Edexcel A Level Maths - Statistics Exam 2025/2026 Questions With Completed & Verified Solutions.

Edexcel A Level Maths - Statistics

... - ANS - ...
\3 different types of random sampling - ANS - Simple random sampling

Systematic sampling
• Stratified sampling
\A ∩ B - ANS - means both A and B
\A ∪ B - ANS - means A or B or both
\advantages / disadvantages of census - ANS - advantages :

gives a completely accurate result

disadvantages
-time consuming and expensive
-hard to process large quantity of data
\advantages/disadvantages of a sample - ANS - 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 - ANS - 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 - ANS - 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 - ANS - - 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 - ANS - beijing vs leuchars
\ASK SIR HOW DO YOU KNOW WHETHER IT IS IN FORM Y=AX^N OR Y=KB^X - ANS -
\bimodal data - ANS - A histogram will have two peaks as the data has two modes.
- peaks do not have to be equal
\binomial CD - ANS - 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 - ANS - - 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? - ANS - - 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 - ANS - probability of n successful
\Census - ANS - Observes/measures every member of a population
\class boundaries - ANS - Tell you the maximum and minimum values that belong in each class
\class width - ANS - the difference between upper and lower class limits. - remember if
continuous above 0.5 and below by 0.5
\coding - inverse function - ANS - means it is the exact inverse function e.g if the x was formed
from 2y+4 you would do x-4 /2 to get x


however for standard deviation it is slightly different
-if standard deviation =b was formed by 3d+8 to get the d you would just divide by 3 and not
account for subtracting the 8. - However IT IS ALWAYS POSITIVE VALUE SO IF WORKING
BACKWARDS IT COULD BE NEGATIVE OR POSITIVE SO YOU WOULD NEED MEAN
INFORMATION TO SOLVE.
\Common Binomial Distribution question:

Probability of desired outcome = P

find the smallest number of weeks/months/rolls/attempts after which it will be - some percentage
e.g 85 percent - certain he has obtained his desired outcome at least once. - ANS - how to solve
;
P and percentage as decimal would be either solved/given in question

*1st Method* -

P(X>=1)=< Percentage as decimal

so P(X=0) >= 1 - [Percentage as decimal]