I need to find the class midpoint, boundaries and class with for the following problem
Tar Cigarette Filter Frequency
2-5 2
6-9 2
10-13 6
14-17 15
I did the midpoint and boundaries
3.5 5.5
7.5 9.5
11.5 13.5
15.5 17.5
But for the width I got an answer of 1.25 can someone please let me know if I have the problem correct.
Example:
Class limit is 11 - 20
Class midpoint is (11 + 20)/2 = 15.5
Class boundary is 10.5 - 20.5 (.5 below and .5 above)
Class width is 20.5 - 10.5 = 10
I hope this example will help.
No it didn't I just wanted to know if I was correct that's all thanks for nothing mathguru
The example was meant to show you how to do the problem without doing it for you.
You are correct on the midpoints.
You are missing the lower class boundaries.
You are missing the class widths for each class.
To find the class midpoint, boundaries, and width for a grouped frequency distribution, you need to follow a specific procedure.
1. Determine the range of the data: The range is the difference between the highest and lowest observed values. In this case, the lowest observed value is 2, and the highest observed value is 17. Therefore, the range is 17 - 2 = 15.
2. Decide on the number of classes or intervals: There is no fixed rule for deciding the number of classes, but it is generally recommended to have between 5 and 20 classes. In this case, there are four data points, so having four classes may not be ideal. Let's choose 5 classes for better representation.
3. Calculate the width: The width of each class is determined by dividing the range by the number of classes. In this case, the width would be 15 / 5 = 3.
4. Determine the lower class limits: The lower class limits represent the lowest values for each class. The first class will start at the lowest observed value, which is 2. From there, you can add the width to get the lower limit for each subsequent class. So the lower class limits would be 2, 5, 8, 11, and 14.
5. Find the upper class limits: The upper class limits represent the highest values for each class. To find these, subtract 0.5 from the lower class limit of the next class. For example, the first class has a lower limit of 2 and a width of 3, so the upper limit of the first class is 2 + 3 - 0.5 = 4.5. Similarly, the upper limits for the other classes would be 7.5, 10.5, 13.5, and 16.5.
6. Calculate the class midpoints: The class midpoint is the average of the lower and upper class limits. So, for each class, you can add the lower and upper limits and divide by 2. The class midpoints would be 3.25, 6.25, 9.25, 12.25, and 15.25.
7. Determine the class boundaries: The class boundaries help represent the true range of the data. To find them, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. The class boundaries would be 1.5-5.5, 4.5-8.5, 7.5-11.5, 10.5-14.5, and 13.5-17.5.
Based on the above steps, the correct class midpoints, boundaries, and width are:
- Midpoints: 3.25, 6.25, 9.25, 12.25, and 15.25.
- Boundaries: 1.5-5.5, 4.5-8.5, 7.5-11.5, 10.5-14.5, and 13.5-17.5.
- Width: 3.
From your provided values, it seems that the class midpoints and class boundaries are slightly off. The correct values are as mentioned above.