Mathematics Assignment

This Mathematics Assignment includes questions related to analytic competencies, epidemiologic study, coefficient of variation, age-group specific rate ratios, crude death rate ratio, standardized morbidity ratio, population pyramid and probability.

Mathematics Assignment
Student Name:
Instructor Name:
Course Number:
12th July 2019

1. Research is a scientific or scholarly investigation that aims to provide insights and
innovative solutions to health problems. Which of the following is NOT an analytic
competency important for conducting research?
a. Determine appropriate use of data and statistical methods for problem identification and
resolution and program planning, implementation, and evaluation
b. Select and define variables relevant to defined public health problems
c. Evaluate the integrity and comparability of data and identify gaps in data sources
d. Make relevant inferences from data
e. All of the above are important analytic competencies
2. Which of the following is indicative that an analytic epidemiologic study is involved?
a. An epidemic curve
b. A description of the clinical characteristics of a disease
c. A description of the frequency and pattern of disease by person, place, and time
d. A comparison group
3. The standard deviation for the data 8, 10, 17, 20 25, 30, 35, and 40, is 11.50. What is the
coefficient of variation?
Coefficient of variation CV=( Standard deviation
mean )× 100
Mean= 8+10+17+20+25+30+35+ 40
8 =185
8 =23.125
Coefficient of variation CV=( Standard deviation
mean )× 100 %= 11.50
23.125 ×100=49.7
a. 49.7
4a)What is the geometric mean for the following data set: 10, 10, 10, 100, 100, 1000, 10000?
Geometric mean=7
√10 ×10 ×10 ×100 ×100 ×1000 ×10000=7
√1014=102=100
a. 100
b) Calculate the age-group specific rate ratios for population A compared with population
B.
Population A
Age(Yrs) Population Number of Observed
deaths(O)
Age specific Rate per
1000 person years
Expected deaths(E)
15-29 1000 34 34 0.034×1000=34
30-49 4000 26 6.5 0.0065×4000=26
50+ 6000 120 20 0.02×6000=120
Total 11000 181 18.1 181

Population B
Age(Yrs) Population Number of Observed
deaths(O)
Age specific Rate per
1000 person years
Expected deaths(E)
15-29 5000 120 24 0.024×5000=120
30-49 2000 10 5 0.005×2000=10
50+ 1000 10 10 0.01×1000=10
Total 8000 140 17.5 140
Age specific rate ratio is calculated in the table below(using the above table for Population A and
Population B respectively)
Population A Population B
Age(Yrs) Rate per
1000 person
years
Rate per 1000
person years
Age specific Rate Ratio per 1000 person
=
Age specific Rate of A per 1000 persons
Age specific Rate of B per 1000 persons ×100000
15-29 34 24 141 667
30-49 6.5 5 130000
50+ 20 10 200000
Total 18.1 17.5 105848
c) Calculate the crude death rate ratio for population A compared with population B.
Crude death rate for population A = total deaths
population × 1000=
( 34+26 +121
1000+4000+ 6000 ) × 1000= 181
10000 × 1000
=18.1 deaths per 1000
Crude death rate for population B = total deaths
population × 1000=
( 120+10+10
5000+2000+1000 )×1000= 140
8000 ×1000
=17.5 deaths per 1000

Crude death rate ratio(population A compared with population B)=
Crude death rate for population A
Crude death rate for population B = 18.1
17.5
=1.034286
5. What is the standardized morbidity ratio (SMR) for Population B using Population A
as the standard?
Using the indirect method, a set of rates for population A is applied to each of the populations
being compared.
Population A
Age(Yrs) Populat
ion
Number of
Observed
deaths(O)
Rate per 1000
person years
Expected
deaths(E)
15-29 1000 34 34 0.034×1000=34
30-49 4000 26 6.5 0.0065×4000=26
50+ 6000 120 20 0.02×6000=120
Total 11000 181 18.1 181
Standardised Mortality
Rate= O
E ×100=181
181 × 100
¿ 100
Population B
Age(Yrs) Populat
ion
Number of
Observed
deaths(O)
Rate per 1000
person years
Expected
deaths(E)
15-29 5000 120 34 0.034×5000=170
30-49 2000 10 6.5 0.0065×2000=13
50+ 1000 10 20 0.02×1000=20
Total 8000 140 18.1 203
Standardised Mortality
Rate= O
E ×100=140
203 ×100
¿ 68.97
Standardized morbidity rate = observed number of deaths
Expected number of deaths × 100 %=68.97
100 ×100=68.97
Standardized morbidity ratio (SMR) for Population B using Population A as the
standard=68.97

