Question

An investigation compiled information about recent nonmilitary plane crashes (www. planecrashinfo.com). The causes, to the extent that they could be determined, are summarized in the table. $$ \begin{array}{l|c} \text { Cause } & \text { Percent } \\ \hline \text { Pilot error } & 40 \\ \text { Other human error } & 5 \\ \text { Weather } & 6 \\ \text { Mechanical failure } & 14 \\ \text { Sabotage } & 6 \end{array} $$ a) Is it reasonable to conclude that the weather or mechanical failures caused only about \(20 \%\) of recent plane crashes? b) In what percent of crashes were the causes not determined? c) Create an appropriate display for these data.

Short answer

a) Yes, it is about 20%. b) 29% were not determined. c) Use a pie chart showing each cause's percentage.

Step-by-step solution

Combine Percentages for Weather and Mechanical Failures

To determine if it is reasonable to conclude that the weather or mechanical failures caused only about 20% of recent plane crashes, we first add the percentages for weather and mechanical failures. Weather: 6% Mechanical Failure: 14% Add these together: 6% + 14% = 20%.

Calculate Undetermined Causes

To find the percentage of crashes where the causes were not determined, first add all the known percentages and then subtract from 100. Pilot Error: 40% Other Human Error: 5% Weather: 6% Mechanical Failure: 14% Sabotage: 6% Sum of known causes: 40% + 5% + 6% + 14% + 6% = 71% Percentage not determined: 100% - 71% = 29%.

Create Display of Data

To visually display the data, create a pie chart where each section represents a different cause type by percentage. Label each section as follows: - Pilot Error (40%) - Other Human Error (5%) - Weather (6%) - Mechanical Failure (14%) - Sabotage (6%) - Not Determined (29%) Ensure the size of each section corresponds proportionally to the percentages.

Key concepts

Probability and Plane Crashes

Probability is a fundamental concept in data analysis, often used to understand the likelihood of events. In the context of plane crashes, it helps us determine how likely certain causes are to result in an incident.

When we say that the weather or mechanical failures accounted for about 20% of plane crashes, we're using probability. By adding the percentage caused by weather (6%) to that caused by mechanical failures (14%), we conclude that there's a 20% probability that a crash was due to either of these factors.

This calculation is straightforward when you have fixed, discrete categories summed to form part of a whole. These probabilities are extit{based on historical data} and can give us insight into potential future risks in similar conditions.

Understanding Statistics in Crash Data

Statistics provides us with tools to collect, analyze, and interpret data, making it invaluable in determining the causes of plane crashes. In this investigation, statistics help us quantify different causes.

For example, by calculating the percentage of crashes where the cause wasn't determined (29%), we allow for better risk management and resource allocation. With a known total of determined causes at 71%, we can determine the undetermined causes by subtracting from 100%.

Such statistical analysis allows airlines, regulators, and policymakers to prioritize investigations and interventions based on available data.

Graphical Representation of Crash Causes

Graphical representations like pie charts turn numerical data into visual information, making it easier to understand complex datasets. Displaying the causes of plane crashes as a pie chart allows for immediate recognition of the different cause proportions.

Each slice of the pie chart represents a cause and is proportional to its percent contribution to the whole. For example, the largest slice, representing pilot error, will visually emphasize the most common cause of plane crashes (40%).

In contrast, the slice for 'undetermined causes' (29%) shows that a significant portion of the data lacks specific causes, highlighting areas for improved data collection.

Quantitative Reasoning and Data Interpretation

Quantitative reasoning facilitates problem-solving and decision-making based on numerical data. It allows us to synthesize information, draw conclusions, and make predictions essential for safety improvements in aviation.

For instance, the quantitative reasoning applied in combining the weather and mechanical failures shows a direct numerical strategy to understanding complex data.

Similarly, calculating undetermined causes requires adding and subtracting percentages to interpret the implication of missing data effectively, influencing how resources might be directed towards future investigations.