Hi MS, thanks for the comment, glad you enjoyed it. It can be a tricky concept to get across, but I’d still encourage you to trackback / release your explanation also – everyone has different insights :).

[…] How To Analyze Data Using the Average @ BetterExplainedThe average is a simple term with several meanings. The type of average to use depends on whether you’re adding, multiplying, grouping or dividing work among the items in your set. […]

To Zac’s point, I just realized the median and mode behave “as if all items had the same value”, in a way.

When choosing the mode (most popular), you are acting as if every value was the mode – it’s the only one that matters. The median is similar: you choose a middle value, and the median doesn’t change if you had replaced every value with it.

Oh… I can understand! yawn

whts the answer anyway:

Quick quiz: You drove to work at 30 mph, and drove back at 60 mph. What was your average speed?

Yours

Poor-in-Maths

Hi Rakesh, just check out the section on the harmonic mean.

Dear Kalid, great post once again although I what I got confused into was why do we multiply to get average return of a portfolio over four years? Why dont we add? Similarly what is the logic behind multiplying the diferent rates of inflation across the three periods and not adding them? Can you please clarify a bit on the geometric mean?

Regards (And also looking forward to more of your math posts)

Hi Mohammad, great question. Most of the time, interest is “compounded” which means you multiply returns over time [there is a type of simple interest that is added, and you’d use the regular arithmetic mean for that – this type is very rare].

When working with interest rates, +10% looks like addition but it really means multiplying by 1.1 – for example, gaining 10% return on 100 is 110, and gaining 10% return on 200 is 220.

If you have 10% return again, you’d do 110 * 1.1 = 121, or 220 * 1.1 = 242.

Simple addition doesn’t work because we are scaling the amount of “stuff” we have. Check out the simple and compound interest rates for more about interest returns. Hope this helps!

Hi Kalid,

what tool do you use to create such a wonderful graphics?

Thank you.

Hi Denis, I use PowerPoint 2007 to make the diagrams.

The ‘identical numbers’ thing reminded me of a nearly aha moment.

I’m more a wordy than numeric person, so I wished math was taught like this:

The average of a set of numbers is the number that all the numbers would be if the sum of the set of numbers was the same number, but all the numbers were the same number, and there was the same number of numbers.

Re Zac’s point, medians and outliers: quite right I think - and thanks for remembering us outliers.

I seem to be a statistical outlier on all sorts of demographics.

Makes me wonder about some people (e.g. politicians, journalists, marketing managers, medical policymakers etc.) and whether they are just using ‘blunt’ averages (i.e. =broad generalities) when they do their correlations - and then make policy and predictions telling us what’s good for us and what’s bad for us etc.

Always makes me think: “that’s very interesting but I have no idea whether it applies to me.”

@The Hermit: Thanks for the comment. Yes, we all have different ways of seeing the same topic – I love thinking about the different interpretations :).

[…] Averages […]

Hello!!

I love maths bcoz i teach maths.

Thanks.

Jitendra

[…] By the way, those special means show up in strange places, don’t they? I don’t have a nice intuitive grasp of the trig identities involved, so we’ll save that battle for another day. […]

WoW…very very very interesting…pls continue your wonderful work…one of the excellent article i came across…I also thank you for the valuable information…short,sweet and crispy…

regards.

Sampath

its so hard…i can’t understand everything…

Wow, wish I had a teacher like you when I was in school

But there is one example I’m not sure I understand :

For the harmonic mean, you give the example of data transmission. At the end you divide the cost by two because each one “do half the job”. I think it would be the opposite, since if we want to transfer 1gb, you have to send it AND received it. Wouldn’t that be doubling the amount of working instead of halving it ?

I would be glad if you could clarify this particular example

Thanks !

Hi David, great question. In this case cost was written as “gigabytes per dollar”, so a higher number is better (like miles per gallon).

Division, in this case, would lower the number (indicating an *increase* in cost).

If we had written the price in terms of dollars/gigabyte, you are correct that we would multiply and double the amount.

Hope this helps!

Can you tell me how to read Perado chart? What are we looking at? Thanks

“After all, we spend twice as much time going 30mph than 60mph: if work is 60 miles away, it’s 2 hours there and 1 hour back.”

In this example it could also be calculated using the arithmetic mean, averaging the speed for 1st, 2nd, and 3rd hour:

(30+30+60)/3 = (60 + 60)/3 = 40

Or in general for rates X1,X2,…,Xn where X1