How Can I Calculate an Unbiased Average Movie Rating?

[DaveC426913]

My website posts my movie reviews and rates them from 1 - 5. I want to post an average*, and I can't figure out how to do it.

Rating Number of movies
1....6
2...10
3...41
4...37
5...12

I can't figure out how to average* them without biasing them in favour of the higher numbers.

(*by average, I mean I should get approx 3.? / 5 .)

 

[d_leet]

When I average them out I get about 3.36 which I would think is approximately 3.

 

[krab]

dunno why this is a problem. avg. is
$$\overline{s}=\sum n_is_i/\sum n_i$$
This doesn't "bias" to high scores: consider if you had 6 1's and 6 5's and nothing else. You would get avg.=(1*6+5*6)/(1+5)=3 exactly as expected, so what do you mean by this "bias"?

 

[JasonRox]

dunno why this is a problem. avg. is
$$\overline{s}=\sum n_is_i/\sum n_i$$
This doesn't "bias" to high scores: consider if you had 6 1's and 6 5's and nothing else. You would get avg.=(1*6+5*6)/(1+5)=3 exactly as expected, so what do you mean by this "bias"?

This is where I am confused.

What do you mean by "bias"?

 

[DaveC426913]

OK, so


(5*12)+(4*37)+(3*41)+(2+10)+(1*6) = 357
1+2+3+4+5 = 15

357/15 = 23.8

 

[DaveC426913]

Oh.

Oh.

It's just 357 / 107.

Duh.

 

[d_leet]

OK, so
(5*12)+(4*37)+(3*41)+(2+10)+(1*6) = 357
1+2+3+4+5 = 15
357/15 = 23.8

Don't divide by the sum of the "choices" divide by the number of total ratings

ie. ((6*1)+(10*2)+(41*3)+(37*4)+(12*5))/(6+10+41+37+12) which is about 3.36

 

[DaveC426913]

I've had it right all along and I keep second-guesing my code. (This is not even the first time I've tried to "fix" it.)

It's been saying 3.3 for a long time now, but that's not because it's "stuck" or broken, that's because 3.3 *is* the point of convergence, and subsequent entries are strongly averaging around it.

BTW, for those interested, my reviews and ratings page is http://www.davesbrain.ca/reviews.php" . It is database driven, and I am rather proud of it.

 

[Integral]

I have split off the movie disscussion to a thread in GD https://www.physicsforums.com/showthread.php?t=105380"

Integral