Edexcel A Level Maths – Statistics | Real Based Questions with Correct Answers| Updated for a Perfect 100% score | Graded A+

Edexcel A Level Maths – Statistics | Real Based Questions with
Correct Answers| Updated for a Perfect 100% score | Graded A+
Guideline|:Question ... - Correct Answer ✅💯...
3 different types of random sampling - Correct Answer ✅💯


Simple random sampling
Systematic sampling
Stratified sampling
A ∩ B - Correct Answer ✅💯means both A and B
A ∪ B - Correct Answer ✅💯means A or B or both
advantages / disadvantages of census - Correct Answer ✅💯advantages :


gives a completely accurate result


disadvantages
-time consuming and expensive
-hard to process large quantity of data
advantages/disadvantages of a sample - Correct Answer ✅💯advantages :


less time consuming and expensive than census
fewer people have to respond
less data to process than in a census


disadvantages


data may not be as accurate
sample may not be large enough to give information about sub groups of the
population

,advantages/disadvantages stratified sampling - Correct Answer
✅💯advantages


- sample accurately reflects the population structure
- guarantees proportional representation of groups within a population


disadvantages


-population must be clearly classified into distinct strata
-selection from strata suffers from same disadvantages as simple random
sampling
advantages/disadvantages systematic sampling - Correct Answer
✅💯advantages


- easy and quick to use
- suitable for large samples/populations


disadvantages


sample frame needed
can introduce bias if sampling frame not random
Approximating The Binomial Distribution : Key points on how to solve -
Correct Answer ✅💯- You may use the Normal distribution for the binomial
B(n,p) when :


- n is large
- p is not too close to 0 or 1

,This means X is approximately N(np, npq)
where
n = trials
p = probability
q=1-p


-now model your distribution
-Now adjust boundaries accordingly with continuity correction BUT ONLY IF
VALUES DISCRETE (usually by adding 0.5 to upper Bound and subtracting
0.5 from LB but this is only to nearest whole number)


Solve as though it is a normal , normal distribution question
Are there cities that have very different weather to others - Correct Answer
✅💯beijing vs leuchars
ASK SIR HOW DO YOU KNOW WHETHER IT IS IN FORM Y=AX^N OR
Y=KB^X - Correct Answer ✅💯
bimodal data - Correct Answer ✅💯A histogram will have two peaks as the
data has two modes.
- peaks do not have to be equal
binomial CD - Correct Answer ✅💯probability of 0-n successful cumulative
Binomial Distribution : Finding the minimum number of trials ( usually always
at least 1 or more) to reach greater/less than probability Y (Y should be given in
question)


How to solve - Correct Answer ✅💯- Model your BD as X~B(n, p)
- Y should be given in question
- If it is asking for P(X>=1) you know this is the same as 1 - P(x=0)
- the question will ask to reach greater than probability Y
- Your answer should be in format 1-P(x=0) >Y
- It could be <Y if stated in question

, - now use binomial distribution formula which will allow leave you with (1-
p)^(n-x) where x =0 so (1-p)^n. as nCx 's will cancel as nC0 = 1 and p^x would
=1


Working shown
- let Y = 0.85
- let p = 0.1
- so using 1-P(x=0) > Y
- 1-P(X=0) > 0.85
- So 0.15 > P(X=0)
- Now use Binomial distribution formula
nCx*P^x*(1-p)n-x
- if you plug this in this should leave you with (1-p)^n <0.15
- so 0.9^n < 0.15 now solve using logs from here
Binomial Distribution questions
how to answer :


If Ben rolls dice six times and wants to see how many 5s he gets (fair dice),
explain the distribution you would use? - Correct Answer ✅💯- binomial
distrbution would be use
- all distributions are modelled with 'X'
- X~B(n,p)
where n is number of trials
p is p(success)


for this question it would be X~B(6,1/6)
binomial PD - Correct Answer ✅💯probability of n successful
Census - Correct Answer ✅💯Observes/measures every member of a
population