6.Go to the web site http://www.census.gov/population/international/data/idb/country.php and
generate a population pyramid for Afghanistan, 2012. Is this population expansive, stationary, or
constrictive?
Afghanistan Population 2012
Age Group Male Female Total % of the total
Total 13 044 400 12 455 700 25 500 100 100
0–4 2 422 244 2 556 304 4 978 548 19.52
5–9 1 941 363 1 880 407 3 821 770 14.99
10–14 1 556 158 1 401 695 2 957 853 11.6
15–19 1 276 563 1 140 810 2 417 373 9.48
20–24 1 059 939 1 009 807 2 069 746 8.12
25–29 843 967 864 738 1 708 705 6.7
30–34 678 577 745 534 1 424 111 5.58
35–39 598 045 652 326 1 250 371 4.9
40–44 546 102 533 524 1 079 626 4.23
45–49 495 190 440 789 935 979 3.67
50–54 435 143 354 633 789 776 3.1
55–59 360 394 275 468 635 862 2.49
60–64 281 627 209 152 490 779 1.92
65–69 204 376 150 137 354 513 1.39
70–74 141 729 102 048 243 777 0.96
75–79 91 164 64 658 155 822 0.61
80–84 55 446 38 699 94 145 0.37
85+ 56 373 34 971 91 344 0.36
Afghanistan Population 2012
Age Group Total Population
in millions)
Male Female
(Population
in millions)
(Population
in millions)
Male
Population (%)
Female
population (%)
0–4 4. 978 548 2 .422 244 -2. 556 304 18.57 -20.52
5–9 3. 821 770 1. 941 363 -1. 880 407 14.88 -9.48
10–14 2. 957 853 1 .556 158 -1. 401 695 11.93 -11.25
15–19 2. 417 373 1 .276 563 -1. 140 810 9.79 -9.16
20–24 2. 069 746 1 .059 939 -1. 009 807 8.13 -8.11
25–29 1. 708 705 0.843 967 -0.864 738 6.47 -6.94
30–34 1. 424 111 0.678 577 -0.745 534 5.2 -5.99
35–39 1. 250 371 0.598 045 -0.652 326 4.58 -5.24
40–44 1. 079 626 0.546 102 -0.533 524 4.19 -4.28
45–49 0.935 979 0.495 190 -0.440 789 3.8 -3.54
50–54 0.789 776 0.435 143 -0.354 633 3.33 -2.85
55–59 0.635 862 0.360 394 -0.275 468 2.76 -2.21

60–64 0.490 779 0.281 627 -0.209 152 2.16 -1.68
65–69 0.354 513 0.204 376 -0.150 137 1.57 -1.21
70–74 0.243 777 0.141 729 -0.102 048 1.07 -0.8
75–79 0.155 822 0.091 164 -0.064 658 0.7 -0.5
80–84 0.094 145 0.055 446 -0.038 699 0.4 -0.3
85+ 0.091 344 0.056 373 -0.034 971 0.4 -0.3
Total 25 .500 100 13 .044 400 12 .455 700
This is expansive population. There is a higher percentage of younger people at the bottom with
the pyramid narrowing towards the top (i.e. each age cohort becoming smaller than the one just
below it).
7.Now generate a population pyramid for the Czech Republic, 2012, and indicate whether this
population is expansive, stationary, or constrictive.
Czech Republic Population 2012
Age Group Male Female Total % of the total
Total 5,250,205 5,424,518 10,674,723 100
0–14 831,150 786,984 1,618,134 15.16%
15–24 527,232 496,530 1,023,762 9.59%
25–54 2,403,333 2,276,261 4,679,594 43.84%
55–64 646,106 681,541 1,327,647 12.44%
60 and above 842,384 1,183,202 2,025,586 18.98%
Czech Republic Population 2012
Age Group Male Female Total Male % Female % % of the total
Total 5,250,205 5,424,518 10,674,72 49.18 50.82 100
0–4
10–14
20–24
30–34
40–44
50–54
60–64
70–74
80–84
-25 -20 -15 -10 -5 0 5 10 15 20 25
AFGHANISTAN POPULATION PYRAMID 2012
male%
female%
Percent
Age group

3
0–14 831,150 786,984 1,618,134 15.83 14.51 15.16
15–24 527,232 496,530 1,023,762 10.04 9.15 9.59
25–54 2,403,333 2,276,261 4,679,594 45.78 41.96 43.84
55–64 646,106 681,541 1,327,647 12.31 12.56 12.44
60 and above 842,384 1,183,202 2,025,586 16.04 12.81 18.98
This is stationary population. The population is not growing. This means that there is almost
equal percentages across the age cohorts.
8. What is another name for .
a. Joint probability-bivariate probability
b. Marginal probability-multivariate probability
0–14
15–24
25–54
55–64
60 and above
-60 -40 -20 0 20 40 60
Czech republic Population pyramid 2012
Male %
Female %
Age group