AQA A Level Mathematics Statistics Unit 1
Comprehensive Questions with Answers
100% Accuracy |Updated 2025.
What are the parameters for a binomial distribution?
X~B(n,p)
(n = number, p = probability)
What are the parameters for a normal distribution?
X~N(µ, σ²)
(µ = population mean, σ² = variance)
What is the binomial equation?
What is the mean of a binomial distribution?
µ = np
What's the variance of a binomial distribution?
σ² = np(1-p)
What values are given in the binomial tables?
P(X < x) - if you want > x then you need to do 1 - P(X < x)
Sigma notation for sample mean?
-x- = ∑x ÷ n
Sigma notation for sample mean of grouped data?
-x- = ∑ƒx ÷ ∑ƒ
Formula for frequency density? (= height on a histrogram)
Class frequency ÷ class width
(More complex) formula for sample standard deviation?
, Simpler formula for sample standard deviation?
s = √(1/n-1) (∑x² - (∑x)²/n)
(More complex) formula for population standard deviation?
Simpler formula for population standard deviation?
σ = √(1/n)(∑x² - µ²)
About what proportion of values lie within 1 standard deviation of the mean?
About ²/₃
About what proportion of values lie within 2 standard deviations of the mean?
About 95%
About what proportion of values lie within 3 standard deviations of the mean?
Almost all values
Formula for sample standard deviation of grouped data?
1/n-1 × (∑fx² - (∑ƒx)²/n)
Formula for population standard deviation of grouped data?
1/n × (∑fx² - (∑ƒx)²/n)
What happens to the mean when adding or subtracting a constant, c from every value?
The mean changes by c
What happens to the standard deviation when adding or subtracting a constant, c from every value?
No change to the standard deviation
What happens to the mean when multiplying every value by a constant, k?
Multiplies the mean by k
What happens to the standard deviation when multiplying every value by a constant, k?
Multiplies the standard deviation by k
Comprehensive Questions with Answers
100% Accuracy |Updated 2025.
What are the parameters for a binomial distribution?
X~B(n,p)
(n = number, p = probability)
What are the parameters for a normal distribution?
X~N(µ, σ²)
(µ = population mean, σ² = variance)
What is the binomial equation?
What is the mean of a binomial distribution?
µ = np
What's the variance of a binomial distribution?
σ² = np(1-p)
What values are given in the binomial tables?
P(X < x) - if you want > x then you need to do 1 - P(X < x)
Sigma notation for sample mean?
-x- = ∑x ÷ n
Sigma notation for sample mean of grouped data?
-x- = ∑ƒx ÷ ∑ƒ
Formula for frequency density? (= height on a histrogram)
Class frequency ÷ class width
(More complex) formula for sample standard deviation?
, Simpler formula for sample standard deviation?
s = √(1/n-1) (∑x² - (∑x)²/n)
(More complex) formula for population standard deviation?
Simpler formula for population standard deviation?
σ = √(1/n)(∑x² - µ²)
About what proportion of values lie within 1 standard deviation of the mean?
About ²/₃
About what proportion of values lie within 2 standard deviations of the mean?
About 95%
About what proportion of values lie within 3 standard deviations of the mean?
Almost all values
Formula for sample standard deviation of grouped data?
1/n-1 × (∑fx² - (∑ƒx)²/n)
Formula for population standard deviation of grouped data?
1/n × (∑fx² - (∑ƒx)²/n)
What happens to the mean when adding or subtracting a constant, c from every value?
The mean changes by c
What happens to the standard deviation when adding or subtracting a constant, c from every value?
No change to the standard deviation
What happens to the mean when multiplying every value by a constant, k?
Multiplies the mean by k
What happens to the standard deviation when multiplying every value by a constant, k?
Multiplies the standard deviation by k
