# Systematic sampling

Selecting every Kth subject from a list.

To remember this think of the following:

Every 10th time the toilet system (systematic) flushed the toilet burst into song.

Example 1

The quality control manager at a cake factory has to check 5% of the cakes they produce each day. The factory operates 3 shifts a day, the 1st produces 300 cakes, the 2nd produces 450 cakes and the 3rd produces 250. If they use systematic sampling at what intervals should they select cakes for testing?

The interval for testing cakes is K

Number of cakes produced per day =300+450+250=1000

1000=100%

x=5%

(see our section on percentages)

1000/x=100/5

Therefore x=(10cancel00times5)/(1cancel00)

x=50

So they should be checked 50 times.

There are 1000 cakes so checking 50 out of 1000 would be:

1000/50=20

Therefore the quality control manager needs to check every 20th cake they produce.

Example 2

Cala wants to survey opinion in a town about a new nightclub. She decides to systematically interview every 10th person coming out of the nightclub. Explain, giving reasons, if this survey is likely to be representative of opinion in the town.