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PIPFA Quantitative Methods Flashcards
60 question-and-answer cards covering Quantitative Methods as it is examined in PIPFA. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Methods deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the difference between variance and standard deviation?
Variance is the mean of the squared deviations from the mean (expressed in squared units). Standard deviation is the square root of the variance, expressed in the same units as the original data.
State the classical definition of probability for equally likely outcomes.
P(event) = (Number of favourable outcomes) / (Total number of possible outcomes). Probability ranges from 0 (impossible) to 1 (certain).
State the addition rule of probability for two events A and B.
P(A or B) = P(A) + P(B) − P(A and B). If A and B are mutually exclusive, P(A and B) = 0, so P(A or B) = P(A) + P(B).
State the multiplication rule of probability for independent events.
For independent events, P(A and B) = P(A) × P(B). For dependent events, P(A and B) = P(A) × P(B | A), where P(B | A) is the conditional probability of B given A.
What does it mean for two events to be mutually exclusive versus independent?
Mutually exclusive events cannot occur together (P(A and B) = 0). Independent events do not affect each other's probability (the occurrence of one does not change the probability of the other).
What are the key properties of the normal distribution?
It is bell-shaped, symmetrical about the mean, with mean = median = mode. The total area under the curve = 1, and it is fully described by its mean (μ) and standard deviation (σ).
State the empirical (68-95-99.7) rule for the normal distribution.
Approximately 68% of values lie within ±1σ of the mean, 95% within ±2σ (more precisely 1.96σ), and 99.7% within ±3σ of the mean.
How do you calculate a z-score and what does it represent?
z = (x − μ) / σ. It standardises a value by measuring how many standard deviations x lies above (positive) or below (negative) the mean, allowing use of the standard normal table.
What conditions must be met for a binomial distribution to apply?
A fixed number of trials (n); each trial has only two outcomes (success/failure); the probability of success p is constant; and trials are independent.
State the binomial probability formula.
P(X = r) = ⁿCᵣ × pʳ × q^(n−r), where ⁿCᵣ = n!/[r!(n−r)!], p = probability of success, q = 1 − p, n = number of trials, r = number of successes.
State the mean and standard deviation of a binomial distribution.
Mean = np; Variance = npq; Standard deviation = √(npq), where n = number of trials, p = probability of success, q = 1 − p.
What is a price index number and what does it measure?
A price index number measures the relative change in the price of an item or basket of items between a base period and a current period. Base period index = 100. Simple price relative = (Current price / Base price) × 100.
What is the difference between the Laspeyres and Paasche price index?
Laspeyres uses base-period quantities as weights: Σ(p₁q₀)/Σ(p₀q₀) × 100. Paasche uses current-period quantities as weights: Σ(p₁q₁)/Σ(p₀q₁) × 100. Laspeyres tends to overstate, Paasche to understate, price changes.
What are the four components of a time series?
Trend (T) - long-term direction; Seasonal variation (S) - regular short-term cycles within a year; Cyclical variation (C) - longer wave-like business cycles; Irregular/Random variation (I) - unpredictable fluctuations.
What is the additive versus multiplicative model of a time series?
Additive model: Y = T + S + C + I (components added; seasonal effect constant in absolute terms). Multiplicative model: Y = T × S × C × I (components multiplied; seasonal effect proportional to the trend).
What is the method of moving averages used for in trend analysis?
Moving averages smooth out short-term seasonal and irregular fluctuations to reveal the underlying trend by averaging successive groups of observations (e.g. a 4-quarter moving average for quarterly data).
How is forecasting carried out using the least-squares trend line and seasonal factors?
Fit a trend line Y = a + bx by least squares, project the trend for the future period, then multiply (multiplicative model) or add (additive model) the relevant seasonal factor to obtain the forecast.
What does the correlation coefficient (r) measure, and what is its range?
It measures the strength and direction of the linear relationship between two variables. r ranges from −1 (perfect negative) to +1 (perfect positive), with 0 indicating no linear relationship.
State Pearson's product-moment correlation coefficient formula.
r = [nΣxy − ΣxΣy] / √{[nΣx² − (Σx)²][nΣy² − (Σy)²]}, where n is the number of paired observations.
What is the coefficient of determination (r²) and how is it interpreted?
r² is the square of the correlation coefficient. It gives the proportion (or percentage) of the total variation in the dependent variable explained by the independent variable through the regression line.
What is Spearman's rank correlation coefficient and its formula?
It measures correlation between the ranks of two variables. R = 1 − [6Σd²] / [n(n² − 1)], where d is the difference between paired ranks and n is the number of pairs.
What is the purpose of simple linear regression?
To model the relationship between a dependent variable (Y) and one independent variable (X) by fitting a straight line, allowing prediction of Y for given values of X.
State the simple linear regression equation and what its coefficients represent.
Y = a + bX, where a is the intercept (value of Y when X = 0) and b is the slope/regression coefficient (the change in Y for each one-unit increase in X).
State the least-squares formulas for the slope (b) and intercept (a) in simple linear regression.
b = [nΣxy − ΣxΣy] / [nΣx² − (Σx)²] and a = ȳ − b·x̄ (equivalently a = (Σy − bΣx)/n). The line passes through the point (x̄, ȳ).
What this deck covers
The Quantitative Methods deck follows the PIPFA Quantitative Methods syllabus — 6 chapters and 18 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 170 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Quantitative Methods flashcards FAQ
How many Quantitative Methods flashcards are in this PIPFA deck?
60 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these PIPFA flashcards free?
Yes. The preview here is free to read with no signup, and the full 60-card deck is free inside the Examius app.
What do the Quantitative Methods cards cover?
They follow the PIPFA Quantitative Methods syllabus — 6 chapters and 18 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.