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Chapter 2: Problem 6

Find the class boundaries, midpoints, and widths for each class. $$ 125-131 $$

Short Answer

Expert verified
Boundaries: 124.5-131.5, Midpoint: 128, Width: 7.

Step by step solution

01

Identify Class Limits

Identify the lower and upper limits of the class. In this case, the lower limit is 125 and the upper limit is 131.
02

Calculate Class Boundaries

Class boundaries are found by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit. Therefore, the class boundaries are 124.5 to 131.5.
03

Compute Class Midpoint

The midpoint of a class is calculated as the average of the lower and upper class limits. Use the formula \( \text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \). Plug the values: \( \frac{125 + 131}{2} = 128 \).
04

Determine Class Width

The class width is the difference between the upper and lower boundaries. Use the formula \( \text{Width} = \text{Upper Boundary} - \text{Lower Boundary} \). Thus, the width is 131.5 - 124.5 = 7.

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Key Concepts

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

Class Midpoint
Understanding the concept of the class midpoint helps you find the central value of a particular data class. A class represents a range in a dataset, such as "125-131" in our example. The midpoint is essentially the average of the lowest and highest values.
To calculate the class midpoint, add together the lower and upper class limits and then divide the result by 2. The formula looks like this:
  • Midpoint = (Lower Limit + Upper Limit) / 2
For instance, using our class of 125-131, we perform the following calculation:
  • Midpoint = (125 + 131) / 2 = 128
The class midpoint can often be used to summarize data in a frequency distribution table, providing insight into where most values in that class are centered.
Class Width
The class width provides the span or range that each class covers within the data set. It tells you how large the intervals are between class boundaries.
To determine the class width, subtract the lower boundary from the upper boundary. Remember, the boundaries are different from limits, and they allow for a smooth transition between classes with no gaps.
  • Class Width = Upper Boundary - Lower Boundary
For our example class 125-131, the boundaries are calculated as 124.5 for the lower boundary and 131.5 for the upper boundary. Thus, the width becomes:
  • Class Width = 131.5 - 124.5 = 7
Having consistent class widths is crucial in histogram creation as they ensure the data is evenly spread.
Lower and Upper Limits
The lower and upper limits define the range that each class can cover in a dataset. These limits mark the start and end of a class.
For any given class, the lower limit is the smallest value, and the upper limit is the largest.
  • Lower Limit = Starting value of the class
  • Upper Limit = Ending value of the class
Taking our example again, for the class of 125-131:
  • Lower Limit = 125
  • Upper Limit = 131
Identifying these limits is the first step in constructing class boundaries and is essential for further calculations like midpoints and widths.

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Most popular questions from this chapter

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