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Question from maria, a student:

how to find range from group data.?i know that it is the difference between largest and smallest value.but confuse to find range of group data e.g

class interval frequency
0------5 6
5------10 7
10------15 9
15------20 4

Maria,

You can't find it exactly. The range could be as small as
15-5 = 10, or as large as 20-0 = 20.

The first (or any value near that) is very unlikely, as it would require all the [0,5] data to be clustered at 5 and all the [15,20] data to be at 15. The second is very much more likely, as it only requires one datum to be at each extreme value.

Though the sample size is small, these data suggest a rather "square" distribution with short tails, not a bell curve. One plausible and very simple model would be a uniform distribution on [0,20]. If so, from what we know, a good estimate for the range would be $20 - \large \frac{5}{6+1} - \frac{5}{4+1}$ which is about 18.3.

If we had other information about the source of the data we might be able to improve our estimate.

Good Hunting!
RD

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