CHSE Odisha Business Mathematics & Statistics key terms

A well-defined collection of distinct objects, called elements, treated as a single entity. Membership is decided by a clear rule, so any object either belongs to the collection or does not.

A set whose every element also belongs to another given set. If A is a subset of B, then no element of A lies outside B; equality is allowed, so every set is a subset of itself.

The set of all subsets of a given set, including the empty set and the set itself. A set with n elements has a power set containing exactly 2 raised to the power n members.

The set formed by collecting every element that appears in at least one of two or more given sets, with duplicates counted once. It is the smallest set containing all the original sets as subsets.

The set of elements common to two or more given sets, that is, elements belonging to all of them simultaneously. If no element is shared, the intersection is the empty set.

The set of all elements of the universal set that do not belong to a given set. It depends on the chosen universal set, so changing the universal set changes the complement.

A rule or set of ordered pairs linking elements of one set to elements of another, or of the same set. A relation is a subset of the Cartesian product of the two sets.

A relation in which every element of the domain is paired with exactly one element of the codomain. Different inputs may share an output, but a single input cannot produce two outputs.

The domain is the full set of input values for which a function is defined; the range is the set of all output values it actually produces. Together they describe a function's scope.

A function that reverses another function, sending each output back to its original input. It exists only when the original function is one-to-one and onto its codomain.

A rectangular arrangement of numbers or expressions in rows and columns, enclosed in brackets. Its order is stated as rows by columns, and each entry is identified by its row and column position.

A single number computed from the entries of a square matrix that indicates whether the matrix is invertible. A zero determinant means no inverse exists; nonzero means an inverse does.

A square matrix whose determinant equals zero, so it has no multiplicative inverse. Its rows or columns are linearly dependent, meaning one can be built from combinations of the others.

For a square matrix A with nonzero determinant, the matrix that multiplies with A to give the identity matrix. It is found using the adjoint divided by the determinant.

A square matrix with ones along the main diagonal and zeros everywhere else. Multiplying any conformable matrix by it leaves that matrix unchanged, so it acts like the number one.

The matrix obtained by interchanging rows and columns of a given matrix. A matrix of order m by n becomes one of order n by m, and entries swap their row and column indices.

A method of solving a system of linear equations using determinants. Each unknown equals the ratio of two determinants: that of a modified coefficient matrix to that of the coefficient matrix.

The product of all positive integers from one up to a given whole number, written with an exclamation mark. By convention the factorial of zero equals one, which keeps counting formulas consistent.

An arrangement of a selection of objects in which the order matters. The number of permutations of n distinct objects taken r at a time is n factorial divided by n minus r factorial.

A selection of objects from a group in which order does not matter. The number of combinations of n objects taken r at a time equals the corresponding permutation count divided by r factorial.

A sequence in which each term after the first is obtained by adding a fixed constant, the common difference, to the previous term. Its nth term and sum have standard closed formulas.

The constant amount added to each term of an arithmetic progression to produce the next term. It may be positive, negative, or zero, and equals any term minus the preceding term.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed nonzero constant, the common ratio. Terms grow or shrink multiplicatively rather than additively.

The fixed factor by which each term of a geometric progression is multiplied to obtain the next term. It equals any term divided by the term immediately before it.

The limiting value approached by the sum of the first n terms of an infinite geometric progression as n grows without bound. It exists only when the common ratio lies strictly between minus one and one.

A measure of the steepness and direction of a straight line, equal to the change in vertical distance divided by the corresponding change in horizontal distance between two points. Horizontal lines have zero slope.

An algebraic relation satisfied by exactly the points lying on a straight line, commonly written in slope-intercept, point-slope, two-point, or intercept form. Each form suits different known data.

Two non-vertical lines are parallel when their slopes are equal, and perpendicular when the product of their slopes equals minus one. These slope conditions let you test or construct such lines quickly.

