QUOTE(watdatlinna @ Jan 17 2017, 09:43 PM)
Thank you for your time and effort to answer my question. How about the scores for a test? Can we take negative boundaries?
It depends on what the question is asking about. You'd need to take negative class boundaries if the data set allows to be in negative values, even in a test. Are you in secondary school? It won't be this tricky most of the time especially in SPM level, but still be careful.
QUOTE(watdatlinna @ Jan 17 2017, 09:52 PM)
If the class boundary is - 0.5 – 4.5, the mid-value is 2 whether we use the limits [(0+4)/2] or boundaries [- 0.5 + 4.5)/2] in calculating the mid-value of a class interval that is important when we want to find the mean of a set of data.
If the class boundary is 0 – 4.5, the mid-value is 2.25. As a result, the mean will be different. So, this raises a question: What do we use in calculating mid-value, class limits or class boundaries, so that the mean is unaffected?
What is your opinion?
To calculate the mean value from a grouped data, in which the data is already grouped into class intervals, the mean calculated is only an estimation.
To get the midpoints, we use the upper and lower limits of the class intervals, not the class boundaries. The boundaries, as stated before, are just to separate the intervals and to serve as boundaries literally. The limits, however, define the width of each class interval. The midpoints that we want to know are also a part of that definition as they are the middle values of each of the class intervals, in order to estimate the mean value of the grouped data.
So for the interval
0 – 4, you take [(0+4/2] to get the midpoint of that interval, no matter what the boundary is. Then, to estimate the mean value, we take the midpoints of each interval and multiply them by the respective frequencies, add them up, and divide it by the total number of frequency.