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Life Expectancy
Today, people live much longer than they did in yesteryears. The increase in the length of period that people live is mainly due to improved health care systems, enhanced technologies, and increased access to food. Life expectancy is simply a statistical measure of the average period that an organism is expected to live depending on its year of birth, current age, and its sex (Chetty et al, 2016). Since the life expectancy shows the remaining length of time that an organism is expected to live, this ratio can be calculated at any age.
Typically, the average life expectancy of the world has significantly changed when compared to that of the early 20th century. The improvement in the public health sector is primarily attributed to the increase in life expectancy in the late 20th century. This paper will evaluate the changes in life expectancy of people in the early 20th century against that of the late 20th century.
Calculations
The calculation of the life expectancy of individuals was done using the following formulas:
Example for “age class” 1-5 years.
Mortality rate, dx  dx=nx/Σnx
dx = 4/25= 0.16
Survivorship, lx = lx-1 – dx-1
lx= 1-0.16= 0.84
Mortality rate, qx = dx/ lx/ (time interval)
qx= 0.16/0.84/5= 0.0381
Average number of alive column, Lx = (lx+ lx+1) / 2
Lx = (0.84+0.68)/2= 0.76
Total years to be alive, Tx = (Lx x time interval) + Tx+1
Tx= (0.76*5)+ 39.3= 43.1
Life expectancy, ex = Tx/ lx
ex= 43.1/ 0.84= 51.310 years
Results and Discussions
In the early 20th century, the average life expectancy of a zero to a one-year male child was 44.02 years. At between 1 and five years, the life expectancy was 51.3 years. In 6-10 years, the life expectancy increased to 57.8 years. The low life expectancy rate at ages of five years and below shows that the rate of child mortality for kids below five years was high during this period (Schaefer & Prskawetz, 2013). Additionally, the lack of proper public healthcare system during this time may have resulted in the low life expectancy for men during this period. The highest life expectancy was for people between the ages of 6-10 years, which was 57.8 years, while the highest mortality rate was for those between 76 and 80 years and those below 5 years, which was 0.16.
Table 1
Male Life Expectancy in the Early 20th Century

 x nx dx lx qx Lx Tx ex Median Age age class Interval Males 0.5 0 1 4 0.16 1 0.16 0.92 44.02 44.02 3 1-5 5 4 0.16 0.84 0.038095 0.76 43.1 51.30952 8 6-10 5 1 0.04 0.68 0.011765 0.66 39.3 57.79412 13 11-15 5 0 0 0.64 0 0.64 36 56.25 18 16-20 5 0 0 0.64 0 0.64 32.8 51.25 23 21-25 5 0 0 0.64 0 0.64 29.6 46.25 28 26-30 5 1 0.04 0.64 0.0125 0.62 26.4 41.25 33 31-35 5 0 0 0.6 0 0.6 23.3 38.83333 38 36-40 5 0 0 0.6 0 0.6 20.3 33.83333 43 41-45 5 1 0.04 0.6 0.013333 0.58 17.3 28.83333 48 46-50 5 1 0.04 0.56 0.014286 0.54 14.4 25.71429 53 51-55 5 1 0.04 0.52 0.015385 0.5 11.7 22.5 58 56-60 5 2 0.08 0.48 0.033333 0.44 9.2 19.16667 63 61-65 5 1 0.04 0.4 0.02 0.38 7 17.5 68 66-70 5 0 0 0.36 0 0.36 5.1 14.16667 73 71-75 5 2 0.08 0.36 0.044444 0.32 3.3 9.166667 78 76-80 5 4 0.16 0.28 0.114286 0.2 1.7 6.071429 83 81-85 5 1 0.04 0.12 0.066667 0.1 0.7 5.833333 88 86-90 5 2 0.08 0.08 0.2 0.04 0.2 2.5 93 91-95 5 0 0 98 96-100 5 0 0 103 101-105 5 0 0 total 25

