ATD Level II

Business Mathematics and Statistics flashcards

Read the question, say the answer to yourself, then turn the card to check. The first 10 of 50 cards are free; the rest come with the subject.

Card 1 of 50

Jump to a card

Complete Flashcard Reference

Review every card in this deck. Open any card to reveal its answer. The first 10 are free; the other 40 come with the subject.

What is the difference between mark-up and margin?

Mark-up = profit / cost price x 100. Margin = profit / selling price x 100. Cost KES 800, selling price KES 1,000: mark-up 25%, margin 20%. The two are never equal unless profit is zero, so check which one the question asks for.

How is a linear inequality solved, and what is the one rule to watch?

Exactly like a linear equation, by isolating the variable. Multiplying or dividing both sides by a negative number reverses the inequality sign. -2x > 6 gives x < -3.

What are the nth term and the sum of the first n terms of an arithmetic progression?

Each term adds a common difference d to the one before. nth term: Tn = a + (n - 1)d. Sum: Sn = (n/2)[2a + (n - 1)d]. 5, 9, 13, ...: T10 = 5 + 9(4) = 41.

How do simple and compound interest differ, and what are their formulas?

Simple interest is earned on the original principal only: I = PRT, A = P(1 + RT). Compound interest also earns interest on interest already added: A = P(1 + r/m)^(mt), where m is the number of compounding periods a year. A compound balance is a geometric progression with common ratio (1 + r).

Name the four types of mean and when each is the right average.

Arithmetic mean: Σx / n (Σfx / Σf for grouped data). Weighted mean: Σwx / Σw, where values differ in importance, as in an index number. Geometric mean: the nth root of the product of n values, for growth rates or ratios. Harmonic mean: n / Σ(1/x), for rates such as speed or price per unit.

Name the six sampling techniques, and say which are non-random.

Simple random: every member has an equal chance. Stratified: split into strata and sample each in proportion to its size. Systematic: every kth member after a random start. Cluster: whole clusters chosen at random. Quota and convenience are the non-random ones: fixed quotas filled by interviewers, or whoever is easiest to reach.

State the additive rule of probability, and its form for mutually exclusive events.

In general: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Mutually exclusive events share no outcome, so P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B). P(A) = 0.4, P(B) = 0.3, P(both) = 0.1: P(A or B) = 0.6.

How do the Laspeyres and Paasche price indices differ?

Laspeyres weights by base-period quantities: Σ(P1 x Q0) / Σ(P0 x Q0) x 100. It tends to overstate price rises, because it ignores buyers shifting away from goods that become relatively dearer. Paasche weights by current-period quantities: Σ(P1 x Q1) / Σ(P0 x Q1) x 100. It tends to understate price rises, for the mirror-image reason.

How is the profit-maximising output found with calculus?

1. Form the profit function: π = TR - TC. 2. Differentiate it. 3. Set dπ/dQ = 0 and solve for Q. This is the output where marginal revenue (dTR/dQ) equals marginal cost (dTC/dQ).

What are the variance, the standard deviation and the coefficient of variation?

Variance: σ² = Σ(x - x̄)² / n, the average squared deviation from the mean, in squared units. Standard deviation: σ = √σ², back in the data's own units. Coefficient of variation: (σ / x̄) x 100, which compares spread fairly across data sets with different means or units.

What are simultaneous equations, and how can they be solved?