Cluster estimating

Cluster estimating is finding a common centre in a group of numbers.

There is a beautiful nut cluster in the centre of this chocolate bar.

Example 1

Add `357+343+355+345+356`

If you rounded each of these numbers to the tens column you would get.

`360+340+360+350+360`

But if you realise the numbers were roughly clustered around `350` i.e.

`350+350+350+350+350`

`5times350` is far easier to work out

`5times350=1,750`

In actual fact the accurate answer would be `1,756` and you can see we were very close.

Example 2

Add `33.90+35.25+34.54+36.21+36.70`

If you rounded each of these numbers to the nearest whole number you would have:

`34+35+35+36+37`

But if you realised the numbers were roughly clustered around `35` i.e.

`35+35+35+35+35`

`5times35` is far easier to work out

`5times35=175`

In actual fact the accurate answer would be `176.6` and you can see we were very close.

Example 3

Estimate the following calculation:

`22times21times18times19`

You should recognise that these numbers are clustered around `20` 

`20times20times20times20`

which is the same as

`2times10times2times10times2times10times2times10`

which is the same as

`2times2times2times2times10times10times10times10`

which is `16times10,000`

which is `160,000`

NOTE:

The real answer is `158,004`