Stats & mechanics edexcel a level maths

Census

Every member of the population

Sample

A selection of observations taken from a subset of the population which is used to find out information about the population as a whole

Simple random sampling

Random sampling- everyone the sample has a equal chance of being selected. E.g. each person given a number and then the numbers are chosen from random

Systematic sampling

Random sampling- the required elements are chosen at regular intervals from an ordered list. E.g. choose a number between 1-10 randomly and if you got 5, choose every 5th person after that

Stratified sampling

Random sampling- Population is in groups, and a proportional random sample is taken for each group. The formula for choosing how many people to take from each group (number in group)/(number in population) x overall sample size

Quota sampling

Non-random- an interviewer selects a sample that reflects the characteristics of the whole population, and keep going until they have done as much as needed.

Opportunity sampling

Non-random- taking the sample from people who are available at the time the study is carried out and who fit the criteria

Locations in the large data set

Leuchars-UK

Leeming- UK

Heathrow-UK

Hurn-UK

Camborne-UK

Jacksonville-USA

Beijing-China

Perth-Australia

What is measured in the large data set

Daily mean temperature

Daily total rainfall

Daily total sunshine

Daily mean wind direction&speed

Daily maximum gust

Daily maximum relative humidity

Daily mean cloud cover

Daily mean visibility

Daily mean pressure

Mode/modal class

the value that comes up most often

Median

The middle value when they are in order

Mean

Sum of all the values divided by the number of values

Lower quartile

25% of the way through the data

Upper quartile

75% of the way through the data

Range

Largest value-smallest value

Interquartile range

Upper quartile-lower quartile

Coding

Used to simplify statistical calculations. Formula y=(x-a)/b

Outlier

Anything above Q3+k(IQR) or below Q1-k(IQR)

Frequency density

Frequency density = frequency/class width

Mutually exclusive events

P(AnB) = P(A)+P(B)

Independent events

P(AUB) = P(A) x P(B)

Probability distribution

A table which fully describes the probability of any outcome in the sample space

Discrete uniform distribution

When all the outcomes have the same probability

Binomial distribution

X~B(n, p) where n is a fixed no. of trials, p is the probability of success and there are only 2 outcomes, success and failure, the trials are independent

H0

The null hypothesis- the hypothesis you assume to be true

H1

The alternative hypothesis- the hypothesis you are trying to prove/disprove

H1:p<0 H1:p>0

One-tailed test

H1:p=/0

Two-tailed test

Average velocity

=total displacement/time taken

Average speed

=total distance travelled/time taken

Gradient in a velocity-time graph

Acceleration

Area in a velocity-time graph

Distance travelled

s-v-a

>dy/dt

y=ax^n

logy = loga + nlogx

y=kb^x

logy = logk + xlogb

Hypothesis testing for 0 correlation

H0 is always that p=0. Find the critical value in the formula booklet

Normal distribution

X~N(mean, variance)

mean=median=mode

are under curve=1

Standard normal distribution

Z~N(0,1^2)

Approximating a binomial distribution

If n is large and p is close to 0.5 the binomial can be approximated as a normal dist where the mean=(numberxprobability)

standard dev=root(numberxprob)x(1-p)

you need to apply a continuity correction

Moment

=force x perpendicular distance Ncm

Equilibrium

The resultant force and moment about any point is 0

Uniform rod

Mass is spread evenly, centre of mass in the middle

Non-uniform rod

Not evenly distributed, centre of mass not in the middle

Frictional force

Fmax = coefficient of friction x reaction force

Horizontal motion of a projectile

Constant velocity. S=ut

Vertical motion of a projectile

Constant acceleration. SUVAT equation

Constant velocity in vectors

r=r0+vt

Constant acceleration in vectors

v=u+at

r+ut+1/2at^2