Basic Maths Help

['Ross]

This is kinda embarrassing, but I've asked several people who couldn't help, wasted enough time on it so I might as well put it out there...

These are my figures for readership for a magazine (based on age groups):

-17: 2.5%
18-24: 12%
25-34: 23.2%
35-49: 28.1%
50+: 34.1%

What I am trying to figure out is the average age of people who buy it, I haven't done maths for about 4 years and its showing

If it helps this is the other magazine:

-17: 2.0%
18-24: 7.9%
25-34: 20.5%
35-49: 30%
50+: 39.6%

And the average age for that one is definitely 47 years old, not sure if they got that info from those numbers or other research though

The whole point I'm trying to construct is magazine A has a slightly younger readership than magazine B, but not remembering how to work it out is kinda ruining my point. Please help!

 

[McBain]

42.73 years.

What you are trying to do is find a weighted mean for a frequency distribution (although I could be very wrong - it has been a long time since I failed first year stats at uni )

So you could calculate it like: sum of (average age per group * respondents per group) / sum of respondents.

Using the average age per group as a weight is pretty crud - if I use 8.5 (avg of 0 and 17), 21 (avg 18 of 24), 29.5, 42 and 67 (so avg of 50 and 84, which works out to what the 2nd set of numbers use to get 47!), I get an average for the first set of 42.73 years.

(Confusing much?)

 

[Rider_of_Fast]

So you could calculate it like: sum of (average age per group * respondents per group) / sum of respondents.

(Confusing much?)

How did u get the figure for sum of respondents?

Surely this would be a known variable, I was gonna ask Ross how many subscribers there are in total and then base the calculations upon that.

 

[MasterOfReality]

Yeah my first thought was a weighted averaged, where the total number of subscribers must be known.

I have just spent the entire day doing length weighed calculations so I may be incorrect

 

['Ross]

Well 42 sounds pretty close to what I was hoping for, your logic sounds like the path I was heading down, just couldn't get the cogs in the brain ticking over properly.

Readership for magazine A was 432,000

Magazine B was 315,000 and lucky I checked that out because their website had some old data that didn't match up to other data in the brief, hopefully everyone else doing the assignment overlooked that and their graphs will look crap

 

[Rider_of_Fast]

Im sure you could work it out in reverse using the 47 years figure from the second set of data, however then this would be assuming that the number of respondents (aka subscribers) is the same for both magazine subscriptions. Is it?

Is that how you conjured your answer McBain?

Otherwise, the only way to a solution is if the total subscription base is known. Ross you're withholding vital information

 

[gixer7]

Whatever you come up with your numbers are pretty rubbery.

Each age range is different for starters. Is taking the average of 0 & 17 a realistic number to determine the average age of the first group? What age do you use for the peak of the 50+ age group? All these things will sway your result depending on the assumptions you make.

Also, any answer you come up with is flawed due to using an average of an age group that in reality is most likely higher or lower.

However, do you actually need to calculate average age anyway?

Loooking at the 2 sets of numbers I see that:

For mag #1 37.7% of readers are 34 or younger

For mag #2 30.4% of readers are aged 34 or younger.

So on the basis of that I think it is fair to conclude the readership of mag #1 is younger. The next age group of 35-49 is in favour of mag #2 but only by 1.9% so not enough to swing the gap back.

Personally I think trying to calculate an impossible average is over complicating the issue.

Hope that helps.

 

[Rider_of_Fast]

So you could calculate it like: sum of (average age per group * respondents per group) / sum of respondents.

Based upon this formula and the given readership totals I got 44.2255 years for your Mag A.

I checked and this formula also gave the resulting avg age of 47.0085 for your Mag B. So I am assuming they also used this primative way to find out that figure.

I just don't know how McBain got 42.73 - unless I crunched a wrong digit on the calc. Try it yourself

Whatever you come up with your numbers are pretty rubbery.

Each age range is different for starters. Is taking the average of 0 & 17 a realistic number to determine the average age of the first group? What age do you use for the peak of the 50+ age group? All these things will sway your result depending on the assumptions you make.

Yeah true. I'd recommend structuring with more realistic and defined parameters.

Oh I love math, thanks for the Q!

 

['Ross]

Whatever you come up with your numbers are pretty rubbery.

