Assam HS Class 11-12 Business Mathematics & Statistics key terms

A well-defined collection of distinct objects, called elements, treated as a single whole. In business problems, sets often represent groups of customers, products, or outcomes that share a stated property.

The set containing every element that belongs to at least one of the given sets, written A ∪ B. It answers the question of how many distinct items appear when two groups are pooled.

The set of elements common to all given sets, written A ∩ B. It represents the overlap between groups, such as customers who bought both of two products.

A diagram using overlapping circles inside a rectangle to show sets and their relationships. Shaded regions display unions, intersections, and complements, making survey and membership problems easier to solve.

A rule or set of ordered pairs linking elements of one set to elements of another. Business examples include pairing each customer with the products purchased or each employee with a department.

A relation in which each input value is paired with exactly one output value. Cost, revenue, and demand models are written as functions so that one quantity determines another uniquely.

The domain is the set of all permitted input values of a function; the range is the set of all resulting output values. In business models, the domain is often restricted to non-negative quantities.

A rectangular arrangement of numbers in rows and columns, enclosed in brackets. Matrices compactly store data such as sales by branch and product, and can be added or multiplied under stated rules.

The size of a matrix stated as number of rows by number of columns, for example 3 × 2. Two matrices can be added only when their orders are identical.

A single number computed from a square matrix that indicates whether the matrix has an inverse. A zero determinant means the system of equations has no unique solution.

A method of solving simultaneous linear equations using determinants, where each unknown equals a ratio of two determinants. It suits small systems such as two-commodity market equilibrium problems.

The matrix obtained by interchanging rows and columns, written Aᵀ. It is used when data stored by rows must be reorganized by columns, for example converting a table of monthly sales.

A sequence in which each term after the first is obtained by adding a fixed constant called the common difference. It models amounts that grow by equal instalments, such as fixed monthly savings.

A sequence in which each term after the first is obtained by multiplying by a fixed constant called the common ratio. It models growth at a constant percentage rate, such as compound interest balances.

The total of the first n terms of a sequence, given by standard formulas for arithmetic and geometric progressions. It is used to total instalments, depreciation amounts, or accumulated deposits.

An arrangement of objects in which the order matters, such as assigning candidates to ranked posts. The number of permutations of n distinct objects taken r at a time is written ⁿPᵣ.

A selection of objects in which order does not matter, such as choosing a committee from a group. The number of combinations of n objects taken r at a time is written ⁿCᵣ.

The product of all positive integers up to a given positive integer n, written n!. By convention 0! equals 1. Factorials appear in the formulas for permutations, combinations, and the binomial expansion.

Interest calculated only on the original principal for the whole period, using the formula I = P × r × t. The interest earned does not itself earn further interest.

Interest calculated on the principal plus previously accumulated interest, so the balance grows geometrically. The amount after t years is P(1 + r)ᵗ when interest is compounded annually.

The original sum of money borrowed, lent, or invested, on which interest is calculated. It is the starting value in all interest, annuity, and present value formulas.

A series of equal payments made at regular intervals over a fixed period. Loan repayments, insurance premiums, and recurring deposits are common examples handled with annuity formulas.

The value today of a future sum or stream of payments, found by discounting at a given rate of interest. It is used to judge whether an investment or project is worth undertaking now.

The amount a present sum or series of payments will grow to after a stated period at a given interest rate. It answers how much savings or deposits will be worth later.

The true annual rate actually earned or paid when compounding occurs more than once a year. It allows fair comparison between loans or deposits that quote different compounding frequencies.

The stated annual interest rate before adjusting for the number of compounding periods within the year. Dividing it by the compounding frequency gives the rate applied each period.

The value a function approaches as the input approaches a specified point, even if the function is not defined there. Limits underpin continuity, differentiation, and marginal analysis in business.

The instantaneous rate of change of a function with respect to its variable, found as the limit of a difference quotient. In business it gives marginal cost, marginal revenue, and marginal profit.

The additional cost of producing one more unit, equal to the derivative of the total cost function. It helps a firm decide whether expanding output is worthwhile.

Points where a function reaches its highest or lowest value locally, located by setting the first derivative to zero. The second derivative then distinguishes a maximum from a minimum.

The reverse process of differentiation, used to recover a total from a rate of change and to measure area under a curve. In business it turns marginal functions back into total cost or revenue.

Data collected fresh by the investigator for the specific purpose at hand, through surveys, interviews, or observation. It is tailored to the problem but usually costs more to obtain.

Data already gathered and published by another source, such as government reports or company records. It is quick and cheap but may not exactly fit the present enquiry.

A table showing how many observations fall in each class or category. It organizes raw data into a compact form from which averages and dispersion can be computed.

The range of values covered by one class in a grouped frequency distribution, defined by a lower and upper limit. Class width affects how much detail the table preserves.

A chart of adjacent rectangles whose areas represent class frequencies in a grouped distribution. It displays the shape and spread of quantitative data at a glance.

The sum of all observations divided by their number, the most widely used measure of central tendency. It uses every value but is strongly affected by extreme observations.

The middle value when observations are arranged in order, or the average of the two middle values. It is resistant to extreme values, making it useful for income and wage data.

The square root of the mean of squared deviations from the arithmetic mean. It expresses dispersion in the same units as the data and is the basis of many statistical tests.

The average of the squared deviations of observations from their mean. Squaring removes signs but changes units, so the square root is usually reported instead.

The standard deviation expressed as a percentage of the arithmetic mean. It compares variability between data sets measured in different units or having very different averages.

One of three values that divide ordered data into four equal parts, denoted Q1, Q2, and Q3. Quartiles summarize spread and support box plots and percentile-based reporting.

A numerical measure of the strength and direction of the linear relationship between two variables, ranging from −1 to +1. It does not by itself prove that one variable causes the other.

A method of fitting an equation that predicts one variable from another, usually by least squares. The regression line describes how the average value of the dependent variable changes.

A graph plotting one observation of each pair as a point on two axes. The pattern of points reveals whether a relationship is positive, negative, or absent before calculating coefficients.

A sequence of values of a variable recorded at successive, usually equal, time intervals. Analysts separate trend, seasonal, cyclical, and irregular components to forecast future values.

The long-term general direction of a time series after short-term fluctuations are smoothed out. It is estimated by moving averages or by fitting a straight line to the data.

A series of averages computed over a fixed number of consecutive periods and shifted forward one period at a time. It smooths out short-term fluctuations to reveal the underlying trend.

A statistical measure expressing the change in a variable or group of variables relative to a chosen base period, usually set at 100. Price indices track inflation and cost of living.

The reference period against which changes in an index number are measured and assigned the value 100. Its choice strongly affects how the index behaves over time.

A number between 0 and 1 expressing how likely an event is, often computed as favourable outcomes divided by total equally likely outcomes. It quantifies risk in insurance, investment, and quality control.

Two or more events that cannot occur at the same time, so their joint probability is zero. For such events the probability that either occurs is the sum of their probabilities.

Events whose occurrence does not change the probability of the other occurring. For two such events, the probability that both happen equals the product of their probabilities.

The probability-weighted average of all possible outcomes of a random variable. It gives the long-run average gain or loss used in decision-making under uncertainty.