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How the right calculations can prevent interplanetary disaster… and also give you the scores that you weren't expecting!

Malcolm Pitcher - Wednesday, January 14, 2015



The champagne’s on ice, as you wait to celebrate the moment when your $125m interplanetary weather satellite will start its first orbit of Mars. Suddenly disaster! Your mega-expensive satellite crashes on the planet’s surface and your team is devastated.


The cause? Someone miscalculated!


It sounds absurd to think that NASA would make such an astronomical miscalculation, but in 1999 a mix up with Metric and Imperial measurements caused the $125m Mars Climate Orbiter to crash into Mars.


Imagine if your calculations showed you’ve hit your targets, your team is already sipping their celebration champagne, and then you find the real results put you on a lower orbit.



The most classic example we hear about, is caused by calculating an “Average of an Average”…


So what’s an “Average of an Average”?

Averages are always being calculated for customer satisfaction scores, sales figures etc. If you were to take multiple averages, and find their average, you have successfully created an “Average of an Average”.

For example, you want to calculate your customer satisfaction score for Quarter 4:

If you add up all the monthly customer satisfaction scores for October, November and December, at 78.1, 86.1 and 84.2 respectively; then divide by 3, you get 82.8.

Let’s say your target is 83.0… You’re inches away! Disaster!

Don’t break the bad news to your team yet!

You may think you’ve crash landed, but you’ve miscalculated your score!

We’re missing some vital information: the number of customers behind those figures. Let’s say in October, November and December there were 8, 18 and 19 customers respectively. The score calculated above isn’t correct, because there’s more than double the amount of customers in November and December. Calculating it like the above means you’ve given 8 customers the same impact as 18 or 19. You’re saying that each customer in October is more important than those in November and December.

That’s not Apples vs Apples.

That’s Metric vs Imperial!

So how do I calculate it properly then?

Now we have all the information we can now calculate the score properly. We start by “Expanding the Averages”. We do this by multiplying the scores, with the number of customers:


78.1 x 08 = 625

86.1 x 18 = 1550

84.2 x 19 = 1600

Now add it all up, and make a new average by dividing by the total number of customers:

  • (625 + 1550 + 1600) ÷ (08 + 18 + 19)
  • 3775 ÷ 45
  • = 83.9

Get that champagne out; you just hit your target by a Metric Mile! Calculating the scores the right way will give you a different result – Good or bad! For NASA it cost them $125m.

Avoid any unhappy surprises. Calculate the scores properly. Don’t crash land!

To summarise:

Don’t use an “Average of an Average”

Get all the information behind the existing scores

Expand the existing averages

Recalculate a new Average

Next Steps:

  • Calculate your own figures? Check the calculations you use internally
  • Make sure you and your team are on the same orbit

Give In-house a call on 01793 84 84 55 if you fear your calculations could spell disaster

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