 51

Chart 1: Lung Cancer incident rates per 100000 people

China Japan Thailand Sweden Poland UK0

10

20

30

40

50

60

70

80

90

100

TotalFemaleMale

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Candidate name: Felix Dyrek Candidate number: 001528-031

Table 2: Adult smokers in total

Country Adult smokers in

total

Adult smokers (per

100000 people)

Adult smokers (%)

China 462.800.000 35600 35.6

Japan 42.132.466 33100 33.1

UK 12.721.380 21000 21

Sweden 1.939.183 19000 19

Poland 13.149.988 34500 34.5

Thailand 15.019.407 23400 23.4

Chart 2: Comparison between percentage of adult smokers in total and countries in %

Adult Smokers

ChinaJapanUKSwedenPolandThailand

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Candidate name: Felix Dyrek Candidate number: 001528-031

Table 3: Average amount of cigarettes smoked per year

Country Total amount of cigarettes

smoked per person

Total amount of cigarettes

smoked per 100000 people

China 1791 179.100.000

Japan 3023 302.300.000

UK 2232 223.200.000

Sweden 1202 120.200.000

Poland 2061 206.100.000

Thailand 1067 106.700.000

Chart 3: Comparison between the average amounts of cigarettes smoked per person / year and

countries in %

Average amount of smoked cigarettes per person / year

ChinaJapanUKSwedenPolandThailand

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Candidate name: Felix Dyrek Candidate number: 001528-031

Calculations

The Pearson Correlation coefficient

The Pearson Correlation coefficient is used to identify if there is a correlation between the lung

cancer incidents and the average amount of smoked cigarettes per person. Table 4 is divided into

6 countries in order to be able to compare them. First of all it is to chart the researched data for

lung cancer incidents (x) and the amount of smoked cigarettes per person / year (y). The next

step is to multiply these data in order to obtain XY. Data in x and y have to be raised by 2 to

obtain the results for the last two columns. The following step is to sum up the obtained data up.

Table 4

Table 4

X Y XY X2 Y2

Country Lung Cancer Incidents

Amount of smoked cigarettes per person / year

1 China 93 179100000 16656300000

8649 32076810000000000

2 Japan 60 302300000 18138000000

3600 91385290000000000

3 UK 73 223200000 16293600000

5329 49818240000000000

4 Sweden 35 120200000 4207000000 1225 14448040000000000 5 Poland 85 206100000 1751850000

07225 42477210000000000

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Candidate name: Felix Dyrek Candidate number: 001528-031

6 Thailand 87 106700000 9282900000 7569 11384890000000000Total 6 433 1137600000 8209630000

033597 241590480000000000

The last step is to insert the collected data into the Pearson Correlation Coefficient formula and

solve the equation.

There is no correlation.

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r= 82096300000−6×72.16×189600000_______________ √33597−6×72.162 √241590480000000000−6×1896000002

r= 82089216000____________ √2354.60√25901520000000000

r= -1.54x1011

Candidate name: Felix Dyrek Candidate number: 001528-031

The X 2 Test

χcalc2 =∑

( f o−f e)2

f e

Where:

f o is an observed frequency

f e is an expected frequency

Observed Value Table (fo): Taken from Table 1, average of the European and Asian countries

within the female and male lung cancer incidents.

Female lung cancer

incidents

Male lung cancer

incidents

Sum

Europe 18.67 45.67 64.34

Asia 25.67 54.33 80

Sum 44.34 100 144.34

Calculation Table: The calculation table will be used to change the observed values into expected

values to have the possibility to calculate the x2 test.

S1 S2 Sum

R1 wy÷n wz÷n w

R2 xy÷n xz÷n x

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Candidate name: Felix Dyrek Candidate number: 001528-031

Sum Y Z n

Expected Value Table (fe): This table represents the lung cancer incidents between Europe and

Asia. The data is based on my previous data on the 6 countries – China, Japan, Thailand,

Sweden, Poland and the United Kingdom divided into their representing continents. It is also

divided between male and female groups.

Female lung cancer

incdents

Male lung cancer

incidents

Sum

Europe 19.76 44.58 64.34

Asia 24.58 55.42 80

Sum 44.34 100 144.34

Now I am going to calculate the x2 test in order to observe if there exists a correlation between observed and expected values extracted from the tables concerning male and female lung cancer incidents within Europe and Asia.

χ2 Calculations:

fo fe fo−fe (fo−fe)2 (fo−fe)2÷fe

18.67 19.76 -1.09 1.1881 0.0601

45.67 44.58 1.09 1.1881 0.0267

25.67 24.58 1.09 1.1881 0.0483

54.33 55.42 -1.09 1.1881 0.0214

Total 0.1565

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Candidate name: Felix Dyrek Candidate number: 001528-031

So, χ2

= 0.1565

The χ2

is small enough to observe that there is a correlation between observed and expected

Degrees of freedom

df = (r – 1)(c – 1)

The next step is find df and using a table to find the meaning of x2 which I just have obtained.

The x2 distribution depends on the number of degrees of freedom (df) where df = (r – 1)(c – 1)

My table equals:

df=(r-1)(c-1)df=(2-1)(2-1)df=1x1=1

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Candidate name: Felix Dyrek Candidate number: 001528-031

Conclusion and Evaluation

Due to the results which I have obtained during my research it can be concluded that there

doesn’t exist a direct correlation between the amount of smoked cigarettes and the lung cancer

incidents. So my hypothesis is proven to be wrong. There can be various factors resulting in lung

cancer such as second hand smoke, car exhaust, multiple alpha, beta and gamma rays. As these

facots can oncrease the chance of lung cancer my data is not 100% accurate as there are external

factors which can increase the lung cancer incidents. Thus lung cancer incidents are not purely

based on the amount of consuming cigarettes even though it is a known fact that excessive

cigarette consumption may cause lung cancer. As Due to the explanation above the investigation

could be improved by including more external factors such as the one previously mentioned.

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