Question

Table 1.26 contains the total number of deaths worldwide as a result of earthquakes from 2000 to 2012.

Use Table 1.26 to answer the following questions.

1. What is the proportion of deaths between 2007 and 2012?
2. What percent of deaths occurred before 2001?
3. What is the percent of deaths that occurred in 2003 or after 2010?
4. What is the fraction of deaths that happened before 2012?
5. What kind of data is the number of deaths?
6. Earthquakes are quantified according to the amount of energy they produce (examples are 2.1, 5.0, 6.7). What type of data is that?
7. What contributed to the large number of deaths in 2010? In 2004? Explain.

Short answer

1. The proportion of deaths between the years 2007 and 2012 is 0.5242.
2. 0.03% of deaths occurred before 2001.
3. The percentage of deaths that occurred in 2003 or after 2010 is 6.86%.
4. The fraction of deaths that happened before 2012 is $\frac{823088}{823856}$.
5. The number of deaths is a quantitative discrete type of data.
6. The given variable, "Earthquakes are quantified according to the amount of energy they produce", is a quantitative continuous type of data.
7. The underwater earthquakes that triggered big tsunamis resulted in large deaths in 2010 and 2004.

Step-by-step solution

Part (a) Step 1: Given Information

A table containing the total number of deaths worldwide as a result of earthquakes from 2000 to 2012 is given as follows:

Part (a) Step 2: Calculation

The proportion of deaths between the years 2007 and 2012 can be given by the below formula:

$\mathrm{Proportion}\mathrm{of}\mathrm{deaths}\mathrm{between}2007\mathrm{and}2012=\frac{\mathrm{sum}\mathrm{of}\mathrm{deaths}\mathrm{occurred}\mathrm{between}2007\mathrm{and}2012}{\mathrm{Total}\mathrm{deaths}}$

The sum of deaths that occurred between 2007 and 2012 is the sum of deaths in the years 2008, 2009, 2010, and 2011.

Hence, by substituting the values from the given table in the above equation, we get,

$$\begin{gathered} \mathrm{Proportion}\mathrm{of}\mathrm{deaths}\mathrm{between}2007\mathrm{and}2012=\frac{88011+1790+320120+21953}{823856} \\ \mathrm{Proportion}\mathrm{of}\mathrm{deaths}\mathrm{between}2007\mathrm{and}2012=\frac{431874}{823856} \\ \mathrm{Proportion}\mathrm{of}\mathrm{deaths}\mathrm{between}2007\mathrm{and}2012=0.5242 \end{gathered}$$

Part (a) Step 3: Final answer

Hence, the proportion of deaths between 2007 and 2012 is calculated to be 0.5242.

Part (b) Step 1: Given Information

A table containing the total number of deaths worldwide as a result of earthquakes from 2000 to 2012 is given as follows:

Part (b) Step 2: Calculation

The percentage of deaths that occurred before 2001 can be given by the following formula:

$\mathrm{Percent}\mathrm{deaths}\mathrm{before}2001=\frac{\mathrm{sum}\mathrm{of}\mathrm{deaths}\mathrm{before}2001}{\mathrm{total}\mathrm{deaths}}\times 100$

By substituting the values from the given table in the above formula, we get,

$$\begin{gathered} \mathrm{Percent}\mathrm{deaths}\mathrm{before}2001=\frac{231}{823856}\times 100 \\ \mathrm{Percent}\mathrm{deaths}\mathrm{before}2001=0.03\% \end{gathered}$$

Part (b) Step 3: Final answer

Hence, the percent of deaths that occurred before 2001 is calculated to be 0.03%

Part (c) Step 1: Given Information

A table containing the total number of deaths worldwide as a result of earthquakes from 2000 to 2012 is given as follows:

Part (c) Step 2: Calculation

The percentage of deaths that occurred in 2003 or after 2010 can be given by the following formula:

$\mathrm{Percentage}\mathrm{of}\mathrm{deaths}\mathrm{occurred}\mathrm{in}2003\mathrm{or}\mathrm{after}2010=\frac{\mathrm{Sum}\mathrm{of}\mathrm{deaths}\mathrm{in}2003\mathrm{and}\mathrm{after}2010}{\mathrm{Total}\mathrm{deaths}}$

The sum of deaths after 2010 is the sum of deaths in the years 2011 and 2012.

