Arithmetic mean Exam Question (No one i know can match the multiple choice answers!)

[Scooby-Doo]

Table:

Spend (£) ------------------------No of respondents
0 ----------------------------------- 22
1 and less than 5 ------------------- 35
5 and less than 10 ------------------ 57
10 and less than 15 ----------------- 42
15 and less than 25 ----------------- 60
25 and less than 50 ----------------- 87

Multiple Choice Answers:

A: 13.42
B: 14.46
C: 15.35
D: 16.10
E: 16.55

I and all my friends and family have tried this and are not matching the multiple choice answers, if anyone gets it please tell me how!

[Rassis]

Here´s my answer: The arithmetic mean is 18.21. Data or answers must be wrong.

I would bet that I am not wrong but...one never knows...

[Glaysher]

I got that too

[Mattywoo2]

I got 18.22 to 2 d.p.

(18.217821782178217821.... (7821 recurring))

But obviousely this doesn't make any difference!!

[Scooby-Doo]

Anouther forum, responded with this interesting way:

>> Table appears in a market research report into the spending habits
>> of 15 to 19 year olds. Estimate the artihmetic mean spending per
>> week on these products.
>>
>> Amount Spend (£) ----------- No of respondents
>> 0 ----------------------------------- 22
>> 1 and less than 5 ------------------- 35
>> 5 and less than 10 ------------------ 57
>> 10 and less than 15 ----------------- 42
>> 15 and less than 25 ----------------- 60
>> 25 and less than 50 ----------------- 87
>>
>> A: 13.42
>> B: 14.46
>> C: 15.35
>> D: 16.10
>> E: 16.55
>>
>> I and all my friends and family have tried this and are not
>> matching the multiple choice answers, if anyone gets it please tell
>> me how!
>
> I think you're right. I couldn't match the answers either, even
> after several attempts at different ways of estimating.
>
> However, assuming you quoted exactly, the fact that the question is
> expressed ungrammatically ("Table appears" instead of "This table
> appears." "Amount spend" instead of "Amount spent") means that it
> is unlikely to come from a particularly reliable source.
>
> Since any mistyping of a single digit will throw the answer off, and
> since there is at least one obvious typo -- "spend" instead of
> "spent" -- the fact that the answers don't match should not be
> surprising.

I think the average of the midpoints of the classes comes close to the
choice C: 15.35. That _might_ what they were thinking. It doesn't have
much to do with the distribution of the different people in the
different classes, of course.

(I also wrote a program with which I was able to get within half penny
to each of the choices A-E, by generating suitable respondents, so any
of them is _possible_.)

This cant possibly be right, although i got 13.42 from adding the midpoints and dividing by six?

[Andy_P]

Hmm, add me to the list of people with the answer 18.21.

[Rassis]

Because data are grouped (raw data are not available), the answer can only be obtained by calculating a weighed average, for which purpose, one has simply to multiply the midpoints of each of the 6 classes by the number of respondents in each class and divide the result by the summation of the respondents. In the end you get 18.21 definitively.

There is no other way.

[Glaysher]

However I have discovered that the median is B 14.46. Are sure the question isn't asking for the median?

[Rassis]

Good point...

[Scooby-Doo]

defiently the arithmetic mean

[Glaysher]

Perhaps its a mistake in the question then because the mean is definitely not one of the answers and the median is is too big a coincidence for me.