Math Is Fun Forum

Alex6969

Guest

Please find the average number

For anyone who both enjoys and is skilled in math:

I conducted a survey of 1000 people that measured how much value they put on something. They were given 9 options and each option has a range. I was wondering what the average single value was of the participants taking into account percentages (if needed using median values 24.5, 74.5, 124.5 etc.) Here are the numbers:

A1    0-49        37.40%    374
A2    50-99        19.30%    193
A3    100-149        14.60%    146
A4    150-199        7.80%    78
A5    200-249        5.30%    53
A6    250-299        2.80%    28
A7    300-349        1.50%    15
A8    350-399        1.30%    13
A9    400+        10.00%    100

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Please find the average number

hi Alex6969

Welcome to the forum. 

There's a formula for expected value which goes like this:

where the x's  are the values and the p's are the probabilities.  So you could take the x values using those midpoints and the probabilities by dividing the percentages by 100 and adding them together like this:

Some might argue that the midpoint is not 24.5 etc as you ought to be considering a continuum from 0 to 50 inclusive which would make the midpoint 25.  In practice it doesn't make much difference as this is only a theoretical statistic.

You'll also have to make a judgement about what to use for A9.

Bob

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