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 Lower Boundary & Mid-Value of A Class Interval, Histogram & Calculating Median

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TSwatdatlinna
post Jan 17 2017, 10:04 AM, updated 8y ago

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For a class interval of 0 - 4, what is the lower boundary? - 0.5 or just 0? What is your reason behind it?

Thank you in advance.

This post has been edited by watdatlinna: Jan 17 2017, 09:49 PM
LightKeyDarkBlade
post Jan 17 2017, 08:55 PM

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Class boundaries serve as the separation of class intervals. Hence, the name "boundary". Basically, a class boundary is the midpoint of the upper limit of a class interval and the lower limit of the next class interval in sequence.

If I'm not mistaken, it would depend on the data you're trying to use for the histogram. Like if the data is the height or the age of a number of people, the lower boundary of the class interval 0 – 4 would be 0. (Note that if you're collecting data of the age of people, it's always an integer as age is always a whole number.)

If the data is something that can extend to negative numbers like the monthly balance of a company's account (negative numbers would mean a deficit), then the lower boundary would be -0.5 and the previous class interval is -5 – -1.

Hope that clarifies the question.
TSwatdatlinna
post Jan 17 2017, 09:43 PM

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QUOTE(LightKeyDarkBlade @ Jan 17 2017, 08:55 PM)
Class boundaries serve as the separation of class intervals. Hence, the name "boundary". Basically, a class boundary is the midpoint of the upper limit of a class interval and the lower limit of the next class interval in sequence.

If I'm not mistaken, it would depend on the data you're trying to use for the histogram. Like if the data is the height or the age of a number of people, the lower boundary of the class interval 0 – 4 would be 0. (Note that if you're collecting data of the age of people, it's always an integer as age is always a whole number.)

If the data is something that can extend to negative numbers like the monthly balance of a company's account (negative numbers would mean a deficit), then the lower boundary would be -0.5 and the previous class interval is -5 – -1.

Hope that clarifies the question.
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Thank you for your time and effort to answer my question. How about the scores for a test? Can we take negative boundaries?
TSwatdatlinna
post Jan 17 2017, 09:52 PM

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QUOTE(LightKeyDarkBlade @ Jan 17 2017, 08:55 PM)
Class boundaries serve as the separation of class intervals. Hence, the name "boundary". Basically, a class boundary is the midpoint of the upper limit of a class interval and the lower limit of the next class interval in sequence.

If I'm not mistaken, it would depend on the data you're trying to use for the histogram. Like if the data is the height or the age of a number of people, the lower boundary of the class interval 0 – 4 would be 0. (Note that if you're collecting data of the age of people, it's always an integer as age is always a whole number.)

If the data is something that can extend to negative numbers like the monthly balance of a company's account (negative numbers would mean a deficit), then the lower boundary would be -0.5 and the previous class interval is -5 – -1.

Hope that clarifies the question.
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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?
LightKeyDarkBlade
post Jan 17 2017, 11:23 PM

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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?
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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.
TSwatdatlinna
post Jan 18 2017, 10:24 PM

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QUOTE(LightKeyDarkBlade @ Jan 17 2017, 11:23 PM)
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.
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.
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I think for SPM, it does not have this type of data. In STPM, this can be tested.

Thank you. Your explanation is very clear. But, I have one thing to clarify. You mentioned that the limits, however, define the width of each class interval. Does it mean that we find the class width by using the limits, instead of boundaries?
LightKeyDarkBlade
post Jan 18 2017, 11:31 PM

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QUOTE(watdatlinna @ Jan 18 2017, 10:24 PM)
I think for SPM, it does not have this type of data. In STPM, this can be tested.

Thank you. Your explanation is very clear. But, I have one thing to clarify. You mentioned that the limits, however, define the width of each class interval. Does it mean that we find the class width by using the limits, instead of boundaries?
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Yes, exactly. The class width is the size of a class interval and all intervals in a grouped data have the same class width. The lower limit is the smallest value in the interval and the upper limit is the greatest value in the interval.

For the class interval 0 – 4,
lower limit = 0
upper limit = 4.

But remember that we don't find the difference of the lower and upper limits of the same interval to get the width. It has to be the difference of the lower limit of the interval and the lower limit of the next interval (or the previous interval).

The first two intervals are 0 – 4 and 5 – 9.

So the class width is
5-0 = 5.
TSwatdatlinna
post Jan 20 2017, 08:12 PM

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QUOTE(LightKeyDarkBlade @ Jan 18 2017, 11:31 PM)
Yes, exactly. The class width is the size of a class interval and all intervals in a grouped data have the same class width. The lower limit is the smallest value in the interval and the upper limit is the greatest value in the interval.

For the class interval 0 – 4,
lower limit = 0
upper limit = 4.

But remember that we don't find the difference of the lower and upper limits of the same interval to get the width. It has to be the difference of the lower limit of the interval and the lower limit of the next interval (or the previous interval).

The first two intervals are 0 – 4 and 5 – 9.

So the class width is
5-0 = 5.
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Thanks for sharing.

In sum, I can say that there are 3 ways of finding the class width.

 

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