Grade 4 Sampling Infer properties of populations or

Grade 4 Sampling Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Random sampling Stratified sampling Systematic sampling

Random sampling • Give every member of the population a number. Then use a random number generator to select the sample. • Alternatively, write the names of every member of the population on pieces of paper, and pull your sample out of a hat. • To do random sampling you must have a complete list of the population.

Stratified sampling • This is random sampling, but with one important addition • The population is split into sub-groups, for example male and female, and the sample is in the same proportion as the population. So if half the population is female and half male, then half the sample will be female and half will be male

Systematic sampling Put the population into a list, and pick, for example, every 20 th member on the list.

Pros and cons – random sampling • Good, but you may pick a biased sample by chance • The bigger the sample, the less likely this is to happen • Can be difficult, costly and time-consuming to do

Example I choose 50 students in a school as my sample when I do a questionnaire about the school canteen. These are 50 specific students – 3 may be on longterm absences and difficult to get in touch with.

Pros and cons – stratified sampling • The sampling method that gives the best results. • Less chance that you may pick a biased sample • Can be even more difficult, costly and timeconsuming than random sampling

Pros and cons – systematic sampling The easiest of the three methods, and results are often as good as random or stratified sampling

. Example 1 A Catering company want to find out if their customers like the new menus the company have introduced in their cafes. The table below gives some information about the number of customers who regularly use the cafes and the sample size of the survey Name of cafe Number of regular customers Sample size John’s cafe 500 60 Katrina’s cafe 350 50 Jane’s cafe 480 100

Example 1 • Which café do you expect to produce the more accurate results? • Explain why. Jane’s café The sample size was much bigger, and it was a bigger proportion of the population (regular customers)

Example 2 • The two-way table below shows information about the number of students at a school Boys Girls Total • • 7 100 197 297 Year Group 8 9 10 101 139 112 164 176 164 265 315 276 11 120 164 284 Total 572 865 1437 Ryan wants to ask students across all age groups. What would be the name of this method? What would be a better sampling method? What might be the disadvantages of either of these two methods, and what might Ryan do instead?

Example 2 • What would be the name of this method? Random sampling • What would be a better sampling method? Systematic sampling • What might be the disadvantages of either of these two methods, and what might Ryan do instead? Could be difficult to ask certain individuals chosen. Systematic sampling is easier and quicker.

Understanding Which is the best method of sampling? Stratified sampling (with random sampling a close second) What are its advantages? Minimises bias What are its disadvantages? Can be difficult to collect the sample You need a list of the whole population