# Systematic sampling

Selecting every Kth subject from a list.

To remember this think of the following:

Every 10^{th} 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 1^{st} produces 300 cakes, the 2^{nd} produces 450 cakes and the 3^{rd} produces 250. If they use systematic sampling at what intervals should they select cakes for testing?

**Answer:**

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 20^{th} 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.

**Answer:**

Although this is a systematic survey it is unlikely to be representative as it will only sample people who use the nightclub. (It is biased)

# Systematic sampling

Selecting every Kth subject from a list.

To remember this think of the following:

Every 10^{th} 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 1^{st} produces 300 cakes, the 2^{nd} produces 450 cakes and the 3^{rd} produces 250. If they use systematic sampling at what intervals should they select cakes for testing?

**Answer:**

The interval for testing cakes is K

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

`1000=100%`

`x=5%`

`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 20^{th} 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.

**Answer:**

Although this is a systematic survey it is unlikely to be representative as it will only sample people who use the nightclub. (It is biased)