Tamil Nadu HSE First Year Statistics key terms

The science of collecting, organising, presenting, analysing and interpreting numerical data so that decisions can be taken under uncertainty. It covers both descriptive summary and inference from samples.

Facts, observations or measurements gathered on individuals or items, usually recorded as numbers or labels. Raw data become information only after editing, classification and tabulation.

Data collected first-hand by the investigator for the specific enquiry at hand, through census, sample survey, interview, questionnaire or direct observation. They are original but costly to obtain.

Data already gathered by someone else and reused for a new purpose, such as government reports, journals or records. Reliability depends on who collected them, when, and by what method.

A complete enumeration in which every unit of the population is observed. It removes sampling error but is expensive, slow, and impractical when the population is large or testing is destructive.

A written schedule of questions used to obtain information from respondents. Good design uses short, unambiguous, unbiased questions, with a pilot test before the main survey.

A small preliminary study conducted before the main investigation to test the questionnaire, fieldwork plan and cost estimates, so that defects are corrected while changes are still cheap.

A table that shows how many observations fall in each class or value of a variable. It may be discrete or continuous, and is the starting point for graphs and summary measures.

The range of values grouped together in a frequency table, written with a lower and upper limit. Its width, or size, affects how much detail the table preserves.

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

The sum of all observations divided by their number. For grouped data each class midpoint is weighted by its frequency. It uses every value but is pulled strongly by extreme observations.

The middle value of a set of observations arranged in order of magnitude. For grouped data it is found by interpolation inside the median class. It is resistant to extreme values.

The value that occurs most frequently in a data set, or the value at the peak of a frequency curve. A distribution may be unimodal, bimodal or have no mode at all.

The nth root of the product of n positive observations. It is appropriate for averaging rates of growth and ratios, because it is less affected by very large values than the arithmetic mean.

The reciprocal of the arithmetic mean of the reciprocals of the observations. It suits averaging speeds, prices per unit and other rates expressed per unit of a base quantity.

An average in which each observation is multiplied by a weight reflecting its relative importance before dividing by the total weight. Used for index numbers and combined group means.

A value that divides an ordered data set into a stated number of equal parts, such as quartiles, deciles and percentiles. Quartiles split the data into four parts at three cut points.

One of the three values Q1, Q2 and Q3 that divide an ordered series into four equal parts. Q2 equals the median, and the interquartile range Q3 minus Q1 measures spread of the middle half.

The difference between the largest and smallest observation in a data set. It is simple and quick but depends only on two values, so a single outlier can distort it badly.

Half the difference between the third and first quartiles, that is (Q3 minus Q1) divided by 2. It measures spread of the middle half and ignores the extreme quarters.

The arithmetic mean of the absolute deviations of observations from a central value such as the mean, median or mode. It uses all values but is awkward algebraically.

The positive square root of the mean of squared deviations from the arithmetic mean. It is expressed in the original units and is the most important absolute measure of dispersion.

The mean of the squared deviations of observations from their arithmetic mean. Its square root is the standard deviation, and it is expressed in squared units of the variable.

The standard deviation expressed as a percentage of the arithmetic mean. Being unit-free, it allows comparison of variability between data sets measured in different units or with different means.

The extent to which observations spread out around a central value. Measured absolutely by range, quartile deviation, mean deviation and standard deviation, and relatively by coefficients.

The degree of asymmetry of a frequency distribution. Positive skew means a longer tail to the right, negative skew a longer tail to the left, and zero skew means symmetry.

The peakedness of a frequency curve, judged against the normal curve. Leptokurtic curves are sharply peaked, platykurtic curves are flat, and mesokurtic curves match the normal shape.

A summary quantity based on powers of deviations from a value. Raw moments use deviations from zero and central moments from the mean; the second central moment is the variance.

The degree and direction of linear association between two variables. It is measured by a coefficient lying between minus one and plus one, with zero indicating no linear relationship.

A plot of paired observations of two variables on a graph, one on each axis. The pattern of points suggests whether association is positive, negative or absent, and whether it is linear.

A coefficient computed from the ranks of observations rather than their actual values, commonly Spearman's formula using differences of ranks. It suits qualitative or ordered data.

A method of estimating the value of one variable from known values of another by fitting an equation to the data. Two regression lines exist, and they meet at the means.

The slope of a regression line, showing the average change in one variable per unit change in the other. The two coefficients share the sign of the correlation coefficient.

An experiment whose outcome cannot be predicted with certainty in advance, although the set of possible outcomes is known. Repeating it under identical conditions may still give different results.

The set of all possible outcomes of a random experiment, usually denoted S. Each elementary outcome is a member, and every event is a subset of this set.

Any subset of the sample space of a random experiment, such as getting an even number on a die. Events may be simple, compound, mutually exclusive, exhaustive or complementary.

Two or more events that cannot occur together in the same trial, so their intersection is empty. For such events the probability of either occurring is the sum of their probabilities.

Events whose occurrence does not alter each other's probability, so the probability of both equals the product of their separate probabilities. Contrasted with events linked by conditional probability.

The probability that one event occurs given that another has already occurred, written as P of A given B. It equals the probability of both divided by the probability of the given event.

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

A listing or formula giving the probability of each value of a discrete random variable, or the density of a continuous one. Probabilities are non-negative and total one.

The probability-weighted average of the values of a random variable, written E of X. It behaves linearly, so the expectation of a sum equals the sum of the expectations.

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

A distribution for the count of rare events in a fixed interval of time, space or material, with a single parameter equal to its mean. Its mean and variance are equal.

A continuous, symmetric, bell-shaped distribution fixed by its mean and standard deviation. About 68 per cent of values lie within one standard deviation of the mean and 95 per cent within two.

The complete set of units about which information is sought in a study. Its size may be finite or infinite, and a parameter describes it exactly but is usually unknown.

A subset of units drawn from a population in order to study it. A statistic computed from the sample is used to estimate the unknown population parameter.

The process of selecting a part of a population to represent the whole. It may be random, giving every unit a known chance of selection, or non-random, relying on judgement or convenience.

A method in which every unit of the population has an equal chance of selection and every sample of a given size is equally likely, usually drawn by lottery or random numbers.

A design in which the population is first divided into homogeneous groups called strata, and a random sample is then drawn from each stratum. It usually reduces sampling error.

The difference between a sample statistic and the true population parameter that arises purely because only part of the population is observed. It shrinks as sample size increases.

The standard deviation of the sampling distribution of a statistic, such as the mean. For the sample mean it equals the population standard deviation divided by the square root of n.

The probability distribution of a statistic, such as the mean, over all possible samples of a fixed size drawn from the population. Its spread measures the precision of the statistic.

A single figure expressing the relative change in a variable or group of variables between two periods or places, usually as a percentage with a chosen base period equal to 100.

The reference period against which changes in an index number are measured, assigned the value 100. It should be a normal period free of unusual disturbances.

The ratio of the price of a commodity in a given period to its price in the base period, usually multiplied by 100. Index numbers are built from such relatives.

A weighted price index that uses base-period quantities as weights. It tends to overstate price rises because it ignores consumers substituting away from goods that became relatively expensive.

A weighted price index that uses current-period quantities as weights. It reflects present consumption patterns but tends to understate price rises and needs fresh quantity data each period.

The geometric mean of the Laspeyres and Paasche price indices. It satisfies both the time reversal and factor reversal tests, and is therefore regarded as an ideal formula.

An index measuring the change over time in the money needed by a typical consumer to buy a fixed basket of goods and services, used to adjust wages and assess real income.