Female under the age of 1 had a mortality rate of 33.18 years in the early 20th century. This mortality increased slightly to 33.54 years for children between 1 and five years. It then fell again to 32.98 years for children between 6 and ten years. Finally, it increased to 35.14 years for children between age 11 and 15. Overall, these variations indicate that childhood mortality was high among females in the 20th century. The low life expectancy during this period may be partly attributed to inadequate public health systems during this time (World Health Organization [WHO], 2009). Additionally, there may have been cases of gender bias and discrimination in the treatment of the girl child. As a result, girls in this time had a lower life expectancy than men. The highest life expectancy was for people between the ages of 11-15 years, which was 35.1 years, while the highest mortality rate was for those between ages 6 and 10, which was 0.16.
Table 2
Female Life Expectancy in the Early 20th Century

 x nx dx lx qx Lx Tx ex Median Age age class Interval Females 0.5 0 1 1 0.04 1 0.04 0.98 33.18 33.18 3 1-5 5 3 0.12 0.96 0.025 0.9 32.2 33.54167 8 6-10 5 4 0.16 0.84 0.038095 0.76 27.7 32.97619 13 11-15 5 1 0.04 0.68 0.011765 0.66 23.9 35.14706 18 16-20 5 1 0.04 0.64 0.0125 0.62 20.6 32.1875 23 21-25 5 3 0.12 0.6 0.04 0.54 17.5 29.16667 28 26-30 5 0 0 0.48 0 0.48 14.8 30.83333 33 31-35 5 2 0.08 0.48 0.033333 0.44 12.4 25.83333 38 36-40 5 1 0.04 0.4 0.02 0.38 10.2 25.5 43 41-45 5 2 0.08 0.36 0.044444 0.32 8.3 23.05556 48 46-50 5 2 0.08 0.28 0.057143 0.24 6.7 23.92857 53 51-55 5 0 0 0.2 0 0.2 5.5 27.5 58 56-60 5 0 0 0.2 0 0.2 4.5 22.5 63 61-65 5 1 0.04 0.2 0.04 0.2 3.5 17.5 68 66-70 5 1 0.04 0.16 0.05 0.14 2.5 15.625 73 71-75 5 0 0 0.12 0 0.12 1.8 15 78 76-80 5 1 0.04 0.12 0.066667 0.12 1.2 10 83 81-85 5 1 0.04 0.08 0.1 0.06 0.6 7.5 88 86-90 5 0 0 0.04 0 0.04 0.3 7.5 93 91-95 5 1 0.04 0.04 0.2 0.02 0.1 2.5 98 96-100 5 0 0 0 103 101-105 5 0 0 total 25

In the late 20th century, the life expectancy of a male child who was less than one year was 80.167 years. At between the ages of 1 and 5, the life expectancy decreased to 79.167 years. The decrease in expected life expectancy shows that during this period, male children below the ages of five years had a high chance of reaching six years. This increase in life expectancy for male children compared to that in the early 20th century may be due to improvement in public health management in the country (Schaefer & Prskawetz, 2013). Additionally, cases of increased medical treatment and better nutrition may have led to this increase. The highest life expectancy was for people less than 1 year, which was 80.17 years, while the highest mortality rate was for those between 76 and 85 years, which was 0.25.
Table 3
Life Expectancy of Male in the Late 20th Century

 x dx lx qx Lx Tx ex Median Age age class Males 0.5 0 0 1 0 1 80.16667 80.16667 3 1-5 0 1 0 1 79.16667 79.16667 8 6-10 0 1 0 1 74.16667 74.16667 13 11-15 0 1 0 1 69.16667 69.16667 18 16-20 0 1 0 1 64.16667 64.16667 23 21-25 0 1 0 1 59.16667 59.16667 28 26-30 0 1 0 1 54.16667 54.16667 33 31-35 0 1 0 1 49.16667 49.16667 38 36-40 0 1 0 1 44.16667 44.16667 43 41-45 0 1 0 1 39.16667 39.16667 48 46-50 0 1 0 1 34.16667 34.16667 53 51-55 2 0.083333 1 0.016667 0.958333 29.16667 29.16667 58 56-60 2 0.083333 0.916667 0.018182 0.875 24.375 26.59091 63 61-65 1 0.041667 0.833333 0.01 0.8125 20 24 68 66-70 1 0.041667 0.791667 0.010526 0.770833 15.9375 20.13158 73 71-75 1 0.041667 0.75 0.011111 0.729167 12.08333 16.11111 78 76-80 6 0.25 0.708333 0.070588 0.6875 8.4375 11.91176 83 81-85 6 0.25 0.666667 0.075 0.541667 5 7.5 88 86-90 2 0.083333 0.416667 0.04 0.291667 2.291667 5.5 93 91-95 2 0.083333 0.166667 0.1 0.125 0.833333 5 98 96-100 1 0.041667 0.083333 0.1 0.041667 0.208333 2.5 103 101-105 0 0 total 24

