2. Describing Data with Tables and Graphs
Frequency Distributions
2:53 minutesProblem 2.c.2
Textbook Question
In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B
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Frequency Distribution For the frequency distribution from Exercise 1, find the following.
a. Class limits of the first class
b. Class boundaries of the first class
c. Class midpoint of the first class
Verified step by step guidance1
Step 1: Identify the data range and the number of classes. The data range is the difference between the maximum and minimum values in the dataset. Divide this range by the number of classes to determine the class width. Round up to the nearest whole number if necessary.
Step 2: Determine the class limits for the first class. The lower class limit of the first class is the smallest value in the dataset. Add the class width to the lower limit to find the upper class limit of the first class.
Step 3: Calculate the class boundaries for the first class. Subtract 0.5 from the lower class limit to find the lower class boundary, and add 0.5 to the upper class limit to find the upper class boundary.
Step 4: Compute the class midpoint for the first class. The class midpoint is the average of the lower and upper class limits. Use the formula: .
Step 5: Verify your results by ensuring that the class boundaries and midpoint align with the data distribution and the class width is consistent across all classes.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Frequency Distribution
A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into classes or intervals, allowing for easier analysis of patterns and trends. In the context of the question, understanding frequency distributions is essential for determining class limits, boundaries, and midpoints, which are foundational for statistical analysis.
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Class Limits
Class limits define the range of values that fall within a specific class in a frequency distribution. The lower class limit is the smallest value in the class, while the upper class limit is the largest. Identifying class limits is crucial for accurately categorizing data points and ensuring that all values are accounted for in the analysis.
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Class Midpoint
The class midpoint is the value that lies halfway between the upper and lower limits of a class in a frequency distribution. It is calculated by averaging the class limits and serves as a representative value for that class. Understanding class midpoints is important for summarizing data and performing further statistical calculations, such as finding the mean.
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