The instantaneous rate at which a function's value changes with respect to its variable, defined as the limit of a difference quotient. Geometrically it gives the slope of the tangent to the curve.

Points where a function reaches a local highest or lowest value, located by setting the first derivative to zero and checking the sign of the second derivative. They model optimisation problems in business.

The additional cost of producing one more unit of output, approximated by the derivative of the total cost function with respect to quantity. It guides decisions about expanding or reducing production.

The tangent is the straight line touching a curve at a point with slope equal to the derivative there; the normal is perpendicular to it at the same point. Their slopes multiply to minus one.

The integral of a function between two limits, evaluated as the difference of an antiderivative at those limits. It represents signed area under a curve and is used to find totals from rates.

The family of all antiderivatives of a function, written with an arbitrary constant of integration. It reverses differentiation, so differentiating the result returns the original function.

The region bounded by a curve, the horizontal axis, and two vertical lines, whose signed measure is found by a definite integral. Areas below the axis count as negative unless absolute values are used.

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

The middle value of a data set arranged in order, or the average of the two middle values when the count is even. It divides the data into two equal halves and resists extreme values.

The value that occurs most frequently in a data set, so it identifies the most typical or popular observation. A distribution may be unimodal, bimodal, or have no mode at all.

The positive square root of the variance, expressing the typical spread of observations around the arithmetic mean in the original units. A larger value means greater dispersion.

The average of the squared deviations of observations from their arithmetic mean. Squaring removes signs, so variance is always non-negative, but its units are squared.

The average of the absolute deviations of observations from a central value such as the mean or median. Using absolute values avoids cancellation between positive and negative deviations.

The standard deviation expressed as a percentage of the arithmetic mean, allowing comparison of variability between data sets measured in different units or having very different averages. Lower values indicate greater consistency.

One of three values dividing ordered data into four equal parts: the lower quartile, the median, and the upper quartile. The interquartile range is the difference between the upper and lower quartiles.

A number between minus one and plus one measuring the strength and direction of linear association between two variables. A value near zero suggests little linear relationship.

The slope in a regression equation, stating how much the dependent variable changes on average for a one-unit increase in the independent variable. Two regression coefficients exist, one for each direction.

The straight line chosen to summarise a scatter of paired observations by minimising the sum of squared vertical deviations. It is used to predict one variable from the other.

A graph plotting paired observations as points on two axes, revealing the form, direction, and strength of association. It is a quick visual check before computing a correlation coefficient.

The set of all possible outcomes of a random experiment, usually denoted S. Every event is a subset of this space, and the probabilities of its outcomes sum to one.

A subset of the sample space, consisting of one or more outcomes of a random experiment. An event occurs when the actual outcome belongs to that subset.

A number between zero and one expressing how likely an event is, computed for equally likely outcomes as favourable outcomes divided by total outcomes. Zero means impossible and one means certain.

The probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success. It is discrete and determined by the trial count and success probability.

A discrete probability distribution modelling the number of occurrences of rare events in a fixed interval of time or space, given a known average rate. Its mean and variance are equal.

A statistical measure expressing the relative change in a variable or group of variables over time or place, with a chosen base period set to one hundred. It simplifies comparison of percentage changes.

A weighted price index using base-period quantities as weights, so it measures the cost of a fixed basket bought in the base year. It tends to overstate price rises because it ignores substitution.

A weighted price index using current-period quantities as weights, reflecting the basket actually bought in the current year. It tends to understate price rises compared with a base-weighted index.

A sequence of values of a variable recorded at successive, usually equally spaced, points in time. Analysis separates trend, seasonal, cyclical, and irregular movements.

The long-term general direction of a time series, obtained by smoothing out short-term fluctuations. It may be rising, falling, or stable and is often estimated by a moving average or least squares.

A series of averages computed over successive overlapping groups of consecutive observations, used to smooth fluctuations and reveal trend. The number of periods chosen determines the degree of smoothing.