Flashcards in Applied maths Deck (43)

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## Definition of population

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

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## Definition of raw data

### Information obtained by a population

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## Definition of census

### Observes or measures every member of a population

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## Definition of parameter

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

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## Definition of sample

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

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## Definition of statistic

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

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## Advantage of census vs sample

### Complete and more accurate result

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## Disadvantages of census vs sample

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Time consuming

Expensive

Hard to process large quantities of data

Cannot be used when testing process destroys item

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## Advantages of sample vs census

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Less time consuming

Cheaper

Easier to process

Fewer people have to respond

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## Disadvantages of sample vs census

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Less reliable

Could be biased

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## Different types of sampling methods

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Simple random

Systematic

Stratified

Cluster

Opportunity

Quota

Self-selected

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## Simple random sampling

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

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## Examples of simple random sampling

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Numbering the population and using a random number generator

Selecting names from a hat

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## Systematic sampling

### 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

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## Stratified sampling

### 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

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## Cluster sampling

### 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

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## Example of cluster sampling

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

sampling

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## Opportunity sampling

### 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

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## Example of opportunity sampling

### Asking members of the public you see first

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## Quota sampling

### 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)

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## Example of quota sampling

### 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

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## Self-selected sampling

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

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## Frequency density

### Frequency/ class width

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## When is a distribution roughly symmetrical

### Q2 - Q1 = Q3 - Q2

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## When is a distribution positively skewed

### Q2-Q1

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## When is a distribution negatively skewed

### Q2 - Q1 > Q3 - Q2

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## Outliers

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Marked on box plot as asterisk

Smaller than (Q1 - 1.5 * IQR)

Larger than (Q3 + 1.5 * IQR)

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## Cumulative frequency diagrams

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Plotted above the upper class boundaries of the intervals

Points joined by straight line

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## Linear interpolation

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To find the median:

Lower class boundary + ((median value - values preceding median)/ values in interval) * class width

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