To determine the actual lower and upper class limits, as well as the class marks for the given classes, we need to understand how class intervals work in statistics. Each class interval has a lower limit and an upper limit, and the actual limits are adjusted to account for the continuous nature of data. Let’s break this down step by step.
Understanding Class Intervals
Class intervals are ranges of values that group data points together. For example, the class interval 1.1-2.0 includes all values from 1.1 up to, but not including, 2.0. However, when we talk about actual limits, we need to consider the precision of the data.
Calculating Actual Limits
To find the actual lower and upper limits, we typically adjust the boundaries of each class interval by half of the smallest unit of measurement. In this case, since the intervals are in tenths, we will adjust by 0.05.
- For the class interval 1.1-2.0:
- Actual lower limit = 1.1 - 0.05 = 1.05
- Actual upper limit = 2.0 + 0.05 = 2.05
- For the class interval 2.1-3.0:
- Actual lower limit = 2.1 - 0.05 = 2.05
- Actual upper limit = 3.0 + 0.05 = 3.05
- For the class interval 3.1-4.0:
- Actual lower limit = 3.1 - 0.05 = 3.05
- Actual upper limit = 4.0 + 0.05 = 4.05
Finding Class Marks
The class mark (or midpoint) is calculated by averaging the actual lower and upper limits of each class. This gives us a representative value for the class.
- For the first class:
- Class mark = (1.05 + 2.05) / 2 = 1.55
- For the second class:
- Class mark = (2.05 + 3.05) / 2 = 2.55
- For the third class:
- Class mark = (3.05 + 4.05) / 2 = 3.55
Summary of Results
Now, let’s summarize the findings:
- Actual lower limits: 1.05, 2.05, 3.05
- Actual upper limits: 2.05, 3.05, 4.05
- Class marks: 1.55, 2.55, 3.55
Based on the calculations, the correct answer corresponds to option A. The actual lower and upper limits, along with the class marks, have been accurately determined. If you have any further questions or need clarification on any part of this process, feel free to ask!
