Finding mean from frequency table with ranges

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deano2727

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I am required to find the mean of the above table. I am not sure how to go about it. I thought to set midpoints for each range, getting the middle value between both, but I am unsure if that is correct or what to do next if it is.

Hopefully someone can point me in the right direction. Cheers.
 
Setting the midpoint is one way to go about it. However, that would be only in the absence of other information.

For example, if 106-152 has these data in it, 106, 106, 106, 106, 106, 106, 152, then a midpoint might be a terrible representation of the interval.

Anyway, let's use the midpoint. (106+152)/2 = 129

The idea is to use the frequency to assume there are that many entries of your midpoint. In other words, with these data, the value 129 is assumed to be in the detail listing 19 times.

Note: I'm not a fan of these data. Gaps are bad unless you know why they exist. Will you be okay with a mean of 155, knowing that absolutely was not in your original ranges? It's possible that the chart means:

-96-51 - 15
52-105 - 0
106-152 - 19
153-211 - 0
212-349 - 11

You haven't actually told us that, so I have to wonder about the gaps.
 
You do realize that you cannot determine the true mean from these summarized data. You can calculate an approximation. Or you can calculate a range exactly.
 
Sorry guys, I'm even more confused than you, believe me. This is exactly the way the question is presented in my exam papers. There was no more data provided.
 
Perhaps in your text or lectures you were told a method to approximate the mean of data summarized into a frequency table, and you are expected to use that. In the absence of any other information, I'd do a weighted mean of the midpoints. I would not have a whole lot of confidence in such a number, but it is probably the number the test maker expects.
 
If you are given this

10-14 2
15-19 3
20-24 4

How might you proceed?

If you are given this

12 12 17 17 17 22 22 22 22

How might you proceed?
 
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