As Level Edexcel Stats and Mechanics

State the meaning of simple random sampling

Every sample has an equal chance of being selected

There are 64 girls and 56 boys in a school. Explain briefly how you could take a random sample of 15 pupils using a simple random sample (3)

Allocate a number between 1 and N(or equiv) to each pupil (1)

Use random number generator to select 15 different numbers between 1 and 120 (1)

Pupils corresponding to these numbers become the sample (1)

What are the advantages of simple random sampling ?

Bias free-each number has a known equal chance of being selected

easy and cheap to implement

What are the disadvantages of simple random sampling?

sampling frame needed

not suitable when pop. size is large

What is a systematic sampling?

Required elements are chosen at regular intervals in ordered list

k=(pop size (N))/(samp size (n) )

starting at random item between 1 and k.

What are the advantages of systematic sampling?

Simple and quick to use

Suitable for large pop.

What are the disadvantages of systematic sampling?

Sampling frame needed

Can introduce bias if sampling frame not random

What is sampling frame?

It is a list formed from sampling units

What is census?

data collected from the entire population

What is the advantage of Census?

Should give completely accurate result.

What are the disadvantages of Census?

Time consuming and expensive

Can’t be used when testing involves destruction

What is Stratified sampling?

Population divided into groups and a simple random sample carried out in each group

What are the advantages of Stratified sampling?

Reflects population structure

Guarantees proportional representation of groups within population.

What are the disadvantages of Stratified sampling?

Population must be clearly classified into distinct strata.

Sampling frame is needed

A school has 15 classes and a sixth form. In each class there are 30 students. In the sixth form there are 150 students. There are equal numbers of boys and girls in each class. There are equal numbers of boys and girls in the sixth form. The head teacher wishes to obtain the opinions of the students about school uniforms. Explain how the head teacher would take a stratified sample of size 40. (7)

Total in School = (15×30)+150=600 (1)

random sample of 30/600 ×40 (1)

= 2 from each of the 15 classes (1)

random sample of 150/600 ×40 (1)

=10 from sixth form (1)

Label the boys in each class from 1-15 and the girls from 1-15 (1)

Use random numbers to select 1 girl and 1 boy (1)

Label the boys in the sixth form from 1-75 and the girls from 1-75. Use random numbers to select 5 different boys and girls (1)

What is quota sampling?

Population divided into groups according to characteristic. A quota of items/people in each group is set to try and reflect the group’s proportion in the whole population. Interviewer selects the actual sampling units

What are the advantages of quota sampling?

Allows small sample to still be representative of population.

No sampling frame required

What are the disadvantages of quota sampling?

Non-random sampling can introduce bias.

Increasing scope of study increases number of groups, adding time/expense

What is opportunity/convenience sampling?

Sample taken from people who are available at time of study, and meet criteria.

What are the advantages of opportunity sampling?

Quick and cheap to carry out

What are the disadvantages of opportunity sampling?

Unlikely to provide a representative sample.

Highly dependent on individual researcher.

State two assumptions you make for a particle model (1)

Rotational forces/air resistance can be ignored (1)

Mass is concentrated at a single point

State two assumptions you make for an object modelled as a rod (2)

One dimension, is negligable, like a pole (1)

Mass is concentrated along line (1)

State one assumption you make for an object modelled as a lamina (1)

Mass is distributed across a flat surface (1)

State one assumption you make of an object modelled as a uniform body (1)

mass of the object is concentrated at the centre (1)

State two assumptions you make of an object modelled as light (2)

Don’t take mass into consideration (1)
tension is the same at both ends of a light string (1)

State one assumption you make with an object modelled as inextensible string (1)

Acceleration is the same in any connected objects (1)

State one assumption you make with a rough/smooth surface (1)

objects in contact with surface don’t experience friction (1)

State one assumption you make when an object is modelled as a wire (1)

treated as 1D (1)

State one assumption you make when an object is modelled as a bead (1)

tension is the same on either side of the bead (1)

State one assumption you make when an object is modelled as a peg (1)

dimensionless and fixed (1)