In the late 20th century, the female life expectancy for children below the age of 1 was 88.403 years. The life expectancy rate for between the age 1 and 5 decreased to 87.403 years. This decrease indicates that during this period, the mortality rate for female children below age five was low. The decline in mortality rate may be attributed to improved public health during, proper nutrition, and equality in the treatment of male and female children (Ohlhorst et al., 2013). Noteworthy, the life expectancy of women during this period was higher than that of men. This increase may partly be due to fewer women engaging in high-risk professions such as military and construction than men. The highest life expectancy was for people less than 1 year, which was 88.4 years, while the highest mortality rate was for those between 81 and 95 years and also those between ages 91-95, which was 0.192.
Table 4
Life Expectancy of Female in the Late 20th Century

 x dx lx qx Lx Tx ex Median Age age class Females 0.5 0 0 1 0 1 88.40385 88.40385 3 1-5 0 1 0 1 87.40385 87.40385 8 6-10 0 1 0 1 82.40385 82.40385 13 11-15 0 1 0 1 77.40385 77.40385 18 16-20 0 1 0 1 72.40385 72.40385 23 21-25 0 1 0 1 67.40385 67.40385 28 26-30 0 1 0 1 62.40385 62.40385 33 31-35 1 0.038462 1 0.007692 1 57.40385 57.40385 38 36-40 0 1 0 1 52.40385 52.40385 43 41-45 1 0.038462 1 0.007692 1 47.40385 47.40385 48 46-50 0 1 0 1 42.40385 42.40385 53 51-55 1 0.038462 1 0.007692 0.980769 37.40385 37.40385 58 56-60 0 0.961538 0 0.961538 32.5 33.8 63 61-65 0 0.961538 0 0.961538 27.69231 28.8 68 66-70 3 0.115385 0.961538 0.024 0.961538 22.88462 23.8 73 71-75 1 0.038462 0.961538 0.008 0.903846 18.07692 18.8 78 76-80 4 0.153846 0.846154 0.036364 0.826923 13.55769 16.02273 83 81-85 5 0.192308 0.807692 0.047619 0.730769 9.423077 11.66667 88 86-90 4 0.153846 0.653846 0.047059 0.557692 5.769231 8.823529 93 91-95 5 0.192308 0.461538 0.083333 0.384615 2.980769 6.458333 98 96-100 1 0.038462 0.307692 0.025 0.211538 1.057692 3.4375 103 101-105 0 0.115385 total 26

Finally, the sampling method used in this paper could have a sampling error. The sample of only about 25 individuals for each analysis is so small to predict the life expectancy of an entire population correctly. Since millions of people have died and lived throughout the whole of the twentieth century, a sample of about two thousand people would have been more appropriate.
In conclusion, the paper has shown that the average life expectancy for both men and women has increased throughout history. In the early 20th century, both men and women had a low life expectancy, of less than 45 years. Currently, the life expectancy for both sexes has almost doubled.

References
Chetty, R., Stepner, M., Abraham, S., Lin, S., Scuderi, B., Turner, N…, Cutler, D. (2016). The association between income and life expectancy in the United States, 2001–2014. The Journal of the American Medical Association, 315(16), 1750-1766.
Ohlhorst, S., Russel, R., Bier, D., Klurfield, D., Li, Z., Mein, J…, Konopka, E. (2013). Nutrition research to affect food and a healthy life span. The American Journal of Clinical Nutrition, 98(2), 620-625.
Schaefer, A., & Prskawetz, A. (2013). Pollution, public health care, and life expectancy when inequality matters. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-13-015
World Health Organization [WHO]. (2009). Women and health: Today’s evidence tomorrow’s agenda. Geneva, Switzerland: WHO Press.

Appendix 1
Survivorship Curve
Male Life Expectancy Early 20th Century

Appendix 2
Survivorship Curve
Female Life Expectancy Early 20th Century

Appendix 3
Survivorship Curve
Male Life Expectancy Late 20th Century

Appendix 4
Survivorship Curve
Male Life Expectancy Late 20th Century

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