Statistics

Question 1

population

Answer 1

A population in statistics means all the individuals/objects you are interested in for a particular investigation

eg. all 6-year-old girls in the UK, all items manufactured by a factory or all the trees in a public park.

Question 2

census

Answer 2

A census observes or measures every member of a population.

Question 3

sample

Answer 3

A sample is a selection of observations taken from a subset of the population which is used to find out information about the population as a whole. We then assume that the results for this sample are representative of the whole population.

Question 4

Census pros

Answer 4

Should give a completely accurate result

Question 5

Census cons

Answer 5

Time consuming and expensive
Can’t be used when testing process destroys the item
Hard to process a large amount of of data

Question 6

sample pros

Answer 6

. Less time consuming and expensive than a census
. Fewer people have to respond
. Less data to process than in a census

Question 7

sample cons

Answer 7

• The data may not be as accurate
• The sample may not be large enough to give information about small sub-groups of the population

Question 8

sampling units

Answer 8

Individual units of a population

Question 9

sampling frame

Answer 9

A list (or other representation) of the items available to be sampled

Question 10

sampling fraction

Answer 10

The proportion of the available items that are actually sampled is called the sampling fraction. A 100% sample is called a census.

Question 11

sampling error

Answer 11

The difference between an estimate of a parameter (e.g. mean) derived from sample data and its true value. To reduce the sampling error, you want your sample to be as representative of the parent population as you can make it.

Question 12

bias

Answer 12

different types of people should be represented in the sample that is chosen. If the sample involves a more of certain group of people within the population, then it is said to be biased. To make good use of a sample we want to avoid bias.

Question 13

representative sample

Answer 13

A sample that is typical of the whole population.

Question 14

Random Sampling Techniques

Answer 14

• Simple random sampling
• Systematic sampling
• Stratified sampling

Question 15

Simple random sampling

Answer 15

A simple random sample of size n is one where every possible sample of size n has an equal chance of being selected. This can be achieved by ensuring every member of a finite population has an equal chance of being selected as long as sampling is without replacement and selections are independent of each other.

Question 16

two methods of choosing the numbers in Simple random sampling

Answer 16

• Using a random number generator (using a calculator, computer or random number table).
• Lottery sampling – eg. writing members of the sampling frame on tickets and drawing them out of a bag.

Question 17

Simple random sampling - pros

Answer 17

• Free of bias
• Easy and cheap to implement for small populations and small samples
• Each sampling unit has a known and equal chance of selection

Question 18

Simple random sampling - cons

Answer 18

• Not suitable when the population size or the sample size is large
• A sampling frame is needed

Question 19

Stratified sampling

Answer 19

In stratified sampling, the population is divided into mutually exclusive strata and a random sample is taken from each.

Divide population into sub-groups or strata: e.g. low income, middle income, high income, male, female

Question 20

proportional stratified sampling

Answer 20

If we randomly sample from each group in proportion to the size of the group then it is called proportional stratified sampling.

Question 21

stratified sampling - pros

Answer 21

• Sample accurately reflects the population structure
• Guarantees proportional representation of groups within a population

Question 22

stratified sampling - cons

Answer 22

• Population must be clearly classified into distinct strata
• Selection within each stratum suffers from the same disadvantages as simple random sampling

Question 23

Systematic sampling

Answer 23

In systematic sampling, the required elements are chosen at regular intervals from an ordered list.

From a list, choose a random starting item, then sample, for example, every 5th item.

To determine the interval required you divide the population by the required sample.

Question 24

Systematic sampling - pros

Answer 24

• Simple and quick to use
• Suitable for large samples and large
• populations

Question 25

Systematic sampling - cons

Answer 25

• A sampling frame is needed
• It can introduce bias if the sampling frame is not random

Question 26

Non-random sampling

Answer 26

• Quota sampling
• Opportunity sampling

Question 27

Quota sampling

Answer 27

• In quota sampling, an interviewer or researcher selects a sample that reflects the characteristics of the whole population.
• The population is divided into groups according to a given characteristic. The size of each group determines the proportion of the sample that should have that characteristic.
• This is similar to a stratified sample but a specific number of people from each particular strata is sampled e.g. male/female, different age groups, etc.

Question 28

use of Quota sampling

Answer 28

This method is often used for market research and is usually used by interviewers. The interviewer would meet people, assess their group and then, after interview, allocate them into the appropriate quota. This continues until all quotas have been filled. If you then begin interviewing someone for whom your quota is full, you just move on. The actual selection of the sample members is up to the interviewer, whereas stratified samples are done at random.

Question 29

Quota sampling - cons

Answer 29

Non-random sampling can introduce bias
Population must be divided into groups, which can be costly or inaccurate
Increasing scope of study increases number of groups, which adds time and expense
Non-responses are not recorded as such

Question 30

Quota sampling - pros

Answer 30

Allows a small sample to still be representative of the population
No sampling frame required
Quick, easy and inexpensive
Allows for easy comparison between different groups within a population

Question 31

Opportunity sampling

Answer 31

Opportunity / convenience sampling consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for.

An example is interviewing passers-by on the street or the first 20 people you meet outside a supermarket on a Monday morning.

Question 32

Opportunity sampling - pros

Answer 32

Easy to carry out
Inexpensive

Question 33

Opportunity sampling - cons

Answer 33

• Unlikely to provide a representative sample
• Highly dependent on individual researcher

Question 34

Qualitative variables or qualitative data

Answer 34

Non-numerical data that come in classes or categories e.g. favourite colours, makes of car.

Question 35

Quantitative variables or quantitative data

Answer 35

Numerical data for which the numbers are meaningful e.g. times to run a race, height.

Question 36

Numerical data categories

Answer 36

Discrete
Continuous

Question 37

Numerical data categories - Discrete

Answer 37

The set of values taken by the data can be listed
e.g. shoe sizes (), number of goals, number of children in a family

Question 38

Numerical data categories - Continuous

Answer 38

Values can’t be listed because data can take any value in a particular range

e.g. heights, mass, time, etc.

Question 39

Bivariate data

Answer 39

Two variables are assigned to each item e.g. height and weight, age and mileage of cars

Question 40

Class boundaries

Answer 40

Class boundaries are the minimum and maximum values that belong in each class.

Question 41

midpoint

Answer 41

The midpoint is the average of the class boundaries.

Question 42

class width

Answer 42

The class width is the difference between the upper and lower class boundaries.