Introduction to Statistics: Understanding Populations, Samples, and Data Collection

okay so we're starting statistics and statistics is the first part of applied maths that we're going to be doing

um and really this is a big overview of what statistics looks like at a level so it says here that the chapter of

stats year one could be broadly organized as followed as follows so we've got these two halves

of things we've got the experimental half experimental means that it's dealing

with experiments it's dealing with data that has been collected and so we're going to start off today

with data collection which is talking about how you sample things different types of data

populations and samples and things like that and then we're going to come to some really familiar kinds of things

like averages and range and some other familiar things about how you represent data

things like box plots and histograms stuff that you've come across at gcse and then i've got this chapter

of correlation which is to do with scatter diagrams that kind of falls in between both of

these things because there's a mixture of some of the real life collection and some stuff to do with theoretical

statistics as well so the second half of statistics is theoretical statistics

which deals more with probabilities and modeling to make inferences or predictions about what we expect to see

and we often use this to reason about or contrast with experimentally collected data so this is going to be

like real data that you will be doing things too this other half will be about making

predictions and then comparing it to the original data and seeing what kinds of patterns there are

so that's basically going to be probability different types of probability distributions

and then something called hypothesis testing which we'll be coming up to right at the end of this because it's

definitely the hardest part that we have here so we're going to start off with data

collection today and for the data collection this is what it kind of breaks down into we're going

to break down into thinking about populations and samples different types of sampling we've got

here different types of data and then something called the large data set which i'll tell you a bit more about

when we get to it so let's kick off and think about what the definitions are there's a lot of definitions in

statistics so i've printed as many of these as i can in your booklet so that you can have

them to refer back to so this says about populations and samples

i've got a picture here to represent the population and then a subgroup of this population

is called the sample now the population is the whole set of items that are of interest

now it's probably used you're probably used to hearing the word population meaning all of the humans or animals

within a country or an ecosystem but a population in statistics could mean other things

it could mean all of the light bulbs in a factory or all of the cars in the uk so

population doesn't mean people or animals in statistics it just means all of the things in the particular

group that we're looking at and then a sample is some subset of the population

intended to represent the population so you take a smaller group because taking the whole

group is often going to be a lot more work so that's what we mean by population and

sample and anytime i've got some of these things underlined they're often like the key parts of the

definitions that we need to know about so some key terms to do with sampling here that you need to know

each individual thing in the population that can be sampled is known as a sampling unit

this isn't something you just need to understand this is something you need to know that a sampling unit

is each of the individual things within the population often sampling units of a population are

individually individually named or numbered to form a list

called the sampling frame so in this particular population that we've got here we could

assign each sample unit a number which would then create a list which is called the sampling frame so

the sampling frame is like the um yeah just the database of all of the population that exists

so we need to talk about some differences between populations and samples

it says that we could collect data either from a sample or from the entire population this is

another keyword that we need to know about it says that data collected from the entire population

is known as a census have you heard of a census before yeah a census is they do that i think

once every 10 years in the in the uk where they try and get a response to a survey

from every single person and it's a huge huge undertaking so some of the advantages of a census is

it should give you completely accurate results because you're speaking to absolutely everyone

in that population that you're talking about but a disadvantage of doing a census is it's really time consuming and

it's expensive so that's why we don't have a census every year we have it every 10 years and

even then it's a huge huge undertaking this cannot be used you cannot do a census

when the testing involves destruction so for example if you wanted to find out how many biscuits were a machine filled

into a box or a bag in a factory if you had to open up every packet of biscuits to find out how many biscuits

were in the packet you can't do a census in that factory because

all of the biscuits they've been making in those packets will have been opened up and will go stale so you can't

do a census if it's going to destroy everything that you've got the other disadvantage is there's just a

large volume of data to process and that takes a lot of work to be able to do that so why do a sample well it's

cheaper it's quicker there's less data to process but the disadvantages is that

the data may not be accurate depending on how you've taken that sample and the data may not be large enough to

represent small subgroups so let's just talk about when the data may not be accurate when we've

seen like after elections often there will be there will be polling before an election to try and

predict who will win the election or even things with like brexit and then when the result actually comes out

it hasn't reflected it carefully and that's because the uh the election itself or the referendum

is trying to be more like a census of speaking to everyone whereas when they do the polling that's

just speaking to a smaller sample so it may not represent the whole group so let's just have a look at an example

here before we'll do some practice questions from exercise 1a it says that a supermarket wants to test

a delivery of avocados for ripeness by cutting them in half and it says to begin with suggest a reason why the

supermarket should not not test all the avocados in the delivery so why shouldn't they test all

the avocados in delivery they're going to destroy all of them they're going to damage all of them

so they shouldn't test all of the avocados because testing destroys

or damages the avocado and that's a really bad idea because you'll have no avocados

even if they're ripe or not and then it says the supermarket tests a sample of five avocados and finds that four of

them are ripe they estimate that 80 of the avocados in the delivery

are ripe suggest one way that the supermarket could improve their estimate yeah they could increase

the sample size so pretty straightforward they could increase the sample size

because a sample size of five is very small increase the sample size

five is a very small sample and so it sounds pretty straightforward about what we're talking here with

populations and samples but i just wanted to look at all of the questions in exercise 1a to begin with

because these are the questions in the exam that people think oh they're really easy they're just like a one marker or

two marker but they actually tend to be the questions that people actually miss the

most so i want to go and have a look now exercise 1a and i want to work through

all the questions that we've got there okay