A Level Maths - Statistics
Alternative hypothesis, H₁ - ANS Tells you about the parameter if your assumption is
shown to be wrong
\Binomial distribution - ANS 'X' can be used to represent the number of successful trials
Model 'X' with a binomial distribution, B(n, p), if
- there are a fixed number of trials, n
- there are two possible outcomes (success and failure)
- there is a fixed probability of success, p
- the trials are independent of each other
\Bivariate data - ANS Data which has pairs of values for two variables
\Census - Adv & Disadv - ANS Adv
- Completely accurate
Disadv
- Time consuming & expensive
- Cannot be used when the testing process destroys the item
- Hard to process large quantity of data
\Census - ANS Observes or measures every member of a population
\Class - ANS When data is presented in a grouped frequency table, the specific data
values are not shown
- boundaries - shows max and min values
- midpoint - average
- width - difference between upper and lower boundaries
\Cleaning the data - ANS Removing anomalies from a data set
\Coding - ANS A way of simplifying statistical calculations. Each data value is coded to
make a new set of data values which are easier to work with
\Coding - formula - ANS y = (x - a) / b
ȳ = (x̄ - a) / b
σᵧ = σₓ / b
σₓ is the standard deviation of the original data
\Comparing data - ANS Comment on:
- a measure of location
- a measure of spread
\Complement - ANS P(not A) = 1 - P(A), A'
\Continuous variable - ANS A variable that can take any value in a given range
\Correlation - ANS Describes the nature of the linear relationship between two variables
\Critical region - ANS A region of the probability distribution which, if the test statistic
fails within it, would cause you to reject the null hypothesis
\Critical value - ANS First value to fall inside the critical region
\Cumulative probability function - ANS For 'X', tells you the sum of all the individual
probabilities up to and including the given value of 'x' in the calculation for P(X ≤ x)
, X > A = 1 - P(X ≤ A)
X ≤ A = P(X ≤ A)
X ≥ A = 1 - P(X ≤ A - 1)
X < A = P(X ≤ A - 1)
\Discrete data rules of quartile - ANS Lower quartile
- divide n by 4. If it's whole, the LQ is halfway between this data point and the one above,
else, round *up* and pick this data point
Upper quartile
- find of n. If it's whole, the UQ is halfway between this data point and the one above,
else, round *up* and pick this data point
\Discrete uniform distribution - ANS When the probabilities of random variables are the
same
ΣP(X = x) = 1 for all x
\Discrete variable - ANS A variable that can take only specific values in a given range
\Event - ANS A collection of one or more outcomes
\Experiment - ANS A repeatable process that gives rise to a number of outcomes
\Histogram - ANS Can be used to represent grouped continuous data
- area of the bar is proportional to the frequency in each class
\Histogram - frequency density equations - ANS area of bar = k x frequency
frequency density = frequency / class width
\Hypothesis test - ANS - Assume the null hypothesis is true
- Consider how likely the observed value of the test statistic is to occur, if this likelihood
is less than a given threshold (called the significance level) of the test, then you reject
the null hypothesis
\Independent events - ANS P(A and B) = P(A) x P(B)
\Interpercentile range - ANS The difference between the values for two given percentiles
\Interpolation - ANS Used when data are presented in a grouped frequency table:
estimates the median, quartiles and percentiles
- assumes the data values are evenly distributed with each class
\Interquartile range - ANS The difference between the upper quartile and the lower
quartile, Q₃ - Q₁
\Intersection - ANS A & B (A ∩ B)
\Lower quartile - ANS Is one-quarter of the way through the data set
\Mean - ANS Average of values
x̄ = Σx / n
\Mean (frequency table) - ANS x̄ = Σxf / Σf
x = midpoint of each class interval
\Median - ANS The middle value when the data values are put in order
\Mode / Modal class - ANS The value or class that occurs most often
Alternative hypothesis, H₁ - ANS Tells you about the parameter if your assumption is
shown to be wrong
\Binomial distribution - ANS 'X' can be used to represent the number of successful trials
Model 'X' with a binomial distribution, B(n, p), if
- there are a fixed number of trials, n
- there are two possible outcomes (success and failure)
- there is a fixed probability of success, p
- the trials are independent of each other
\Bivariate data - ANS Data which has pairs of values for two variables
\Census - Adv & Disadv - ANS Adv
- Completely accurate
Disadv
- Time consuming & expensive
- Cannot be used when the testing process destroys the item
- Hard to process large quantity of data
\Census - ANS Observes or measures every member of a population
\Class - ANS When data is presented in a grouped frequency table, the specific data
values are not shown
- boundaries - shows max and min values
- midpoint - average
- width - difference between upper and lower boundaries
\Cleaning the data - ANS Removing anomalies from a data set
\Coding - ANS A way of simplifying statistical calculations. Each data value is coded to
make a new set of data values which are easier to work with
\Coding - formula - ANS y = (x - a) / b
ȳ = (x̄ - a) / b
σᵧ = σₓ / b
σₓ is the standard deviation of the original data
\Comparing data - ANS Comment on:
- a measure of location
- a measure of spread
\Complement - ANS P(not A) = 1 - P(A), A'
\Continuous variable - ANS A variable that can take any value in a given range
\Correlation - ANS Describes the nature of the linear relationship between two variables
\Critical region - ANS A region of the probability distribution which, if the test statistic
fails within it, would cause you to reject the null hypothesis
\Critical value - ANS First value to fall inside the critical region
\Cumulative probability function - ANS For 'X', tells you the sum of all the individual
probabilities up to and including the given value of 'x' in the calculation for P(X ≤ x)
, X > A = 1 - P(X ≤ A)
X ≤ A = P(X ≤ A)
X ≥ A = 1 - P(X ≤ A - 1)
X < A = P(X ≤ A - 1)
\Discrete data rules of quartile - ANS Lower quartile
- divide n by 4. If it's whole, the LQ is halfway between this data point and the one above,
else, round *up* and pick this data point
Upper quartile
- find of n. If it's whole, the UQ is halfway between this data point and the one above,
else, round *up* and pick this data point
\Discrete uniform distribution - ANS When the probabilities of random variables are the
same
ΣP(X = x) = 1 for all x
\Discrete variable - ANS A variable that can take only specific values in a given range
\Event - ANS A collection of one or more outcomes
\Experiment - ANS A repeatable process that gives rise to a number of outcomes
\Histogram - ANS Can be used to represent grouped continuous data
- area of the bar is proportional to the frequency in each class
\Histogram - frequency density equations - ANS area of bar = k x frequency
frequency density = frequency / class width
\Hypothesis test - ANS - Assume the null hypothesis is true
- Consider how likely the observed value of the test statistic is to occur, if this likelihood
is less than a given threshold (called the significance level) of the test, then you reject
the null hypothesis
\Independent events - ANS P(A and B) = P(A) x P(B)
\Interpercentile range - ANS The difference between the values for two given percentiles
\Interpolation - ANS Used when data are presented in a grouped frequency table:
estimates the median, quartiles and percentiles
- assumes the data values are evenly distributed with each class
\Interquartile range - ANS The difference between the upper quartile and the lower
quartile, Q₃ - Q₁
\Intersection - ANS A & B (A ∩ B)
\Lower quartile - ANS Is one-quarter of the way through the data set
\Mean - ANS Average of values
x̄ = Σx / n
\Mean (frequency table) - ANS x̄ = Σxf / Σf
x = midpoint of each class interval
\Median - ANS The middle value when the data values are put in order
\Mode / Modal class - ANS The value or class that occurs most often
