Maths Statistics - Sampling Methods and Large Data set

Definitions of sampling and their methids, as given by the aqa board Large Data set key facts listed by TLMaths

Simple Random Definition

Simple Random Definition

Every possible sample (of a given size) has an equal chance of being selected

Simple Random method

Assign number to each member of the population

Use a random number generator to generate n numbers, limiting the numbers it can generate from 1 - n. Skip and repull for any numbers that are pulled twice. Once n numbers have been generated, re assign the numbers back to the associated member of the population

Stratified Definition

splitting population into groups relevant to research, then random sampling from each group in proportion to the size of the group

Stratified method

Identify groups to split the population to

Calculate how many of each group shoukd be included, (group/population size * sample size wanted)

Conduct random sample to find sample size wanted in each group

Opportunity Definition

Selecting sample based on convenience and availability

Opportunity Adv

• does not find random sample#

• may produce good estimate of population parameters

• cheap

• convenient

• may not be generalisable

Stratified Adv

srs is representative of overall population, but strat equalizes frequency

requires list of entire population

determining which factors are relevanty to research not always obvious

random

Simple random Adv

requires list of entire population

may be hard to get responses from generated numbers

time consuming and expensive

random and unbiased

Systematic Definition

Taking participants at regular intervals

Systematic Method

Give each name a number from 1 - n

calculate how often a number needs to be selected (population/sample size wanted) = x

Randomly select a number between 1 and x and select every x person on the register from the first person selected

Systematic Adv

avoids unwanted clustering

if there was a fault every x sample, the systematic may end up clustering/fail

practically easier than number generators

random

less random than srs as no longer independent

requires list of entire population

Quota Defintion

Splitting population into groups relevant to research, then selecting participants from those groups using opportunity sampling

Quota Adv

cheap

easy

convenient

alternative to strat when list of population not available

ensures samples relevant to factors identified

NOT RANDOM

Cluster Definition

Splits population into groups bases on convenience (eg location) called clusters, the randomly choosing which group to study further

Cluster Adv

RANDOM

least random out of random methods

worse than strat, high chance of choosing unrepresentative sample

significantly cheaper than alternatives

does not require list of entire population

Large Data Set Headings

Car Brands

Regions

Propulsion Types

Keeper Title IDS

Year Registered

Body Type

Emission Type

Body Types

LDS Car brand details

5 car brands,

BMW
Ford
Toyota
Vauxhall
Volkswagan

LDS DETAIL REgions

3 regions

North west

south west

London

not enough regions to make comparion across entire UK

LDS DETAIL KEEPER TITLE IDS

5 titles

Male

Female

not used - literally not used at all

unknown (eg dr)
Company

LDS Units used

g/km - emissions

cm³ - engine size

kg - weight of car and driver

+75 kg added to each car for driver mass

Missing Data/ Errors LDS

missing data for hydrocarbon and particulate emissions

masses of some cars recorded as zero - ERROR

data needs to be cleaned before being used for parameter calculations

LDS DETAIL Propulsion Types

5 types

Petrol

Diesel

Electric - 1 (!!!) car

Petrol/Gas - 1 car

Petrol/ Electric

LDS DETAIL Emission Types

CO2

CO

NOX

Hydrocarbon

Particulate - only for diesel cars

What years in LDS

2002 and 2016 due to emissions scandel

LDS DETIALS Body types

eg saloon, convertible, 3 or 4 door hatchback