Applied maths

Question 1

Definition of population

Answer 1

Whole set of items that are of interest e.g. items manufactured in a factory or people living in a town

Question 2

Definition of raw data

Answer 2

Information obtained by a population

Question 3

Definition of census

Answer 3

Observes or measures every member of a population

Question 4

Definition of parameter

Answer 4

Memorable characteristic of a population e.g. mean or standard deviation

Question 5

Definition of sample

Answer 5

Selection of observations taken from a subset of the population which is used to find out info about the population as a whole

Question 6

Definition of statistic

Answer 6

Single measure of some attribute of a sample e.g. mean value

Question 7

Advantage of census vs sample

Answer 7

Complete and more accurate result

Question 8

Disadvantages of census vs sample

Answer 8

Time consuming
Expensive
Hard to process large quantities of data
Cannot be used when testing process destroys item

Question 9

Advantages of sample vs census

Answer 9

Less time consuming
Cheaper
Easier to process
Fewer people have to respond

Question 10

Disadvantages of sample vs census

Answer 10

Less reliable

Could be biased

Question 11

Different types of sampling methods

Answer 11

Simple random
Systematic 
Stratified 
Cluster 
Opportunity
Quota 
Self-selected

Question 12

Simple random sampling

Answer 12

Any sampling method in which very member has an equal chance of being selected

Question 13

Examples of simple random sampling

Answer 13

Numbering the population and using a random number generator

Selecting names from a hat

Question 14

Systematic sampling

Answer 14

For a population of size N, to find a sample of size n we first set k=N/n. We now take a random member of the first k members, then take the kth member after that

Question 15

Stratified sampling

Answer 15

This is when a population is divided into subgroups (called strata). A sample is then taken from each group of a size proportional to the group size

Question 16

Cluster sampling

Answer 16

Used when a population can be divided into subgroups which are each reasonably representative of the whole population. Then we take a sample from just a few of those subgroups

Question 17

Example of cluster sampling

Answer 17

Researcher wants to survey academic performance of students. Population could be divided by city and within the cities perform simple random or systematic
sampling

Question 18

Opportunity sampling

Answer 18

This is used when you are unable to list a population. Member of a population are chosen for the sample as you have access to them

Question 19

Example of opportunity sampling

Answer 19

Asking members of the public you see first

Question 20

Quota sampling

Answer 20

This is used if you are unable to list a population, but you want to represent distinct groups within the sample. Use opportunity sampling until you have the specified size of sample for each group (or stratum)

Question 21

Example of quota sampling

Answer 21

Interviewers meet and assess people before allocating them into the appropriate quota. This continues until all quotas have been filled - if someone refuses or their quotas is full you move onto the next person

Question 22

Self-selected sampling

Answer 22

This is where the individuals in a population choose to be in a sample

Question 23

Frequency density

Answer 23

Frequency/ class width

Question 24

When is a distribution roughly symmetrical

Answer 24

Q2 - Q1 = Q3 - Q2

Question 25

When is a distribution positively skewed

Answer 25

Q2-Q1

Question 26

When is a distribution negatively skewed

Answer 26

Q2 - Q1 > Q3 - Q2

Question 27

Outliers

Answer 27

``` Marked on box plot as asterisk Smaller than (Q1 - 1.5 * IQR) Larger than (Q3 + 1.5 * IQR) ```

Question 28

Cumulative frequency diagrams

Answer 28

``` Plotted above the upper class boundaries of the intervals Points joined by straight line ```

Question 29

Linear interpolation

Answer 29

``` To find the median: Lower class boundary + ((median value - values preceding median)/ values in interval) * class width ```

Question 30

Sample space

Answer 30

Set of all possible outcomes | Example - in a test with 70 questions, the sample space for correct answers is {0, 1, 2, ..., 70}

Question 31

Event

Answer 31

Collection of some of the outcomes from an experiment | Example - getting >40 on the quiz

Question 32

Relative frequency

Answer 32

No. of times event occurs/ number of times experiment is repeated

Question 33

Mutually exclusive

Answer 33

If two events can’t occur at the same time

Question 34

Independent events

Answer 34

If the occurrence of one has no effect on the probability on the second occurring

Question 35

Conditional probability

Answer 35

Probability of event A happening given that event B has happened

Question 36

Correlation

Answer 36

Measure of relationship

Question 37

Variables in scatter graph

Answer 37

``` Independent variable (explanatory) is horizontal Dependent (response) variable is vertical ```

Question 38

Correlation coefficient

Answer 38

-1 is perfect negative correlation 0 is no correlation 1 is perfect positive correlation

Question 39

Discrete data

Answer 39

Can take any one of a finite set of categories or values, but nothing in between those values. Often the values are different categories

Question 40

Continuous data

Answer 40

Always numbering and can take any value between two points on a number line

Question 41

Probability distribution

Answer 41

Random experiment shows how the total probability of 1 is distributed between all the possible outcomes

Question 42

Discrete distribution

Answer 42

Shown in a bar chart - height of each bar represents probability Total height of all bars = 0

Question 43

Conditions for binomial distribution

Answer 43

Two possible outcomes in each trial Fixed number of trials (n) Independent trials The probability of a success (p) is constant