91Ó°ÊÓ

Consider the following data on types of health complaint ( \(J\) = joint swelling, \(F\) = fatigue, \(B=\) back pain, \(M=\) muscle weakness, \(\mathrm{C}=\) coughing, \(\mathrm{N}=\) nose running/ irritation, \(O=\) other) made by tree planters. Obtain frequencies and relative frequencies for the various categories, and draw a histogram. (The data is consistent with percentages given in the article "Physiological Effects of Work Stress and Pesticide Exposure in Tree Planting by British Columbia Silviculture Workers," Ergonomics, 1993: 951-961.) \(\begin{array}{llllllllllllll}\mathrm{O} & \mathrm{O} & \mathrm{N} & \mathrm{J} & \mathrm{C} & \mathrm{F} & \mathrm{B} & \mathrm{B} & \mathrm{F} & \mathrm{O} & \mathrm{J} & \mathrm{O} & \mathrm{O} & \mathrm{M} \\ \mathrm{O} & \mathrm{F} & \mathrm{F} & \mathrm{O} & \mathrm{O} & \mathrm{N} & \mathrm{O} & \mathrm{N} & \mathrm{J} & \mathrm{F} & \mathrm{J} & \mathrm{B} & \mathrm{O} & \mathrm{C} \\ \mathrm{J} & \mathrm{O} & \mathrm{J} & \mathrm{J} & \mathrm{F} & \mathrm{N} & \mathrm{O} & \mathrm{B} & \mathrm{M} & \mathrm{O} & \mathrm{J} & \mathrm{M} & \mathrm{O} & \mathrm{B} \\ \mathrm{O} & \mathrm{F} & \mathrm{J} & \mathrm{O} & \mathrm{O} & \mathrm{B} & \mathrm{N} & \mathrm{C} & \mathrm{O} & \mathrm{O} & \mathrm{O} & \mathrm{M} & \mathrm{B} & \mathrm{F} \\\ \mathrm{J} & \mathrm{O} & \mathrm{F} & \mathrm{N} & & & & & & & & & & \end{array}\)

Step by step solution

01

Count Frequency of Each Category

To find the frequency for each category, we need to count how many times each health complaint appears in the data. Let's count the occurrences:- Joint swelling (\(J\)): 10 times- Fatigue (\(F\)): 8 times- Back pain (\(B\)): 7 times- Muscle weakness (\(M\)): 4 times- Coughing (\(C\)): 2 times- Nose running/irritation (\(N\)): 5 times- Other (\(O\)): 24 times

02

Calculate Total Number of Observations

To compute relative frequencies, we need the total number of observations. Sum the frequencies obtained in the previous step:\[10 + 8 + 7 + 4 + 2 + 5 + 24 = 60\]The total number of observations is 60.

03

Calculate Relative Frequencies

Relative frequency is calculated by dividing the frequency of each category by the total number of observations. Let's compute:- \(J\): \(\frac{10}{60} = 0.1667\)- \(F\): \(\frac{8}{60} = 0.1333\)- \(B\): \(\frac{7}{60} = 0.1167\)- \(M\): \(\frac{4}{60} = 0.0667\)- \(C\): \(\frac{2}{60} = 0.0333\)- \(N\): \(\frac{5}{60} = 0.0833\)- \(O\): \(\frac{24}{60} = 0.4000\)

04

Draw a Histogram

The histogram visually represents the frequencies of the health complaints. Arrange the categories on the x-axis and the frequency counts on the y-axis. Draw bars for each category using their frequency counts calculated: - Create a bar for each health complaint.- Heights should correspond to the following frequencies: \(J: 10\), \(F: 8\), \(B: 7\), \(M: 4\), \(C: 2\), \(N: 5\), \(O: 24\).- Ensure the x-axis is labeled with health complaint codes and the y-axis with frequency (or relative frequency if chosen).

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Key Concepts

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

Frequency Distribution

Frequency distribution is a way to organize data to see how often different categories appear. In our exercise, the data consists of various health complaints reported by tree planters, like joint swelling (J), fatigue (F), and others. Each complaint represents a different category. To create a frequency distribution, you start by counting how many times each category appears in your data set.

• For example, joint swelling was reported 10 times.
• Fatigue showed up 8 times.

Simply make a list showing each health complaint alongside its frequency, as seen above. This structure helps to quickly identify which health problems are the most common and the least common among the tree planters.

Relative Frequency

Relative frequency offers a deeper insight into data by showing what portion of the total each category represents. It is the frequency of a category divided by the sum of all frequencies. For instance, if you want to know how often joint swelling occurred relative to all complaints, you would calculate it by dividing the number of joint swelling instances by the total complaints made.
The formula for relative frequency is:\[\text{Relative Frequency} = \frac{\text{Frequency of category}}{\text{Total frequency}}\]

• Calculating for joint swelling, it is \(\frac{10}{60} = 0.1667\).
• This means that joint swelling accounts for approximately 16.67% of all cases.

This relative frequency helps in understanding the prominence of each complaint, aiding in necessary health measures or prioritizations.

Histogram

A histogram is a visual tool to represent the frequency or relative frequency of data across different categories. Like a bar graph, each bar's height shows the frequency for a given category. For our data, creating a histogram involves arranging health complaints on the x-axis and their counts on the y-axis.

• Bar heights show actual frequencies, such as joint swelling occurring 10 times.

This visual representation allows one to quickly see which health complaints are more common. In the case of relative frequency, you can use percentage bars if you find it more intuitive. It bridges the gap between raw data and a comprehensive overview, making it easier to digest.

Data Analysis

Data analysis is the process of cleaning, transforming, and modeling data to discover useful information and make informed decisions. In our exercise, by organizing and analyzing the data on health complaints using frequency distributions and histograms, you can extract meaningful insights.

• Identify which complaints are most frequent, like 'Other' or joint swelling.
• Consider interventions or support mechanisms for the most common complaints.

By analyzing relative frequencies, you highlight the significance of less frequent complaints, ensuring they aren't overlooked when evaluating health measures. Data analysis in this context supports effective decision-making and highlights areas that might require more attention.