Statistics

Question 1

Define population

Answer 1

The whole set of items that are of interest to

Question 2

Define census

Answer 2

Observes or measures every member of a population

Question 3

Define sample

Answer 3

A selection of observations taken from a subset of the population which is used to find out information about the population as a whole

Question 4

Advantages of disadvantages of a census and of a sample

Answer 4

Advantages of census
• It should give a completely accurate result

Disadvantages of census
• Time consuming and expensive
• Cannot be used when the testing process destroys the item
• Hard to process large quantity of data

Advantages of sample
• Less time consuming and expensive than
a census
• Fewer people have to respond
• Less data to process than in a census

Disadvantages of sample
• The data may not be as accurate
• The sample may not be large enough to give information about small subgroups of the population

Question 5

Define sampling units

Answer 5

Individual units of a population

Question 6

Define sampling frame

Answer 6

List where sampling units of a population are individually named or numbered

Question 7

3 methods of random sampling

Answer 7

•simple random sampling
•systematic sampling
•stratified sampling

Question 8

Define and give Advantages and disadvantages of simple random sampling

Answer 8

the researcher randomly selects a subset of participants from a population

Advantages
• 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 of workers is not a whole number round to the nearest whole number.

Disadvantages
• Not suitable when the population size or the sample size is large as it is potentially time consuming, disruptive and expensive.
• A sampling frame is needed

Question 9

Advantages and disadvantages of systematic sampling

Answer 9

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

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

Question 10

Advantages and disadvantages of stratified sampling

Answer 10

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

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

Question 11

Define a simple random sample of size n

Answer 11

Every sample of size n has an equal chance of being selected

Question 12

Define systematic sampling

Answer 12

The required elements are chosen at regular intervals from an ordered list

Question 13

Define stratified sampling

Answer 13

The population is divided into mutually exclusive strata (e.g. males and females) and a random sample is taken from each

Question 14

Formula to calculate the number of people we should sample from each stratum

Answer 14

The number samples in a stratum = (number in stratum / number in population) x overall sample size

Question 15

2 types of non-random sampling

Answer 15

•quota sampling
•opportunity sampling

Question 16

Define quota sampling

Answer 16

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

Question 17

Define opportunity sampling

Answer 17

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 18

Advantages and disadvantages of quota sampling

Answer 18

Advantages
• 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

Disadvantages
• 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 19

Advantages and disadvantages of opportunity sampling

Answer 19

Advantages
• easy to carry out
• Inexpensive

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

Question 20

Define quantitative variables/data

Answer 20

Variables or data associated with numerical observations

Question 21

Define qualitative variables/data

Answer 21

Variables or data associated with non-numerical observations

Question 22

Define continuous variable

Answer 22

A variable that can take any value in a given range

Question 23

Define discrete variable

Answer 23

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

Question 24

Define mode or modal class

Answer 24

The value or class that occurs most often

Question 25

Define median

Answer 25

The middle value when the data values are put in order

Question 26

Formula of mean

Answer 26

_ x = Ex / n

Question 27

Formula for mean in frequency table

Answer 27

_ x = Efx / Ef

Question 28

Find median of both listed data and of grouped data

Answer 28

listed data: Find n -if decimal round up -if whole - halfway between this item and the one after Grouped data: find n/2 then use linear interpolation

Question 29

Linear interpolation

Answer 29

Lower class boundary + ((amount into frequency / frequency of class) x class width)

Question 30

P_57 n=43

Answer 30

43x0.57=24.51

Question 31

Q_1 of 100 numbers

Answer 31

100/4=25th Interpolation using 25th number

Question 32

P_10 of 41 numbers

Answer 32

41 x 10%=4.1 4.1st Interpolation using 4.1st number

Question 33

Variance formula

Answer 33

Small sigma squared = (sum of squared values / number of values) - mean^2

Question 34

Standard deviation

Answer 34

Sigma = root of variance

Question 35

Coding standard deviation

Answer 35

Only multiply or divide affect

Question 36

Common definition of an outlier

Answer 36

Either greater than Q_3 + k(Q_3 - Q_1) Or less than Q_1 - k(Q_3 - Q_1)

Question 37

Cleaning the data

Answer 37

= the process of removing anomalies from a data set

Question 38

Formula to calculate the height of each bar (frequency density) on a histogram

Answer 38

Area of bar = k x frequency

Question 39

Frequency polygon from histogram

Answer 39

Join the middle of the top of each bar with equal class widths

Question 40

When comparing data sets comment on:

Answer 40

A measure of location A measure of spread

Question 41

What is Bivariate data

Answer 41

data which has pairs of values for two variables

Question 42

What does Correlation describe

Answer 42

the nature of the linear relationship between two variables

Question 43

causal relationship

Question 44

regression line

Question 45

The coefficient b tells you the change in y for each unit change in x How does correlation change b

Answer 45

• If the data is positively correlated, b will be positive • If the data is negatively correlated, b will be negative

Question 46

When should you use the regression line

Answer 46

to make predictions for values of the dependent variable that are within the range of the given data

Question 47

Venn diagram

Question 48

Mutually exclusive events

Answer 48

P (A or B) = P(A) + P(B)

Question 49

Independent events

Answer 49

P (A and B) = P(A) x P(B)

Question 50

Tree diagram