Edexcel A level Maths: Statistics
and Mechanics
What is population? correct answers The whole set of items that are of
interest
What is a sample? correct answers some subset of the population
intended to represent the population
What is a census? correct answers Data collected from the entire
population
Advantages and disadvantages of a census correct answers > should give
completely accurate result
but...
> time consuming and expensive
> can't be used when testing involves destruction
> large volume of data to process
Advantages and disadvantages of a sample correct answers > cheaper
> quicker
>less data to
process but...
> data may not be
accurate
> data may not be
large enough to
represent small
sub-groups
A supermarket
wants to test the
ripeness of
avocado's by
cutting them in
half.
a. why shouldn't
they not test all
of the avocados
b.they test that 4/5 are ripe so estimate 80% are ripe, suggest one way
that they could improve their estimate correct answers a- testing avocados
destroys them so thus cannot be sold
c. use a larger sample size as it is a better estimate for the proportion of
ripe avocados
What is random sampling? correct answers everyone in the population
has an equal chance of being chosen to avoid bias.
Simple random sampling what is it and method? correct answers > every
sample has an equal chance to be selected
> each item has a identifying number
, but...
> not suitable when population size is large
> sampling frame needed
There are 64 girls and 56 boys in a school. Explain briefly how you could
take a random sample of 15 pupils using a simple random sample. correct
answers > Allocate a number between 1 and N to each pupil
>use random number tables, computer to select 15 different numbers
between 1 and 120
>pupils corresponding to these numbers become the sample
What is systematic sampling? correct answers The required elements are
chosen at regular intervals from an ordered list
k= pop size/ samp size
Advantages and disadvantages of systematic sampling correct answers >
simple and quick to use
>suitable for large
samples/population but...
>sampling frame again needed
>bias if sample frame not random
A telephone directory contains 50,000 names a researcher wishes
to select a systematic sample of 100 names from the directory.
Explain in detail how the researcher should obtain such a sample.
correct answers 50,000/100=500
>randomly select a number between 001 and 500
>select every 500th person
What is stratified sampling? correct answers > population divided into
groups and a simple random sample carried out in each group
>samp size/ pop size
>used when sample is large and population naturally divides into groups
Advantages and disadvantages of stratified sampling correct answers
> reflects population structure
>guarantees proportional representation of groups within
population but...
>population must be clearly classified into distinct strata
>same disadvantage as simple random sampling
A school has 15 classes and a sixth form. Each class 30 students and in
sixth form 150 students. Equal number of boys and girls in class and sixth
form. Explain how the head teacher would take a stratified sample of size
40. 7 correct answers > Total in school (15×30)+150= 600
>30/600×40= 2 from each of the 15 classes
>150/600×40= 10 from sixth form
and Mechanics
What is population? correct answers The whole set of items that are of
interest
What is a sample? correct answers some subset of the population
intended to represent the population
What is a census? correct answers Data collected from the entire
population
Advantages and disadvantages of a census correct answers > should give
completely accurate result
but...
> time consuming and expensive
> can't be used when testing involves destruction
> large volume of data to process
Advantages and disadvantages of a sample correct answers > cheaper
> quicker
>less data to
process but...
> data may not be
accurate
> data may not be
large enough to
represent small
sub-groups
A supermarket
wants to test the
ripeness of
avocado's by
cutting them in
half.
a. why shouldn't
they not test all
of the avocados
b.they test that 4/5 are ripe so estimate 80% are ripe, suggest one way
that they could improve their estimate correct answers a- testing avocados
destroys them so thus cannot be sold
c. use a larger sample size as it is a better estimate for the proportion of
ripe avocados
What is random sampling? correct answers everyone in the population
has an equal chance of being chosen to avoid bias.
Simple random sampling what is it and method? correct answers > every
sample has an equal chance to be selected
> each item has a identifying number
, but...
> not suitable when population size is large
> sampling frame needed
There are 64 girls and 56 boys in a school. Explain briefly how you could
take a random sample of 15 pupils using a simple random sample. correct
answers > Allocate a number between 1 and N to each pupil
>use random number tables, computer to select 15 different numbers
between 1 and 120
>pupils corresponding to these numbers become the sample
What is systematic sampling? correct answers The required elements are
chosen at regular intervals from an ordered list
k= pop size/ samp size
Advantages and disadvantages of systematic sampling correct answers >
simple and quick to use
>suitable for large
samples/population but...
>sampling frame again needed
>bias if sample frame not random
A telephone directory contains 50,000 names a researcher wishes
to select a systematic sample of 100 names from the directory.
Explain in detail how the researcher should obtain such a sample.
correct answers 50,000/100=500
>randomly select a number between 001 and 500
>select every 500th person
What is stratified sampling? correct answers > population divided into
groups and a simple random sample carried out in each group
>samp size/ pop size
>used when sample is large and population naturally divides into groups
Advantages and disadvantages of stratified sampling correct answers
> reflects population structure
>guarantees proportional representation of groups within
population but...
>population must be clearly classified into distinct strata
>same disadvantage as simple random sampling
A school has 15 classes and a sixth form. Each class 30 students and in
sixth form 150 students. Equal number of boys and girls in class and sixth
form. Explain how the head teacher would take a stratified sample of size
40. 7 correct answers > Total in school (15×30)+150= 600
>30/600×40= 2 from each of the 15 classes
>150/600×40= 10 from sixth form
