# Class Limits, boundaries, midpoint, relative frequency?

I have a list:

85 45 75 60 90 90 115 30 55 58 78 120 80 65 65 140 65 50 30 125 75 137 80 120 15 45 70 65 50 45 95 70 70 28 40 125 105 75 80 70 90 68 73 75 55 70 95 65 200 75 15 90 46 33 100 65 60 55 85 50 10 68 99 145 45 75 45 95 85 65 65 52 82

Sorry for the poor formatting, but I created a program that would count the frequencies, etc. and I still am getting the problem wrong.

The class limits make sense to me since the smallest value is 10 and you just need to add 28 (the class width), and the next should be 48, right? Or am I completely off base?

Class boundaries will make sense once I get the right values for the class limits.

The midpoint should be the lower limit + the upper, so wouldn't the midpoint of (10 + 38)/2 be 24??

And relative frequency is just the frequency divided by the total frequencies, right?

http://www.flickr.com/photos/92711644@N08/8421983384/ (sorry, image linking didn't work for me)

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If one class goes from $10$ to $38$, then the next class should start from $39$. Otherwise, if you get a data point of, say, $42$, what class would you put it in? – Rahul Aug 18 '13 at 1:09

Here's the tally of your numbers:

{{65, 8}, {75, 6}, {45, 5}, {70, 5}, {90, 4}, {50, 3}, {55, 3}, {80,
3}, {85, 3}, {95, 3}, {15, 2}, {30, 2}, {60, 2}, {68, 2}, {120,
2}, {125, 2}, {10, 1}, {28, 1}, {33, 1}, {40, 1}, {46, 1}, {52,
1}, {58, 1}, {73, 1}, {78, 1}, {82, 1}, {99, 1}, {100, 1}, {105,
1}, {115, 1}, {137, 1}, {140, 1}, {145, 1}, {200, 1}}


And here's the histogram with bin width = 1, thus replicating the above tally:

The mean is 73.7, the quartiles are {54.3, 70, 90}. There's many more summary statistics that can computed.

What method are you using to classify (ie, partition the x-axis) or cluster the data?

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I did the calculations on Statiscope and they match your. Regards – Amzoti Jan 27 '13 at 23:37
These stats are great, thanks so much! So if I made a frequency table, would the limits be 10-38, 48-76, etc? Or is that wrong? Thanks for your help! – m00nbeam360 Jan 28 '13 at 4:49
I'm not sure what you mean by limits. I take it you want to cluster the data into classes but based on what method? Different methods give different "limits". Where did the numbers: 10-38, 48-76, etc come from? – alancalvitti Jan 28 '13 at 5:01
Hmm, I'm not exactly sure what method the problem suggested. I made a frequency table and am supposed to find the class limits when I divide the problem into seven classes (from the image I linked to). So with 7 classes, (200-10/2) = 28 (the class width), but how would I find the class limits for each class? – m00nbeam360 Jan 28 '13 at 17:08
You can certainly do that: partition the range [10,200] into 7 (or any number) of equal segments. In that case no other information about the data is needed, only the Min=10 and Max=200. But it is more informative to partition the range into quantiles (check wikipedia). For example, if you split into quartiles, you get the partition [10,54.7],[54.7,70],[70,90],[90,120]. Each quartile contains approximately 1/4 of the data points. 70 here is the median value, and [54.7,90] is called the interquartile range. These are commonly used summary stats. – alancalvitti Jan 28 '13 at 17:28