Karnataka II PUC Statistics (KSEAB) key terms

Information collected fresh by the investigator for the specific purpose at hand, through surveys, experiments, interviews or direct observation, rather than taken from records already gathered by someone else.

Data that already exist because another person or agency collected them earlier, such as census reports, departmental records or published statistical tables, reused by a new investigator for a different purpose.

A small preliminary trial of a questionnaire or data-collection plan on a few respondents, used to detect unclear questions, excessive length and practical difficulties before the full survey is launched.

A complete enumeration in which information is gathered from every unit of the population, giving no sampling error but requiring far more time, cost and organisation than a sample survey.

A written schedule of questions sent to or filled in by respondents, designed with clear, unbiased and logically ordered items so that comparable information is obtained from every unit.

The range of values covered by one class in a frequency distribution, found as the difference between its upper and lower class limits and used as the width for histogram and formula work.

The midpoint of a class interval, calculated as the average of its lower and upper class limits, and commonly used as the representative value of all observations in that class.

A table that lists the possible values or class intervals of a variable together with the number of observations falling in each, summarising raw data into a compact and readable form.

A graph of a continuous frequency distribution in which adjacent rectangles have widths equal to class intervals and heights proportional to frequencies, so the total area represents the total frequency.

A cumulative frequency curve, drawn as less-than or more-than type, from which the median and other partition values can be read off at the corresponding cumulative frequency level.

The sum of all observations divided by their number; it uses every value, is simple to compute and algebraically tractable, but is strongly affected by extreme values.

The middle value of a data set arranged in order, or the average of the two middle values when the count is even; it is a positional average unaffected by extreme observations.

The value that occurs most frequently in a data set, or the value around which observations cluster most densely; it is useful for qualitative and highly skewed data.

The nth root of the product of n positive observations, appropriate for averaging rates of growth and ratios; it is computed by taking antilogarithms of the mean of the logarithms.

The reciprocal of the arithmetic mean of the reciprocals of the observations, used for averaging speeds and rates where the same distance is covered at different speeds.

The arithmetic mean of two or more groups pooled into one, obtained as the weighted average of the group means with the group sizes as weights.

The approximate relationship between the three averages of a moderately skewed distribution, usually written as mode equals mean minus three times the difference between mean and median.

The average of the absolute deviations of observations from a chosen average, usually the median; it is easy to interpret but ignores signs and is not well suited to algebraic treatment.

The positive square root of the mean of squared deviations taken from the arithmetic mean; it is the most widely used absolute measure of dispersion and is expressed in original units.

The average of the squared deviations of observations from their arithmetic mean, equal to the square of the standard deviation and measured in squared units of the original variable.

Half the difference between the third and first quartiles, also called semi-interquartile range; it measures spread of the middle half of the data and ignores the extreme halves.

The ratio of standard deviation to arithmetic mean, usually expressed as a percentage; being unit-free, it compares variability between series with different units or very different means.

One of the three values dividing an ordered data set into four equal parts; the first, second and third quartiles correspond to cumulative proportions of one quarter, one half and three quarters.

The degree to which a frequency distribution departs from symmetry, described as positive when the longer tail lies to the right and negative when the longer tail lies to the left.

The peakedness or flatness of a frequency curve relative to the normal curve, classified as leptokurtic, mesokurtic or platykurtic and measured by moments of the fourth order.

A quartile-based measure of skewness equal to the difference between the third and first quartiles minus twice the median, divided by the interquartile range; it lies between minus one and plus one.

A summary quantity based on powers of deviations from a chosen point; the first moment about the mean is zero, the second gives variance, and the third and fourth indicate skewness and kurtosis.

A measure of the strength and direction of linear association between two variables, obtained by dividing the covariance by the product of their standard deviations and lying between minus one and plus one.

A plot of paired observations of two variables on a graph, whose pattern of points reveals whether the relationship is positive, negative, linear or absent.

The slope of a regression line, showing the average change in one variable for a unit change in the other; the two coefficients differ in value and each equals the correlation times the ratio of standard deviations.

The straight line fitted by least squares to paired data, used to predict one variable from the other and chosen so that the sum of squared vertical deviations is minimum.

A coefficient computed from the ranks assigned to the observations of two variables rather than their actual values, useful for qualitative rankings and for detecting monotonic rather than strictly linear association.

A statistical measure that expresses the relative change in a variable or group of variables between two periods or places, usually shown as a percentage with a chosen base period set to one hundred.

The reference period against which values in an index number series are compared, normally assigned an index value of one hundred and chosen to be a normal, economically stable year.

A weighted price index that uses base-period quantities as weights, so it measures the changing cost of a fixed basket of goods and tends to overstate price rises.

A weighted price index that uses current-period quantities as weights, so the basket changes each period; it tends to understate price rises and needs current quantity data.

A set of observations of a variable arranged in chronological order at equal time intervals, analysed to isolate trend, seasonal, cyclical and irregular movements.

The long-term general direction of movement of a time series over a sufficiently long period, reflecting underlying growth or decline and usually estimated by moving averages or least squares.

Short-term regular movements in a time series that repeat within a year, such as festival or harvest effects, measured by seasonal indices and removed by seasonal adjustment.

A smoothing device that replaces each observation by the average of a fixed number of neighbouring observations, thereby suppressing short-term fluctuations and revealing trend in a time series.

The set of all possible outcomes of a random experiment, denoted usually by S; every event is a subset of this set and its total probability is one.

Two or more events that cannot occur together in the same trial, so the probability of their joint occurrence is zero and their union probability equals the sum of their probabilities.

Events whose occurrence does not affect each other's chances, so the probability that both happen equals the product of their individual probabilities.

The probability that an event occurs given that another event has already occurred, defined as the joint probability divided by the probability of the conditioning event.

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

A real-valued function defined on a sample space that assigns a number to each outcome, either discrete when it takes countable values or continuous when it takes values in an interval.

The probability-weighted average of the values of a random variable, obtained by summing value times probability for discrete cases or integrating over the density in continuous cases.

The distribution of the number of successes in a fixed number of independent Bernoulli trials with constant success probability, defined by the parameters n and p.

A discrete distribution giving the probability of a count of rare events in a fixed interval of time or space, with mean and variance both equal to the parameter lambda.

A continuous symmetric bell-shaped distribution defined by mean and variance, whose density curve is mesokurtic and within which fixed proportions of values lie within one, two and three standard deviations of the mean.

The standardised value obtained by subtracting the mean from a normal observation and dividing by the standard deviation, which follows a normal distribution with mean zero and variance one.

The probability distribution of a statistic such as the sample mean over all possible samples of a given size drawn from a population, whose spread shrinks as sample size grows.

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

The result that the sampling distribution of the sample mean approaches normality as sample size increases, whatever the shape of the population, provided the population has finite variance.

A selection procedure in which every possible sample of a given size has an equal chance of being chosen, so every unit has the same probability of inclusion.

A design in which the population is divided into homogeneous groups called strata and independent random samples are drawn from each, usually improving precision over simple random sampling.