Each age range is different for starters. Is taking the average of 0 & 17 a realistic number to determine the average age of the first group? What age do you use for the peak of the 50+ age group? All these things will sway your result depending on the assumptions you make.

I hear what you say and agree, but these are the numbers provided by Roy Morgan research commissioned by ACP magazines, in some cases the demographic brackets don't even add up (eg some have a 59-65 age group, some have a 30-50 group, lots of information is missing or not provided)

No the average age isn't really essential, I'll explain my full point:

I'm studying magazine B (Good Food magazine)...their target market is 30-45 according to them, and its made pretty clear by the content of the magazine, their current advertising and marketing etc....

But based on the figures the average buyer is 47, its not hitting the market they want. I was looking at magazine A (Recipes+) to find someone who's average age is a bit lower, so I can then compare the content and explain why the changes I want to make will work with that audience.....

Probably might have to find another magazine to compare, or maybe some more decent figures, but there isn't much decent data out there, and Recipes+ is the only other ACP magazine that fits the category I want.



The real point here is I'm wasting my time on something that is not really that important in the overall scheme of things

 

[McBain]

Im sure you could work it out in reverse using the 47 years figure from the second set of data, however then this would be assuming that the number of respondents (aka subscribers) is the same for both magazine subscriptions. Is it?

I don't make any claim to my result being anything but dodgy, but I don't think you need to know total numbers because we've got percentages of total.

As for respondents being the average of all the age brackets, that's absolutely dodgy, but we need to find some approximation without all the data. I was plugging numbers into a spreadsheet at work, so can't check what I've done now, and I'll probably forget by tomorrow.

Anyway, you can prove anything with statistics, 109% of people know that. Let's go with 42, it is a good number.

 

[gixer7]

OK so ignore the maths part of the question, I can dial up whatever result you want.

As Rider of Fast has done the numbers the average age of 47 years for Mag B is (we think) based on averages of the age groups which essentially makes it useless.

I feel it is best to stick with the numbers that we do know.

I would question the point of a survey that splits the target group into 2 disparate parts. If you are after the 30-45 age group, why split it into 25-34 & 35-49. Seems pointless to me.

But moving on, if they are targeting the 30-45 age group, then 50.5% of their readership is in that age group or 4 years younger or older. Given that almost 40% of their remaining readers are 50+ (often with more spending power than 30-45 age group) and given the nature of the magazine I'd say they are hitting their market pretty well.

Also, many 50+ people often have the grandkids to stay or look after them while parents are away/working and as Good Foods is targeting 30-45 year olds with kids at home, then I would posit that the 50+ market is a valid demographic for them.

I'd be stunned if Good Food magazine could narrow their readership down as it has a fairly broad appeal. Also, Good Food has been around for how many years? I'd hazard a guess that as their readership ages then it would be natural for the target market to age a little - not a bad thing per se.

Don't want to rain on your parade but if someone suggested they needed to make a change based purely on the calculated "average age" then I would suggest they are looking at the wrong info.

Of course, feel free to completely ignore me

But thanks for the question anyway gave me something more to think about for the arvo than just the new wheels that arrived in the mail!!

 

['Ross]

^^^Maybe I made it sound like a bigger point then it was, its just one little part of a 14 week study really, forgot how to do the calculations. This is just me trying to come up with to numbers in order to highlight a point I am making.

Roy Morgan Research splits all the numbers up into demographic segments because that is what they do for all ACP magazines, the 30-45 target is provided by Good Food itself and is open to change.

Maybe the numbers I gave are a bit vague, but taking into all the other research we have been doing they are missing the mark drastically, and there is a big hole (which we will try to fill)
Spending power is not an issue in this market, grandkids don't come into consideration either...but yes basically the oldies are buying it because of the way its positioned (which is basically the point I'm making, positioning and perception)

Good Food magazine is less than 2 years old, its owned by BBC, had its launch and all that now its future is a bit undecided...my goal is to expand its target audiences and give it a broader fuller appeal.

Thanks for the input, amazing how people in my class can make no insight at all after 7 weeks of information, but given a few dodgy numbers people here are already able to make decent points and conclusions.

 

[gixer7]

Thanks for the input, amazing how people in my class can make no insight at all after 7 weeks of information, but given a few dodgy numbers people here are already able to make decent points and conclusions.

Benefits of age. Supposedly.