A level Stats

population

whole set of items that are of interest

census

observes or measures every member of a population

sample

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

advantages of a census

it should give a completely accurate result

disadvantages of a census

• time consuming and expensive

• cannot be used when testing process destroys the item

• hard to process large quantity of data

advantages of a sample

• less time consuming and expensive than a census

• fewer people have to respond

• less data to process than in a census

disadvantages of a sample

• data may not be as accurate

• the sample may not be large enough to give information about small sub-groups of the population

sampling units

individuals (units) of a population

sampling frame

list of sampling units

what are the three types of random sampling?

Simple random, stratified, and systematic sampling

simple random sampling

the elements of the sample have an equal chance of being selected

two types of simple random sampling

random number and lottery sampling

advantages of simple random sampling

• free of bias

• each sampling unit has a known and equal chance of selection

• easy and cheap to implement for small populations and small samples

disadvantages of simple random sampling

• not suitable when population size or sample size is large as it is potentially time consuming,disruptive and expensive

• a samplign frame is needed

systematic sampling

the required elemenrs are chosen at regular intervals from an ordered list/take every kth unit when k = pop/sample (first person is chosen at randomly)

advantages of systematic random sampling

• simple and quick to use

• suitable for large samples and large populations

disadvantages of systematic sampling

• sampling frame is needed

• can introduce bias if the sampling frame is not random

stratified sampling

population is divided into mutually exclusive strata (groups) and a random sample is taken from each.

no. sampled in a stratum = no. in stratum/no.in population x overal sample size

advantages of stratified sampling

• reflect population structure

• guarantees proportional representation of groups within a population

disadvantages of stratified sampling

• population must be clearly classified into strata

• selectrion within each stratum suffers from the same disadvantages as simple randomsampling.

two types of non-random sampling

quota and opportunity sampling

quota sampling

interviewer or researcher selects a sample that reflects the characteristics of a whole population - like stratified sampling, strata are filled by interviwer or researcher

advantages of quota sampling

• no sampling frame required

• allows a small sample to still be representative of a whole population

• quick, easy and inexpensive

disadvantages of quota sampling

• non-random sampling can introduce bias

• non-responses are not recorded as such

opportunity sampling

taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for.

advantages of opportunity sampling

easy to carry out and cheap

disadvantages of quota sampling

unlikely to be representative and highly dependent on individual researcher

quantitative data

numerical data eg. shoe size

qualitative data

non-numerical data eg. hair colour

discrete

a variable that can take only specific values in a given range eg. number of girls in a family has to be an integer

comtinuous

a variable that can take any value in a given range eg. time

what are the five UK weather stations?

• Leuchars (most northern)

• Leeming

• Heathrow

• Hurn

• Camborne (most southern)

map of Uk weather stations

what are the 3 international stations?

• Jacksonville (Nothern Hemisphere)

• Beijing (Northern Hemisphere)

• Perth (southern hemisphere)

map of international stations

when for large data sets?

may - october 1987 and 2015

coastal weather stations

windier and rainier areas in UK

southern weather stations

more sunshine and warmer in the day in the UK

perth

summer and winter switched around + very hot in summer

beijing

really hot, really rainy in the summer, very cold in the winter (more extreme)

jacksonville

warm and prone to hurricanes, two hurricans in oct 87 and oct 15

daily mean temp

(°C) - average of the hourly temperature readings during a 24 hour period

daily total rainfall

includes snow and hail - amounts less than 0.05 mm are recorded as ‘tr’ or ‘trace’ (treat as 0 in calculations)

n/a

means reading is not available, can’t be used in a sample

daily total sunshine

recorded to the nearest tenth of an hour

daily mean cloud cover

meaured in oktas or eigths of the sky covered by clouds (integers from 0 - 8)

daily maximum gust

strongest windspeed 1 knot = 1.15mph, great storm UK ocr 15/16th ‘87

daily mean wind direction and windspeed

knots, averaged over 24 hours, wind directions are given as bearings and as cardinal (compass) directions. data for mean windspeed is also categorised according to beauford scale

daily max relative humidity

percentage air saturation with water - relative humidities abpove 9% give rise to misty and foggy conditions

daily mean visbility

measured in (Dm) decametres. - greatest horizontal distance at which an object can be seen in the distance

daily mean pressure

measured in hPa, hectopascals

casual relationship

if a change in one variable causes a change in the other (however, just because 2 variables show correlation does not necessarily mean they have a casual relationship)

regression line

y = a + bx

when is using a regression line valid

regression line should only be used to predict a value of y when given x

interpolation

estimate inside the data range - reliable

extrapolation

estimate outside the data range