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Chapter 2: Problem 5

For Exercises 5鈥�8, find the class boundaries, midpoints, and widths for each class. 58鈥�62

Short Answer

Expert verified
Class boundaries: 57.5 and 62.5; Midpoint: 60; Width: 5.

Step by step solution

01

Identify the Class Interval

The class interval is given as 58-62. This means our class starts at 58 and ends at 62.
02

Calculate the Class Width

The class width is calculated by subtracting the lower class limit from the upper class limit and then adding 1. Thus, the class width is \[62 - 58 + 1 = 5.\]
03

Determine the Class Boundaries

Class boundaries are calculated by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class limit. So, the class boundaries are \[57.5\text{ and } 62.5.\]
04

Calculate the Class Midpoint

The class midpoint is the average of the lower class limit and the upper class limit. It is calculated as follows:\[\frac{58+62}{2} = 60.\]

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Key Concepts

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

Understanding Class Boundaries
Class boundaries are an essential part of organizing data in statistics. They help us define the limits of a class interval that includes boundary values between subsequent classes. This is important to ensure that there is no overlap or gap between classes.

For example, in the class interval 58-62, to find the class boundaries, we need to think about the "space" around the class limits. Here's how we adjust the class limits to find the boundaries:
  • Subtract 0.5 from the lower class limit. In this case, 58 minus 0.5 gives us 57.5.
  • Add 0.5 to the upper class limit. Here, 62 plus 0.5 results in 62.5.
Therefore, the class boundaries are 57.5 and 62.5. These boundaries ensure there's no gap or overlap between this class and any adjacent class.
Exploring Class Midpoints
The class midpoint is basically the "center" of a class interval and represents the average value of the class limits. The midpoint gives us an idea of the typical values within the class interval.

To find the class midpoint, you simply add the lower and upper class limits together and divide by 2. For our example of the class interval 58-62:
  • Add the lower limit, 58, to the upper limit, 62, getting a sum of 120.
  • Then, divide this sum by 2. So, 120 divided by 2 results in a midpoint of 60.
The class midpoint of 60 tells us about the balancing point of the class interval and is especially useful in various statistical analyses.
Calculating Class Width
Class width is a measure of how "wide" each class interval is, providing insight into the spread of the classes.

To find the class width, you subtract the lower class limit from the upper class limit and then add 1. This adjustment accounts for the range of values that the class interval encompasses.
  • For our class interval 58-62, subtract 58 from 62, which equals 4.
  • Now, add 1 to this result, making the class width 5.
This class width of 5 indicates the number of units within this class interval, thereby helping to standardize comparisons between classes in statistical datasets.

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