Naive Averaging

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From the course by Princeton University

Networks Illustrated: Principles without Calculus

43 ratings

Princeton University

Networks Illustrated: Principles without Calculus

43 ratings

What makes WiFi faster at home than at a coffee shop? How does Google order its search results from the trillions of webpages on the Internet? Why does Verizon charge $15 for every GB of data we use? Is it really true that we are connected in six social steps or less? These are just a few of the many intriguing questions we can ask about the social and technical networks that form integral parts of our daily lives. This course is about exploring the answers, using a language that anyone can understand. We will focus on fundamental principles like “sharing is hard”, “crowds are wise”, and “network of networks” that have guided the design and sustainability of today’s networks, and summarize the theories behind everything from the social connections we make on platforms like Facebook to the technology upon which these websites run. Unlike other networking courses, the mathematics included here are no more complicated than adding and multiplying numbers. While mathematical details are necessary to fully specify the algorithms and systems we investigate, they are not required to understand the main ideas. We use illustrations, analogies, and anecdotes about networks as pedagogical tools in lieu of detailed equations. All the features of this course are available for free. It does not offer a certificate upon completion.

From the lesson

Product Rating on Amazon

The decision of whether or not to purchase something online is often driven by the ratings that previous customers have left for it. In this lesson, we will take a look at Amazon's review system, and the see how "crowds are wise" is another important networking principle.

Amazon & eCommerce4:28

Average Ratings10:21

The Wisdom of Crowds10:03

Rating Aggregation Challenges4:11

Naive Averaging5:57

Bayesian Ranking: Part I5:32

Bayesian Ranking: Part II9:14

Bayesian Ranking in Practice5:41

What does Amazon do? Part I5:00

What does Amazon do? Part II5:29

Meet the Instructors

Christopher Brinton
Lecturer
Electrical Engineering
Mung Chiang
Professor
Electrical Engineering

We'll now turn our attention to two

different rating methods or two different ranking methods.

The first one's just naive averaging, which is

basically a computation of the average customer review.

And so, we'll just walk through that briefly.

Let's consider a set of five DVD players, that

were taken from Amazon at some day in 2012.

So, what's shown here is the name of the DVD player or the manufacturer.

Panasonic, Sony, Philips, Curtis, and Toshiba.

As well as the total for each, number of stars.

And the number of stars that, in each category for each DVD player.

So, the Panasonic, for instance, had five,

five-stars, three four-stars, three three-stars, and so forth.

And then, throughout the column, it, at the end, the, the totals are totaled up.

So we can see the total number of reviews to the Panasonic is 11 and so forth.

So we can use this table to run through the, average rating computation.

So the procedure, and the reason we call this naive averaging, is that

we're not taking account into account anything other than just the average, so.

There's a lot of implications to be discussed before.

Why their, what's the population size.

If so, having 11 versus 77 people, maybe that'll have some impact.

So that's why we call it naive because it's

not taking into account anything other than the simple average.

The procedure is to first find the total number of stars.

Which is, just adding up the total number of stars.

so, in the case of, having five, five stars,

that's a total of 25 stars, and so forth.

And then divide by the total number of ratings.

So, a very simple procedure.

So we can do this for the Panasonic, as follows.

RIght, as we said we have five, five stars.

That's going to be 5 times 5 which is 25.

Plus three, four stars.

So 3 times 4 which is 12.

Plus three, three stars.

Which is 3 times 3.

Plus no two stars.

So 0 times 2.

Plus no 1 stars.

So 0 times 1.

And then, we divide that by the total number.

Which is 5 plus 3 plus 3 plus 0 plus 0 which is 11.

So 5 plus 3 plus 3 plus 0 plus 0.

And when we do this out, we get 46 over 11, which is equal to 4.182.

So, for the

Panasonic, the average is 4.182.

We'll just write that here.

So the average rating calculation, just to generalize that and write it out.

We take the number of five stars times five, plus the number of four

stars times four, plus the number of three stars times three, plus dot, dot, dot.

All the way down to the end.

And we divide by the total number of stars.

Which is the number of five stars plus the number of

four stars plus the number of three stars and so forth.

So we can go through and do this to the rest of the DVD players.

Let's, for instance, do it for say the Sony player.

So we'll do it for the second one now.

So for the Sony, we have 18 five stars, plus

nine four stars, plus five three stars,

plus two two stars, plus three, one star.

And we divide that by the total, which is 18

plus 9 plus 5 plus 2 plus 3, which is 37.

And so

this comes out to be 148 over 37, which is equal to 4.

So it actually comes out to exactly 4.

And so this is average rating is 4.

And we can follow this same procedure for the other ones too.

We can write out the Philips, I'll just do that one

and then we'll just, call a day on the computation side.

23 times 5 plus 15 times 4 plus 11 times 3 plus 5 times 2 plus 13 times 1.

Over the total.

So again we just add up the total.

So that's just 67.

And that gives us 231 over 67, which is 3.448.

Now I encourage you to do the same for the Curtis and the Toshiba as well.

We have 3.448 here.

And if you do it for the Curtis in the Toshiba, the

Curtis is going to be 3.431 and the Toshiba is

going to be 3.407 so, 3.431 and 3.407.

So the ordering now is exactly the order, if we,

if we wanted to order it by the average rating now.

So we wanted to rank them by the

average rating in descending order, so the highest first.

It would be the exact order here.

4.182, so Panasonic comes first, followed by the Sony which is at

four, followed by the Phillips, followed by the Curtis followed by the Toshiba.

So that goes from highest average rating to lowest average rating.

So we have.

The Panasonic.

[SOUND] The Sony.

[SOUND] The Phillips.

[SOUND] The, Curtis.

[SOUND] And the Toshiba.

[SOUND] So, the question was, is this the correct order?

And, the reason, we can really ask that is

that the, the Panasonic has the smallest number of reviews.

Right, so it has the highest average rating, but it also has only 11 reviews.

As opposed to the other ones which have 37, 67, and so forth.

So the question is can we really trust this average rating with Panasonic?

And should we try to do something where we can

factor in the population size into each of these computations.

In order to leverage the fact that there's

a different number of reviews in each case.

And we'll look at that next.

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