CHSE Odisha Elective Statistics key terms

The sum of all observations divided by their number. It uses every value, is affected by extreme values, and for grouped data is computed from class midpoints weighted by frequencies.

The middle value when observations are arranged in order; for even counts it is the average of the two central values. It resists distortion by outliers and suits open-ended classes.

The value occurring most frequently in a data set. A distribution may be unimodal, bimodal or have no mode; for grouped data it is located in the modal class by an interpolation formula.

The nth root of the product of n positive observations, usually computed by taking antilogs of the mean of logarithms. It suits ratios, growth rates and index number construction.

The reciprocal of the arithmetic mean of the reciprocals of the observations. It is appropriate for averaging rates such as speeds over equal distances and for certain price-averaging problems.

An average in which each observation is multiplied by a weight reflecting its importance, and the total is divided by the sum of weights. Grouped-data means are weighted means of class midpoints.

One of three values dividing an ordered data set into four equal parts. The first quartile has 25 percent of observations below it, the second is the median, the third has 75 percent below.

A value below which a stated percentage of ordered observations fall. Percentiles describe position within a distribution and are widely used in educational and health measurement.

The difference between the largest and smallest observation. It is simple to compute but depends only on two values and is therefore highly unstable.

The difference between the third and first quartiles, covering the middle half of the data. It is a resistant measure of spread and pairs naturally with the median.

The average of the absolute deviations of observations from a central value, usually the median or mean. It uses all observations but is less tractable algebraically than the variance.

The average of squared deviations from the mean. Population variance divides by N, sample variance by n minus one to remove bias; its square root gives the standard deviation.

The positive square root of variance, expressed in the same units as the data. It measures typical distance from the mean and underpins standard scores and many inference procedures.

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

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

A measure of the peakedness or tail heaviness of a distribution relative to the normal curve. Excess kurtosis is zero for a normal distribution, positive for leptokurtic and negative for platykurtic curves.

A plot of paired observations on two axes, used to inspect the direction, strength and form of association before computing any numerical measure of correlation.

A measure of linear association between two variables, computed as covariance divided by the product of their standard deviations. It lies between minus one and plus one and is unit-free.

Spearman's coefficient obtained by applying the Pearson formula to ranks rather than raw values. It detects monotonic association and suits qualitative or ordinal data.

The slope in a regression equation, giving the expected change in the dependent variable for a one-unit change in the independent variable. Two regression lines exist, one for each direction of prediction.

A fitting principle that chooses parameters minimising the sum of squared vertical deviations of observations from the fitted line. It yields the normal equations used for regression coefficients.

The square of the correlation coefficient in simple linear regression, interpreted as the proportion of variation in the dependent variable explained by the fitted regression.

The set of all possible outcomes of a random experiment. Events are subsets of this set, and probability is assigned to events according to stated axioms.

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.

Events whose joint probability equals the product of their separate probabilities. Knowing that one has occurred gives no information about the occurrence of the other.

The probability of an event given that another event has occurred, defined as the joint probability divided by the probability of the conditioning event, provided that is not zero.

A rule for revising prior probabilities in the light of evidence, expressing a posterior probability as prior times likelihood divided by total probability of the evidence.

A function assigning a numerical value to each outcome of a random experiment. It may be discrete, taking countable values, or continuous, taking values in an interval.

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

A non-negative function whose integral over an interval gives the probability that a continuous random variable lies in that interval. Probability at a single point is zero.

The probability-weighted average of the values of a random variable, also called its mean. For a function of the variable it is computed by weighting function values by their probabilities.

The distribution of the number of successes in n independent trials, each with constant success probability p. Its mean is np and variance np times one minus p.

A distribution for counts of rare events in a fixed interval, with a single parameter equal to both mean and variance. It arises as a limit of the binomial when n is large and p small.

A continuous symmetric bell-shaped distribution fixed by its mean and standard deviation. Standardising converts it to the standard normal, whose tables give areas and probabilities.

A normal variable with mean zero and standard deviation one, obtained by subtracting the mean and dividing by the standard deviation. Its tabulated areas serve all normal probability problems.

The probability distribution of a statistic over all possible samples of a given size from a population. Its standard deviation is called the standard error of the statistic.

The standard deviation of a sampling distribution. For a sample mean it equals population standard deviation divided by the square root of sample size, estimated from the sample when necessary.

The result that the sampling distribution of the sample mean approaches normality as sample size grows, regardless of the population shape, provided variance is finite.

A selection procedure in which every sample of a given size has an equal chance of being chosen and every unit has an equal inclusion probability, typically drawn without replacement.

A design in which the population is divided into homogeneous strata and independent samples are drawn from each. It usually reduces variance compared with simple random sampling of the same size.

The statement of no effect or no difference that a significance test examines. It is assumed true while computing the probability of results as extreme as those observed.

The statement that contradicts the null hypothesis and represents the effect the investigator hopes to detect. It may be one-sided or two-sided and determines the critical region.

Rejecting a true null hypothesis. Its probability equals the significance level chosen by the investigator, commonly five or one percent.

Failing to reject a false null hypothesis. Its probability is denoted beta, and one minus beta is the power of the test to detect a real effect.

The probability of correctly rejecting a false null hypothesis, equal to one minus the Type II error rate. Power increases with larger samples, larger effects and lower variability.

The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as that observed. Small values argue against the null hypothesis.

A technique that partitions total variation into components attributable to specified sources, then compares mean squares by an F test to judge whether group means differ.

An experimental layout in which homogeneous blocks are formed and every treatment appears once in each block. It removes block-to-block variation from the error term.

A layout in which treatments are assigned to experimental units entirely at random, appropriate when units are homogeneous. Analysis proceeds by one-way analysis of variance.

The number of independent pieces of information available for estimating a quantity or computing a sum of squares. It indexes t, chi-square and F distributions in inference.

A sequence of observations of a variable recorded at successive, usually equally spaced, times. Analysis separates trend, seasonal, cyclical and irregular components.

A smoothed series obtained by averaging consecutive groups of observations. It removes short-term fluctuations and is a standard tool for isolating trend in a time series.

A numerical measure of the recurring within-year pattern in a time series, typically expressed as a percentage of the average. It is used to deseasonalise data before trend fitting.

A relative measure expressing change in a variable or group of variables between a base period and a current period, usually as a percentage. Price and quantity indices are common examples.

A weighted price index using base-period quantities as weights. It tends to overstate price rises because it ignores substitution toward cheaper goods.

A weighted price index using current-period quantities as weights. It tends to understate price rises relative to Laspeyres and requires current quantity data each period.