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Flashcards in Applied maths Deck (43)
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1

Definition of population

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

2

Definition of raw data

Information obtained by a population

3

Definition of census

Observes or measures every member of a population

4

Definition of parameter

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

5

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

6

Definition of statistic

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

7

Advantage of census vs sample

Complete and more accurate result

8

Disadvantages of census vs sample

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

9

Advantages of sample vs census

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

10

Disadvantages of sample vs census

Less reliable
Could be biased

11

Different types of sampling methods

Simple random
Systematic
Stratified
Cluster
Opportunity
Quota
Self-selected

12

Simple random sampling

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

13

Examples of simple random sampling

Numbering the population and using a random number generator
Selecting names from a hat

14

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

15

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

16

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

17

Example of cluster sampling

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

18

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

19

Example of opportunity sampling

Asking members of the public you see first

20

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)

21

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

22

Self-selected sampling

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

23

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

27

Outliers

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

28

Cumulative frequency diagrams

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

29

Linear interpolation

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

30

Sample space

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