Kerala Plus Two Statistics (DHSE) key terms

The sum of all observations divided by the number of observations; for grouped data it uses class midpoints weighted by frequencies. It is the most common measure of central location and its deviations always sum to zero.

The middle value of an ordered data set, or the average of the two middle values when the count is even. For grouped data it is found by interpolation within the median class using cumulative frequency.

The observation or class that occurs most frequently in a data set. A distribution may be unimodal, bimodal or have no mode at all; for grouped data the modal class is located by the highest frequency.

One of three values dividing an ordered data set into four equal parts: Q1, Q2 (the median) and Q3. Quartiles are positional averages located by interpolation in the corresponding cumulative frequency class.

The average of the absolute deviations of observations from a central value such as the mean or median. It measures spread but is less tractable algebraically than the standard deviation.

The positive square root of the variance, expressed in the same units as the data. It measures typical distance of observations from the mean and is unaffected by shifting all values by a constant.

The average of the squared deviations of observations from their mean. For a population it is divided by N; for a sample, dividing by n minus one gives an unbiased estimator.

The ratio of standard deviation to mean, usually expressed as a percentage. Because it is unit-free, it compares variability between data sets measured in different units or with very different means.

A measure of asymmetry in a distribution. Positive skew means a long right tail with mean greater than median; negative skew means a long left tail with mean less than median.

A table showing classes of values and the number of observations falling in each class. Class limits, class width and class midpoints are read from it to compute further summary measures.

The running total of frequencies up to and including a given class. It is used to locate medians and quartiles and to draw an ogive curve.

A bar chart of a frequency distribution in which bars touch and bar area is proportional to frequency. With unequal class widths, heights are adjusted as frequency density rather than raw frequency.

A smooth curve obtained by plotting cumulative frequency against the upper class boundaries. Medians and quartiles can be read from it graphically.

A plot of paired observations on two variables, one on each axis. The pattern of points suggests the direction and strength of association before any numerical correlation is computed.

A number between minus one and plus one measuring the strength and direction of linear association between two variables. It is symmetric in the two variables and is unaffected by change of origin or scale.

A coefficient computed from the ranks of observations rather than their actual values, often used when data are qualitative or contain outliers. Tied ranks are handled by averaging the ranks concerned.

The straight line that best predicts one variable from another by minimising the sum of squared vertical deviations. There are two such lines, and they coincide only when correlation is perfect.

The slope of a regression line, giving the expected change in the dependent variable per unit change in the independent variable. The two slopes multiply to give the square of the correlation coefficient.

A procedure whose outcome cannot be predicted with certainty in advance but whose set of possible outcomes is known. Repeating it under identical conditions need not give identical results.

The set of all possible outcomes of a random experiment, usually denoted S. Each elementary outcome appears exactly once, and events are subsets of this set.

Any subset of the sample space, to which a probability may be assigned. Events can be combined by union, intersection and complement to form new events.

Two events that cannot occur together, so their intersection is empty. For such events the probability of either occurring is the sum of their individual probabilities.

The rule that the probability of the union of two events equals the sum of their probabilities minus the probability of their intersection. For mutually exclusive events the last term vanishes.

The probability that an event occurs given that another event has already occurred, defined as the probability of the intersection divided by the probability of the given event, provided that is nonzero.

The rule that the probability of two events occurring together equals the probability of the first times the conditional probability of the second given the first. It extends to any number of events.

Events whose joint probability equals the product of their separate probabilities, meaning that occurrence of one gives no information about the other. Equivalently, the conditional probability equals the unconditional probability.

A rule for reversing conditional probability: it updates the prior probability of a cause after observing an effect, using the likelihood of the effect under each cause and the total probability of the effect.

If a set of mutually exclusive and exhaustive events partitions the sample space, the probability of any event equals the sum over the partition of the prior times the conditional probability given that part.

A real-valued function defined on the sample space that assigns a number to each outcome. It may be discrete, taking isolated values, or continuous, taking any value in an interval.

A function giving the probability that a discrete random variable equals each of its possible values. The values are non-negative and sum to one over the whole support.

A non-negative function whose integral over an interval gives the probability that a continuous random variable lies in that interval. Its total integral over the real line equals one.

A function giving the probability that a random variable takes a value less than or equal to a given number. It is non-decreasing, runs from zero to one, and works for both discrete and continuous variables.

The probability-weighted average of all values of a random variable, also called its mean. For a function of a random variable, the same weighted averaging is applied to the transformed values.

The distribution of the number of successes in a fixed number of independent trials, each with the same probability of success. Its mean is the product of the number of trials and the success probability.

A distribution for counts of rare events occurring in a fixed interval of time or space, with a known average rate and independent occurrences. Its mean and variance are equal.

A selection procedure in which every sample of a given size has an equal chance of being chosen. It removes selection bias and underlies the standard error formulas used in inference.

The probability distribution of a statistic such as the sample mean over repeated samples of the same size. Its spread shrinks as sample size grows, which is the basis of standard error.

The standard deviation of a statistic's sampling distribution. For a sample mean it equals the population standard deviation divided by the square root of the sample size.

The statement about a population parameter that is assumed true for the purpose of a test and is rejected only when sample evidence is strongly against it. It usually specifies no difference or no effect.

The maximum probability, chosen in advance, of rejecting a true null hypothesis. Common choices are five per cent and one per cent, and the critical region is fixed accordingly.

Rejecting the null hypothesis when it is actually true. Its probability is controlled by the chosen level of significance, and it is traded off against the risk of failing to detect a real effect.