Applied Maths Flashcards
A population is
The whole set of items that are of interest
A sample is
Some subset of the population intended to represent the population.
Sampling unit
Each individual thing in the population that can be sampled
Sampling frame
Often sampling units of a population are individually named or numbered to form a list
Census
Data collected from the entire population
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
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
Random sampling
Each sampling unit in our sampling frame has an equal chance of being selected (avoids bias)
How to carry out random sampling
In sampling frame each item is assigned a number. Use random number generator or lottery sampling
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
Systematic sampling
Required elements are chosen at regular intervals in ordered list
How to carry out systematic sampling
Take every kth element where: k=population size/ sample size starting at random item between 1 and k
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
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
How to carry out stratified sampling
Same proportion (sample size/ population size) sampled from each strata
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
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
How to carry out quota sampling
Interviewer selects the actual sampling units
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
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
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.
Modelling assumptions (inextensible)
Does not stretch under a load. Acceleration in constant in objects connected by a taut inextensible string
Uniform acceleration
Constant acceleration
Retardation
Deceleration
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
0
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)
