Requiring maths/stats help

[Ninshub]

So I figured I'd ask here as I'm sure there are several people that could help me with the answer.

Let's say I want to give each track on an album a rating and make an average rating for the whole album. Pretty easy, right?

E.g.


Track 1:  7
Track 2:  8.25
Track 3:  6.75
Track 4:  8.75
Track 5:  5.25
Track 6:  7
Track 7:  7.5
Track 8:  8.5

Sum it up and divide by the number of tracks:  59 divided by 8 = 7.375

But let's say I want to give each track a weight according to the length of the track, how would I go ahead and do that?

E.g.

Track 1:  7               length (minutes & seconds): 3.23
Track 2:  8.25          length (minutes & seconds): 5.47
Track 3:  6.75          length (minutes & seconds): 2.24
Track 4:  8.75          length (minutes & seconds): 6.55
Track 5:  5.25          length (minutes & seconds): 7.43
Track 6:  7              length (minutes & seconds): 2.23
Track 7:  7.5            length (minutes & seconds): 3.45
Track 8:  8.5           length (minutes & seconds): 4.53

My old stats courses probably gave me the answer but that was in the last millennium and my memory only goes so far.

Thanks in advance.

Instead of adding the ratings and dividing by the number of ratings, you'd need to multiply each rating by the length of the track before adding them together, and then divide by the sum of all the lengths. Probably easiest to convert all the lengths to seconds rather than dealing with fractions of minutes.

[Ninshub]

So, you mean, and I'll just do this for 3 tracks

e.g. track 1: 7 x 203 (seconds, which is 3min23 sec) = 1421
track 2: 8.25 x 347 = 2862.75
track: 6.75 x 144 = 972

Total divided by 3 = 1751.9266


OK. But my intention was to achieve a summary that is still between 0 and 10, a regular album rating, but one that reflects the length of the quality (or lack therefore) of each track on the album.

Should I do instead something where I multiply the track rating by a number that is that track's percentage of the total legnth of the album (e.g. 15%)?

Confused.

So, you mean, and I'll just do this for 3 tracks

e.g. track 1: 7 x 203 (seconds, which is 3min23 sec) = 1421
track 2: 8.25 x 347 = 2862.75
track: 6.75 x 144 = 972

Total divided by 3 = 1751.9266


OK. But my intention was to achieve a summary that is still between 0 and 10, a regular album rating, but one that reflects the length of the quality (or lack therefore) of each track on the album.

Should I do instead something where I multiply the track rating by a number that is that track's percentage of the total legnth of the album (e.g. 15%)?

Confused.

Instead of dividing the total by the number of tracks, you'll need to divide by the sum of the lengths.

So for the first three tracks, the sum of the lengths is 694, and the weighted average is 5255.75/694 = approx 7.57.

[Ninshub]

Brilliant Chris (for me anyway! ).

Thanks so much.

For that, you win a year's free subscription to PsienceQuest - oh wait, it's already free.

Thanks again. Many useless but fun hours ahead for me.