Statistics

Question 1

what is a population?

Answer 1

the whole set of items that are of interest.

Question 2

what is a sample?

Answer 2

some subset of the population intended to represent the population.

Question 3

what is a sampling unit?

Answer 3

each individual thing in the population that can be sampled.

Question 4

what is a sampling frame?

Answer 4

sampling units of a population are individually named or numbered to form a list.

Question 5

what is a census?

Answer 5

observes or measures every member of a population (gathering information from every person in the population).

Question 6

what are the advantages of a census?

Answer 6

it should give a completely accurate result.

Question 7

what are the disadvantages of a census?

Answer 7

• time consuming and expensive.
• cannot be used when the testing process destroys the item.
• hard to process large quantity of data.

Question 8

what are the advantages of a sample?

Answer 8

• less time consuming and expensive than a census.
• fewer people have to respond.
• less data to process than in a census.

Question 9

what are the disadvantages of a sample?

Answer 9

• 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 10

what are the 3 methods of random sampling?

Answer 10

simple random sampling, systematic sampling and stratified sampling.

Question 11

what is simple random sampling?

Answer 11

every sample has an equal chance of being selected.

Question 12

what is the method of simple random sampling?

Answer 12

a sampling frame is needed, each person or thing is given a unique number and a selection of these numbers are chosen at random - done through generating random numbers or lottery sampling (written on tickets and placed in a hat).

Question 13

what are the advantages of simple random sampling?

Answer 13

• free of bias.
• easy and cheap for small populations and small samples.
• each sampling unit has an equal chance of selection.

Question 14

what are the disadvantages of simple random sampling?

Answer 14

• not suitable for large population / sample size as it is time consuming, disruptive and expensive.
• a sampling frame is needed.

Question 15

what is systematic sampling?

Answer 15

the required elements are chosen at regular intervals from an ordered list.

Question 16

what is the method of systematic sampling?

Answer 16

a sampling frame is needed, the first person or thing is chosen at random then the next people / items are chosen in intervals.

Question 17

what are the advantages of systematic sampling?

Answer 17

• simple and quick to use.
• suitable for large samples and large populations.

Question 18

what are the disadvantages of systematic sampling?

Answer 18

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

Question 19

what is stratified sampling?

Answer 19

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

Question 20

what is the method of stratified sampling (the formula)?

Answer 20

the proportion of each strata sample should be equal, the formula is:
number sampled in a stratum = (number in stratum / number in population) x overall sample size

Question 21

what are the advantages of stratified sampling?

Answer 21

• the sample accurately reflects the population structure.
• guarantees proportional representation of groups within a population.

Question 22

what are the disadvantages of stratified sampling?

Answer 22

• the population must be clearly classified into distinct strata.
• selection within each stratum is not suitable when population is large.

Question 23

what are the 2 types of non-random sampling?

Answer 23

quota sampling and opportunity/convenience sampling.

Question 24

what is quota sampling?

Answer 24

when an interviewer or researcher selects a sample that reflects the characteristics of the whole population.

Question 25

what is the method of quota sampling?

Answer 25

the population is divided into groups according to a given characteristics, the size of each group determines the proportion of the sample, the interviewer would meet people, assess group and allocate into appropriate quota - this would be continuously until all quotas have been filled.

Question 26

what are the advantages of quota sampling?

Answer 26

- allows small samples to be representative of population. - no sampling frame is required. - quick, easy and inexpensive. - allows easy comparison between different groups within a population.

Question 27

what are the disadvantages of quota sampling?

Answer 27

- can introduce bias. - population must be divided into groups which can be costly or inaccurate. - time consuming and expensive. - non-responses are not recorded.

Question 28

what is opportunity / convenience sampling?

Answer 28

it 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.

Question 29

what is the method of opportunity / convenience sampling (example)?

Answer 29

an example would be going outside the football stadium asking people their favourite sports.

Question 30

what are the advantages of opportunity / convenience sampling?

Answer 30

- easy to carry out. - inexpensive.

Question 31

what are the disadvantages of opportunity / convenience sampling?

Answer 31

- unlikely to provide a representative sample. - highly dependent on individual researcher.

Question 32

what is quantitative variables / data?

Answer 32

variables or data associated with numerical observations.

Question 33

what is qualitative variables / data?

Answer 33

variables or data associated with non-numerical observations.

Question 34

what is a continuous variable?

Answer 34

a variable that can take any value in a given range.

Question 35

what is a discrete variable?

Answer 35

a variable that can take only specific values in a given range.

Question 36

in a grouped frequency table, what do the class boundaries tell us?

Answer 36

the maximum and minimum values that belong in each class.

Question 37

in a grouped frequency table, what does the midpoint tell us?

Answer 37

average of class boundaries.

Question 38

in a grouped frequency table, what does the class width tell us?

Answer 38

the difference between upper and lower class boundaries.

Question 39

what are measures of location?

Answer 39

single values which describe a position in a data set.

Question 40

what are measures of central tendency?

Answer 40

single values which describe the centre of the data, i.e. notion of average.

Question 41

what are the measures of central tendency used in maths?

Answer 41

mean, median and mode/modal class.

Question 42

what is the mean?

Answer 42

it is .... and it can be calculated using the formula

Question 43

what is the median?

Question 44

what is the mode/modal class?

Question 45

how do you find the position of the median for listed discrete data?

Answer 45

find n/2 - if a decimal, round up - if whole use halfway between this item and one after.

Question 46

how do you find the position of the median for grouped continuous data?

Answer 46

find n/2, then use linear interpolation.