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Lobsters are crustaceans commonly found in the waters of the Atlantic Ocean off the North American coast between Maine and North Carolina. Researchers studied the weights of these creatures over a period of a few years. Some of the results are displayed in the table below. $$ \begin{array}{|c|c|} \hline \text { Year } & \text { Average Weight (kg) } \\ \hline 2005 & 0.43 \\ \hline 2006 & 0.41 \\ \hline 2007 & 0.37 \\ \hline 2008 & 0.43 \\ \hline 2009 & 0.38 \\ \hline \end{array} $$ The researchers hope to find the most commonly occurring lobster weight for the lobsters studied during the five-year period shown above. The researchers must calculate the Select... of the weights, which is You may use a calculator.

Step by step solution

01

Identify the dataset

We first need to identify the dataset of the average lobster weights for each year: Years: 2005, 2006, 2007, 2008, 2009 Weights: 0.43 kg, 0.41 kg, 0.37 kg, 0.43 kg, 0.38 kg

02

Calculate the frequency of each value

Next, we will calculate the frequency of occurrence of each value in the dataset. 0.43 kg: 2 times (2005, 2008) 0.41 kg: 1 time (2006) 0.37 kg: 1 time (2007) 0.38 kg: 1 time (2009)

03

Determine the mode

To find the most commonly occurring lobster weight, we must identify the value with the highest frequency. In this case, the weight 0.43 kg occurred the most (2 times) during the five-year period.

04

Answer the question

The most commonly occurring lobster weight for the lobsters studied during the five-year period is 0.43 kg.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mode in Statistics

The mode is a fundamental concept in statistics and is particularly useful when conducting data analysis. It relates to identifying the most frequently occurring number in a dataset. Finding the mode allows researchers to understand what is most common or typical within a set of values.
To identify the mode:

• List all numbers in the dataset.
• Count how often each number appears.
• The number with the highest count is the mode.

For example, in our dataset of average lobster weights, we calculated the frequency of each weight. The mode was identified as 0.43 kg since it occurred more frequently than the other weights. Understanding the mode can help in various practical situations, from inventory management to understanding consumer preferences.

Introduction to Data Analysis

Data analysis is the process of inspecting, cleaning, transforming, and modeling data to discover useful information. It enables informed decision-making in fields ranging from business to environmental research.
Data analysis involves several key steps:

• Collection: Gathering raw data from various sources.
• Cleaning: Removing inaccuracies and correcting errors.
• Exploration: Summarizing main characteristics through statistics like mean and median.
• Visualization: Using graphs and charts to represent data.

In the study of lobster weights, data analysis helped determine patterns and trends over time, providing valuable insights into how weights varied from year to year.

Understanding Frequency Distribution

Frequency distribution is a method to visualize how often different values occur in a dataset. It organizes data into a summary that shows the number of times each value appeared.
To create a frequency distribution:

• List each unique value in your dataset.
• Count how many times each value occurs 鈥� this is its frequency.
• Display these counts, often using a chart or graph.

In the lobster weight dataset, we calculated the frequency of each average weight per year. This frequency distribution enabled us to quickly see which weights appeared most often. Frequency distributions are invaluable for highlighting general trends and are often used in histograms to give a visual representation at a glance.