# Calculate mean of sample size based on relative frequency in histogram [duplicate]

I have the following data of number of vouchers redeemed :

How can i calculate the mean value of total vouchers?

• You don't have information for computing the total. By "mean value of total vouchers" shall we presume you mean the arithmetic mean of the value? If so, please see the duplicate.
– whuber
Jun 22, 2022 at 21:08
• i don't have the N that's what is questioned... i also am not seeing how can i answer this but it is an excercise and it's just as it is here... Jun 22, 2022 at 21:29
• Some of the mean values listed in the third column do not fall within the range of values in the first column. Can you explain this apparent incongruity?
– Ben
Jun 23, 2022 at 9:52
• sorry, i will update is not correct Jun 23, 2022 at 11:02

Do you know how many vouchers were sold in total?

If so - and if I understood the problem correctly - you could find the mean by
$$\frac{(mean\_val\_vouch_1*\%\_vouchers_1*total\_vouchers)+(mean\_val\_vouch_2*\%\_vouchers_2*total\_vouch)+...}{total\_vouchers}$$

So in your case it would be
$$\frac{(4*0*total+14*1*total+25*2*total+...+850*3*total)}{total}$$

You're basically reconstructing the number of items in each line by multiplying the % with the total, and the rest of the formula is the traditional combined mean (see e.g. https://www.statisticshowto.com/combined-mean/)

• I don't...but i need right? i just have this information and that's why i asked here because either i am not aware how is this done or the exercise doesn't have all the information, at least at my point of view Jun 23, 2022 at 13:43
• btw, mean value is in € so it's the midpoint Jun 23, 2022 at 13:53
• That's incorrect: the midpoints of the bins are at 5, 15, 25, etc. The mean value is the sum of the numbers in each bin divided by their bin count. This is crucial for the last (unlimited) bin, which has no midpoint. Nevertheless, from the means and the percentages you can recover the overall mean exactly (at least up to the precision with which the data are displayed) using the duplicate answer. You don't need to know the total.
– whuber
Jun 24, 2022 at 14:33