Averages?

[redsoxnation]

I hope I'm submitting my question in the correct category. How do I figure the average when given a range of numbers? I'm looking at a range of housing prices ($0-100, 100-200, etc.). I know how to calculate an average, but not from a range? Thank you so much!

 

[JeffM]

I hope I'm submitting my question in the correct category. How do I figure the average when given a range of numbers? I'm looking at a range of housing prices ($0-100, 100-200, etc.). I know how to calculate an average, but not from a range? Thank you so much!

I am new to the site, but this question would probably go better under probability / statistics. If you repost there, please make sure to say it is a repost from this category. Some people get angry about reposts. In any case, you will need to give more data about the problem than you have given.

Do you have the number of houses in each range? Do you have the mean within each range?

 

[redsoxnation]

Thanks. The class I'm taking is called "Quantitative Reasoning", so I wasn't sure exactly under which category this question belonged.

Since I'm here, the price ranges run from "0-100....2000-2100". I would need to estimate, from a vague bar graph, how many units there are in each range. I'm guessing (and this is where I get into trouble) that I would take the midpoint from each range and multiply it by the number of units? And then add that number, and divide it by the total number of units?

The class is all word problems, and although I'm a pretty decent (albeit long-winded) writer, I can't extract information to save my life.

Thanks for any help you can offer. I'll try the "Stats" section, too.

 

[Deleted member 4993]

Say you have following data:

Price..........................# of houses

0 - 100.............................5

100-200...........................15

200-300..........................12

300-400......................... 7

For many purposes - you can re-arrange the data by taking the "mid-point" of the range as the x value . Then the above data becomes:

Price..........................# of houses

50..............................5

150...........................15

250..........................12

350......................... 7

Then 'average' price would be [(50*5)+(150*15)+(250*12)+(350*7)]/(5+15+12+7)

This treatment of data may NOT be desirable in some cases.

 

[JeffM]

Thanks. The class I'm taking is called "Quantitative Reasoning", so I wasn't sure exactly under which category this question belonged.

Since I'm here, the price ranges run from "0-100....2000-2100". I would need to estimate, from a vague bar graph, how many units there are in each range. I'm guessing (and this is where I get into trouble) that I would take the midpoint from each range and multiply it by the number of units? And then add that number, and divide it by the total number of units?

The class is all word problems, and although I'm a pretty decent (albeit long-winded) writer, I can't extract information to save my life.

Thanks for any help you can offer. I'll try the "Stats" section, too.

No need to repost. As I say, it makes some people very angry.

Without a word-for-word transcription of the question, it is dangerous for me to say what you should do.

HOWEVER, even from a vague bar graph, you should be able to tell what is the modal range (or modal ranges). If there is a unique modal range, its mid-point is one reasonable measure of central tendency. You do realize I presume that there are many valid measures of central tendency, mode, median, and mean (and several types of mean). The arithmetic mean is the most common measure of central tendency, but it is heavily influenced by extreme values and may not be calculable from the data available. Based on the limited data that seems to be available, you probably have enough to approximate fairly closely the mode. And if the distribution is not heavily skewed, the mode will not differ too much from the arithmetic mean. You MAY have enough data to compute the median range. If that is possible, I'd compare the mid-points of the modal range and the median range. If they do not differ by much, probably either would do.
By the way, given that the ranges are fairly small compared to the overall range, endpoints would probably do pretty much as well as mid-points. (I'd stay away from beginning points because almost no houses sell for close to zero).

Does this make sense??

 

[redsoxnation]

You were both very helpful! I applied what you both suggested, and ended up with the results that my Professor was looking for. Thank you guys ("gals"?) for your help!