Hence, by substituting the values from the given data table in the above equation, we get,

$$\begin{gathered} \mathrm{Percentage}\mathrm{of}\mathrm{deaths}\mathrm{occurred}\mathrm{in}2003\mathrm{or}\mathrm{after}2010=\frac{33819+21953+768}{823856}\times 100 \\ \mathrm{Percentage}\mathrm{of}\mathrm{deaths}\mathrm{occurred}\mathrm{in}2003\mathrm{or}\mathrm{after}2010=\frac{56540}{823856}\times 100 \\ \mathrm{Percentage}\mathrm{of}\mathrm{deaths}\mathrm{occurred}\mathrm{in}2003\mathrm{or}\mathrm{after}2010=6.86\% \end{gathered}$$

Part (c) Step 3: Final answer

Hence, the percentage of deaths that occurred in 2003 or after 2010 can be calculated as 6.86%.

Part (d) Step 1: Given Information

A table containing the total number of deaths worldwide as a result of earthquakes from 2000 to 2012 is given as follows:

Part (d) Step 2: Calculation

The fraction of deaths that occurred before 2012 can be given as:

$\mathrm{Fraction}\mathrm{of}\mathrm{deaths}\mathrm{before}2012=\frac{\mathrm{Sum}\mathrm{of}\mathrm{deaths}\mathrm{before}2012}{\mathrm{Total}\mathrm{deaths}}$

Hence, by substituting the values from the given data in the above equation, we get,

$$\begin{gathered} \mathrm{Fraction}\mathrm{of}\mathrm{deaths}\mathrm{before}2012=\frac{231+21357+11685+33819+228802+88003+6605+712+88011+1790+320120+21953}{823856} \\ \mathrm{Fraction}\mathrm{of}\mathrm{deaths}\mathrm{before}2012=\frac{823088}{823856} \end{gathered}$$

Part (d) Step 3: Final answer

Hence, the fraction of deaths that happened before 2012 is calculated as$\frac{823088}{823856}$.

Part (e) Step 1: Concept Introduction

A variable is a type of data and it can be of qualitative, quantitative discrete, or quantitative continuous type based on the given data in statistics.

Part (e) Step 2: Explanation

A qualitative variable is one that assigns categories to the variable as a value. The variable gender, for example, is a qualitative variable since it assigns male or female categories to the variable gender.

A quantitative discrete variable is one that assigns values that has a definite number of values. Quantitative discrete variables include things like the number of students in a class and the number of days in a month.

A quantitative continuous variable is one that assigns values that have an infinite number of possible values. A quantitative continuous variable is, for example, the weight of students in a class or the distance between two cities.

"Number of deaths" can have certain values up to the total population, hence, it is a quantitative discrete type of data.

Part (e) Step 3: Final answer

Hence, the variable "number of deaths" is a quantitative discrete type of data.

Part (f) Step 1: Concept Introduction

A variable is a type of data and it can be of qualitative, quantitative discrete, or quantitative continuous type based on the given data in statistics.

Part (f) Step 2: Explanation

A qualitative variable is one that assigns categories to the variable as a value. The variable gender, for example, is a qualitative variable since it assigns male or female categories to the variable gender.

A quantitative discrete variable is one that assigns values that has a definite number of values. Quantitative discrete variables include things like the number of students in a class and the number of days in a month.

A quantitative continuous variable is one that assigns values that have an infinite number of possible values. A quantitative continuous variable is, for example, the weight of students in a class or the distance between two cities.

As per the given information, "Earthquakes are quantified according to the amount of energy they produce (examples are 2.1, 5.0, 6.7)", it can take any possible value between two values, hence, it is a quantitative continuous type of data.

Part (f) Step 3: Final answer

Hence, "Earthquakes are quantified according to the amount of energy they produce (examples are 2.1, 5.0, 6.7)" is a quantitative continuous type of data.

Part (g) Step 1: Given Information

A table containing the total number of deaths worldwide as a result of earthquakes from 2000 to 2012 is given as follows:

Part (g) Step 2: Explanation

According to the available data, the number of deaths in 2010 was 320,120, while the number of deaths in 2004 was 228,802. When compared to other years, the years 2010 and 2004 have the highest number of deaths. The reason for the high number of deaths is that underwater earthquakes in 2010 and 2004 created major tsunamis, resulting in a large number of deaths in those two years.

Part (g) Step 3: Final answer

Large numbers of people died in 2010 and 2004 as a result of underwater earthquakes that generated large tsunamis.