2. Describing Data with Tables and Graphs
Frequency Distributions
3:06 minutesProblem 2.1.13
Textbook Question
use the given information about the data set and the number of classes to find the class width, the lower class limits, and the upper class limits.
min=17, range=118, 8 classes
Verified step by step guidance1
Step 1: Calculate the class width using the formula: \( \text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} \). Substitute the given values: \( \text{Range} = 118 \) and \( \text{Number of Classes} = 8 \). Round up the result to the nearest whole number if necessary.
Step 2: Determine the lower class limits. Start with the minimum value (\( \text{Min} = 17 \)) as the first lower class limit. Add the class width repeatedly to find the subsequent lower class limits.
Step 3: Determine the upper class limits. For each class, subtract 1 from the next lower class limit to find the upper class limit. For the last class, add the class width to the last lower class limit and subtract 1.
Step 4: Organize the lower and upper class limits into intervals. Each interval will be of the form \([\text{Lower Class Limit}, \text{Upper Class Limit}]\).
Step 5: Verify the intervals by ensuring that the total number of classes matches the given number (8 classes) and that the range of the data is covered completely.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Class Width
Class width is the difference between the upper and lower limits of a class interval in a frequency distribution. It is calculated by dividing the range of the data set by the number of classes. In this case, the range is 118, and with 8 classes, the class width can be determined by dividing 118 by 8, which helps in organizing the data into manageable intervals.
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Lower Class Limits
The lower class limit is the smallest value that can belong to a particular class interval in a frequency distribution. For the first class, it is typically the minimum value of the data set, which in this case is given as 17. Subsequent lower class limits can be found by adding the class width to the previous lower class limit, establishing a structured way to categorize the data.
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Upper Class Limits
The upper class limit is the largest value that can belong to a particular class interval. It is calculated by adding the class width to the lower class limit of each class. For example, if the lower class limit is 17 and the class width is calculated as 14.75, the upper class limit for the first class would be 31.75, allowing for a clear definition of the range of values within each class.
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