Calculating 2 weighted averages in one equation

[rifaiii]

Hello Everyone,

this is my first post in your topic, am having a big time problem calculating the weighted average in my below sample of Data:

Lifetime Users # Occurrences
1 Month 50000 24
2 Months 10000 24
3 Months 5000 24
4 Months 2500 24
5 Months 1500 24


As you can see the sample includes data about the lifetime of users and the number of users as well as the occurences of each lifetime period. the question is how can i calculate the average of user lifetime according to this sample.

Note: Am sorry, if this topic is not posted in the right section, but am not really an expert at statistics.

Waiting for your replys.

Thanks.

[Decrement]

Well obviously the first sample is based on alot more data so you can just weight the means by the proportion of the data attributable to that group.

ie. [m1*n1 + m2+n2 + ... + m5*n5] / (n1+n2+..+n5) So if i understand your question correctly you are after the average # of users per occurance? so m1 = 208.33 etc, n1 = 50,000 and the denominator would be the sum of all the users. Hope this helps.

[rifaiii]

first i would like to thank for your help.

Actually am not really that good at statistics, i will try to explain it in a simple way so you can understand what i mean. As you see the set of data includes 3 columns; the first one represents the number of months the users spends using our service, the second represents the number of users who spent the period coresspondant in the first columns, and as the data were collected starting from January 2008, the are variation in the occurence of each period, so the third column represents the occurence of each period.

What am trying to calculate here is the average of the time spent by our users using our services, taking in the eye of consideration the occurence of each period.

Thanks alot.

[Decrement]

Oh im sorry i have misunderstood your question, i still don't understand what you mean by "occurence of each period, so the third column represents the occurence of each period"? Do you mean for example that of 50,000 users, 24times the service was used for a duration of 1 month since the start of the data collection? etc? Please inform if my understanding is correct.

[rifaiii]

I will try to explain it again, am trying to calculate the average of the time spent by users using our services, and as i started collecting the date starting from January 2008, and ending with June 2009. So baed on that the maximum period of time a user can spend using our services will be 30 months which occured only 1 time, while the period of 1 month occured 24 times. So i want to calculate the average taking in the eye of consideration the occurance of each period.

[Decrement]

You have a total of 360 months of use spread over 120 different users giving an average time of 3 months.

Depending on how you want to weight this towards paticular months im not sure, but it would make sense to weight towards month 1 because it has the most number of users. So then you multiply the contribution by the fraction of the number of person months of users in that month divided by the total number of person months.

The total number of person months is 102500

So you have [1*24*(50000/102500) + 2*24*(20,000/102,500) + 3*24*(15,000/102,500) + 4*24*(10,000/102,500) + 5*24*(7,500/102,500)]/120

So average # of users weighted by the volume of data is .4146

I'm not sure weighting is such a good idea, because the number of users is heavily skewed towards 1 month?

Hope this helps.