# A Level Maths Question

Watch
Announcements
Thread starter 3 months ago
#1
A lake contains three different types of carp.
There are an estimated 450 mirror carp, 300 leather carp and 850 common carp. Tim wishes to investigate the health of the fish in the lake.
He decides to take a sample of 160 fish.
(a) Give a reason why stratified random sampling cannot be used.
(b) Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented.
You should state the name of the sampling method used.
Last edited by dogsgomoo; 3 months ago
0
3 months ago
#2
(Original post by dogsgomoo)
A lake contains three different types of carp.
There are an estimated 450 mirror carp, 300 leather carp and 850 common carp. Tim wishes to investigate the health of the fish in the lake.
He decides to take a sample of 160 fish.
(a) Give a reason why stratified random sampling cannot be used.
(b) Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented.
You should state the name of the sampling method used.
Not 100% with this answer.

a) Stratified random sampling uses random sampling to pick the sample in each strata and it would be impractical to number each individual fish in the lake.

b) Cluster sampling may be used since it involves taking a group of fish which would represent the average population of the lake. You may want to take 4 groups of 40 fish or 10 groups of 16 fish.
1
Thread starter 3 months ago
#3
(Original post by jadenmeister)
Not 100% with this answer.

a) Stratified random sampling uses random sampling to pick the sample in each strata and it would be impractical to number each individual fish in the lake.

b) Cluster sampling may be used since it involves taking a group of fish which would represent the average population of the lake. You may want to take 4 groups of 40 fish or 10 groups of 16 fish.
you might be right for a), but not so sure for b)- cluster sampling isnt in our spec
0
3 months ago
#4
(Original post by dogsgomoo)
you might be right for a), but not so sure for b)- cluster sampling isnt in our spec
Hmm yeah, not sure what the answer could be then since we are probably on different exam boards. Do you have the answer? Normally, in OCR, these stats questions on sampling are quite rare so don't really come up!
0
2 months ago
#5
(Original post by dogsgomoo)
A lake contains three different types of carp.
There are an estimated 450 mirror carp, 300 leather carp and 850 common carp. Tim wishes to investigate the health of the fish in the lake.
He decides to take a sample of 160 fish.
(a) Give a reason why stratified random sampling cannot be used.
(b) Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented.
You should state the name of the sampling method used.
i'm doing edexcel and trying to find a solution lol but these are my thoughts:
a). stratified random sampling cannot be used because the population is too large so it won't be effective
i got this answer because in the textbook (y1 stats + mechanics) one of the disadvantages is that it's not suitable when the population size is large that's my guess
b). systematic sampling (and then explain the method) this could be wrong but simple random sampling seems a bit vague to write but i have no idea sorry
0
2 months ago
#6
(Original post by dogsgomoo)
A lake contains three different types of carp.
There are an estimated 450 mirror carp, 300 leather carp and 850 common carp. Tim wishes to investigate the health of the fish in the lake.
He decides to take a sample of 160 fish.
(a) Give a reason why stratified random sampling cannot be used.
(b) Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented.
You should state the name of the sampling method used.
There was a similar question to this on the 2012 stats paper:

a) A sampling frame within each species of fish in the lake is impossible to obtain.
‘You can’t / it’s very difficult to number all the fish’ or equivalent is accepted
(Once you’ve calculated sample size for each strata, you must conduct a simple random sample within each strata - this requires a sampling frame as you have to number every individual)
b) Use quota sampling:
(attached a pic)
0
2 months ago
#7
(Original post by Zaftihawlk)
There was a similar question to this on the 2012 stats paper:

a) A sampling frame within each species of fish in the lake is impossible to obtain.
‘You can’t / it’s very difficult to number all the fish’ or equivalent is accepted
(Once you’ve calculated sample size for each strata, you must conduct a simple random sample within each strata - this requires a sampling frame as you have to number every individual)
b) Use quota sampling:
(attached a pic)
Isn't the working in the pic just a stratified sample? You're taking a sample of 160 from each group which isn't a quota sample.
0
2 months ago
#8
(Original post by frogtoasted)
Isn't the working in the pic just a stratified sample? You're taking a sample of 160 from each group which isn't a quota sample.
You want a stratified sample method to find the proportion of samples needed per strata as there are 3 different species of carp (question says “ensure populations of every carp is represented”) but seeming as you can’t do the 2nd part (random sampling of each strata as you need a sampling frame) you can use opportunity sampling in order to fill your quota for that strata (so keep fishing until each carp quota is full and if you fish (eg: mirror carp) and that strata is full you ignore it)
1
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Are you tempted to change your firm university choice on A-level results day?

Yes, I'll try and go to a uni higher up the league tables (17)
28.33%
Yes, there is a uni that I prefer and I'll fit in better (4)
6.67%
No I am happy with my choice (36)
60%
I'm using Clearing when I have my exam results (3)
5%

View All
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.