Applied Maths Flashcards by Peter Abdul-Ahad

A population is

The whole set of items that are of interest

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A sample is

Some subset of the population intended to represent the population.

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Sampling unit

Each individual thing in the population that can be sampled

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Sampling frame

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

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Census

Data collected from the entire population

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Census pros and cons

Should give you a completely accurate result
Time consuming and expensive
Cannot be used when testing involves destruction
Large volume of data to process

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Sample pros and cons

Cheaper, quicker, less data to process

Data may not be accurate
Data may not be large enough to represent small sub-groups

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Random sampling

Each sampling unit in our sampling frame has an equal chance of being selected (avoids bias)

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How to carry out random sampling

In sampling frame each item is assigned a number. Use random number generator or lottery sampling

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Random sampling Pros and cons

Bias free, easy and cheap to implement, each number has a known equal chance of being selected

Not suitable when population size is large, sampling frame needed

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Systematic sampling

Required elements are chosen at regular intervals in ordered list

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How to carry out systematic sampling

Take every kth element where: k=population size/ sample size starting at random item between 1 and k

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Systematic sampling Pros and cons

Simple and quick to use, suitable for large samples and populations

Sampling frame required
Can introduce bias if sampling frame not ramdom

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Stratified sampling

Population divided into groups (strata) and a simple random sample carried out in each group.

Used when sample is large and population naturally divides into groups

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How to carry out stratified sampling

Same proportion (sample size/ population size) sampled from each strata

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Stratified sampling Pros and cons

Reflects population structure, guarantees proportional representation of groups within population

Population must be clearly classified into distinct strata, selection within each strata suffers from same disadvantages as simple random sampling

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Quota sampling

Population divided into groups according to characteristic. A quota of times/ people in each group is set out to try and reflect the group’s proportion in the whole population

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How to carry out quota sampling

Interviewer selects the actual sampling units

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Quota sampling Pros and cons

Allows small sample to still be representative of population
No sampling frame required
Quick easy inexpensive
Allows for quick and easy comparison between different groups in population

Non random sampling can introduce bias
Population must be divided into groups, could be costly and Inaccurate
Increasing scope of study increases number of groups, adding time) expensive
Non-responses are not recorded

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Model assumptions (light)

It’s mass is very small (regarded as zero), such as a string or pulley, tension is the same at both ends of a light string

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Modelled assumption (particle)

Dimensions of the object are negligible. It’s mass is concentrated at a single point. Air resistance and rotational forces can be ignored.

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Modelling assumptions (inextensible)

Does not stretch under a load. Acceleration in constant in objects connected by a taut inextensible string

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Uniform acceleration

Constant acceleration

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Retardation

Deceleration

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If there’s no air resistance for a falling object it’s acceleration is..

Constant

When is the max height of a particle reached

When v=0

The speed of a projectile is another name for the objects...

Initial speed

Opportunistic sampling method

Sample taken from the people who are available at time of study, who meet criteria

Opportunistic sampling pros and cons

Easy to carry out, inexpensive Unlikely to present a representative sample, Highly dependent on individual researcher

Types of data

Qualitative (non-numerical values) Quantitative (numerical values), discrete (can only take specific values, shoe size), continuous (can take any decimal value).

List the 5 locations in UK (starting from south up)

Cambourne Hearn Heathrow Leeming Leuchars

Coastal areas are more likely to be...

Rainy and windy

The area lower down (southern) tend to be...

Warmer and have high levels of sunlight

International stations (3)

Perth, Australia (really hot in summer) Beijing, China (extreme weathers due to season) Jacksonville, Florida (prone to hurricanes, 2 hurricanes Oct 87 Oct 15, warm for most of year)

Rainfall, tr

Means trace, treat this as 0.025 in calculations

N/A

Means reading is not available, so can’t use in a sample

Cloud cover

Measured in oktas, discrete value integers 0-8

Max gust

Measured in knots 1kn=1.15mph Great storm Oct 15th/16th 1987 in Uk

For grouped data do you round

Don't round

What's advantage of IQR

Ignores extreme values

Equation for variance

Mean of the squares minus square if the means

For coding if y=ax + b What's the mean for of y and its standard deviation

Mean: a(mean x)+b Standard deviation: a(mean x)

When should you use a histogram

If the data is continuous No gaps

What's frequency density equal to

Freq/ class width

Area of a histogram

Freq x k

What do u compare when asked for comparisons of data

Location Spread Put them into context

What's a regression line

The line of best fit

What's interpolation

Estimating inside the data range More reliable

What's Extrapolation

Estimating outside the data range Not reliable

What does it mean if A and B are mutually exclusive

Probability A and B =0 (can't happen at the same time) Probability A or B= P(A) + P(B)

What does it mean if A and B are independent

Probability A and B = P(A)xP(B) P(A/B)=P(A) Can't tell from Venn diagram if they're are independent

What is the discrete uniform distribution

Probabilities of outcomes all equal P

When can you use a binomial distribution (4), FFIT

F ixed number of trials F ixed probability of success (p) I ndependent trials T wo outcomes, success/ failure

Null Hypothesis

Ho, what we assume to be true

Alternative hypothesis

H1, what would be true if Ho is incorrect

One tailed Tests

When H1, p less than k, p greater than k

Two tailed testing

When H1, p is not equal to k (Halve the value of the significance level, for each end).

For variable acceleration what do we do

Differentiate or integrate

What's the acceleration for the Horizontal motion in projectiles

What's the acceleration for the vertical component in projectiles

-g

How is the horizontal and vertical assets of projectiles linked

By time (the same)

Modelling assumptions, smooth pulley

Tension on either side of pulley is equal, no friction

Modelling assumptions, Rod

Rigid so it doesn't bend, it has no thickness

Which direction does tension act Which direction does thrust act

Tension: inwards Thrust: away from each other (the arrows)