Question

12. The following frequency table contains the total number of deaths worldwide as a result of earthquakes from 2000 to 2012. Year Deaths 2000 231 2001 21,357 2002 11,685 2003 33,819 2004 228,802 2005 88,003 2006 6,605 2007 712 2008 88,011 2009 1,790 2010 320,120 2011 21,853 2012 768 Total 823,346 What is the relative frequency of deaths that occurred in 2003 or earlier? State your answer as a decimal, rounded to the nearest hundredth.

Answer 1

The relative frequency is the proportion of the absolute frequency of a category of the variable. You can calculate it as the quotient between the frequency and the sample size, following the formula:

`h_i=(f_i)/(n)`

hi represents the relative frequency of the i-category

fi represents the absolute frequency of the i-category

n is the sample size

"The relative frequency of the deaths that occurred in 2003 or earlier" refers to the accumulated relative frequency up to 2003. That is the sum of the relative frequency for 2000 plus the relative frequency for 2001, plus the relative frequency for 2002, plus the relative frequency for 2003.

To calculate this frequency you have to divide the accumulated frequency (sum of the number of deaths from years 2000 to 2003) up to 2003 by the total number of deaths registered.

`H_i=(F_i)/(n)`

The year 2003 is the fourth category of the variable so I will use subindex 4 to name the frequencies:

`\begin{gathered} H_4=(F_4)/(n) \\ H_4=(231+21357+11685+33819)/(823346) \\ H_4=(67092)/(823346) \\ H_4=0.081\approx0.08 \end{gathered}`

The relative frequency of deaths that occurred in 2003 or earlier is 0.08