Assam Higher Secondary Statistics key terms

Data collected firsthand by the investigator for the specific purpose of the enquiry, through surveys, experiments, interviews or direct observation. It is original, but usually costlier and slower to obtain than data already on record.

Data that were collected earlier by another person or agency and are reused, such as census reports, government bulletins or published tables. They are cheaper and quicker to obtain, but their accuracy and definitions must be checked.

A table that sorts observations into classes or distinct values and records how many observations fall in each, that count being the frequency. It condenses raw data so that patterns, shape and averages can be seen.

One of the groups into which the range of a grouped frequency distribution is divided, written with a lower and an upper limit. Its width is the upper limit minus the lower limit, and its midpoint is the class mark.

A graph of a continuous frequency distribution in which adjacent rectangles stand on the class intervals and their areas are proportional to the class frequencies. The outline of the rectangles reveals the form of the distribution.

A curve obtained by plotting cumulative frequencies against the class boundaries. It rises for a less-than series and falls for a more-than series, and the median and quartiles can be read from it graphically.

The sum of all observations divided by their number. It uses every value and is simple to compute, but a single extreme observation can pull it noticeably away from the typical value.

The middle observation when the data are arranged in order of magnitude, so that half the observations lie below it. It is a positional average, unaffected by extreme values, and suits open-ended distributions.

The value that occurs most frequently in a set of observations. For grouped data it is obtained from the modal class by formula. It can be used for qualitative data and is not disturbed by outliers.

The nth root of the product of n positive observations, equivalently the antilog of the mean of their logarithms. It is appropriate for averaging ratios, percentages and rates of growth over successive periods.

The three values Q1, Q2 (the median) and Q3 that divide ordered data into four equal parts. With deciles and percentiles they are called partition values and describe position within a distribution.

The difference between the largest and the smallest observation. It is the simplest measure of dispersion and easy to calculate, but it depends on only two values and ignores everything in between.

The arithmetic mean of the absolute deviations of the observations from a chosen average, usually the median or the mean. Taking absolute values prevents cancellation, but the measure is awkward to handle algebraically.

The positive square root of the mean of the squared deviations from the arithmetic mean. It is expressed in the same units as the data and is the most widely used measure of dispersion.

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

A summary quantity formed by averaging powers of the deviations of observations from a fixed point. Moments about zero are raw moments, while moments about the mean are central moments used to describe shape.

A measure of how lopsided or asymmetric a frequency distribution is. It is positive when the longer tail stretches to the right and negative when the longer tail stretches to the left.

A measure of the peakedness of a frequency distribution compared with the normal curve. Distributions are described as mesokurtic (normal-like), leptokurtic (sharply peaked) or platykurtic (flat-topped).

A graph in which each pair of observations is plotted as a point, with the two variables on the two axes. The pattern of the points shows whether the relationship is positive, negative or absent.

A measure of the strength and direction of the linear relationship between two variables, written r. It lies between minus one and plus one, and equals zero when there is no linear association.

The Pearson correlation applied to the ranks of the observations instead of their original values. It suits ordinal data and situations where the relationship is monotonic but not necessarily linear.

The slope of a fitted regression line. In the line of y on x it gives the average change in y for a one-unit rise in x, and it carries the units of y divided by x.

The square of the correlation coefficient, usually written r squared. It states the proportion of the total variation in the dependent variable that is explained by the fitted regression on the independent variable.

A procedure whose possible outcomes are known in advance but whose actual result cannot be predicted with certainty. Tossing a coin or drawing a card from a well-shuffled pack are familiar examples.

The probability that event A occurs given that event B has already occurred, written P(A|B). It equals the probability of both events divided by the probability of B, provided that probability is not zero.

A rule for revising the probability of a hypothesis after evidence is observed. It combines prior probabilities with likelihoods to produce posterior probabilities, and underlies diagnostic and decision problems.

A real-valued function that assigns a number to each outcome of a random experiment. It is discrete if its possible values can be listed, and continuous if they form an interval.

The probability distribution of the number of successes in n independent trials, each having the same probability p of success. Its mean is np and its variance is np(1 minus p).

A continuous, symmetric, bell-shaped distribution fixed by its mean and standard deviation. Its total area is one, and roughly 68 per cent of the area lies within one standard deviation of the mean.

A sampling method in which every possible sample of a given size has an equal chance of being selected, so that each unit of the population is equally likely to be included.

A method in which the population is first divided into internally similar groups called strata, and independent random samples are then drawn from every stratum, often giving more precise estimates than simple random sampling.

The difference between a value estimated from a sample and the true value for the population, arising because only part of the population is observed. It generally falls as the sample size grows.

The standard deviation of the sampling distribution of a statistic. It measures how much an estimate such as a sample mean is expected to vary from one sample to another.

A statement, usually of no difference or no effect, assumed true for the purpose of carrying out a test. It is rejected only when the sample evidence tells strongly against it.

The error committed by rejecting a null hypothesis that is in fact true. Its probability is the level of significance, alpha, chosen by the investigator before the test is applied.

An interval calculated from sample data, together with a stated confidence level, that is expected to contain the unknown population parameter in a specified proportion of repeated samples.

A set of values of a variable recorded at successive points in time, such as annual production figures. Its movement is studied through trend, seasonal, cyclical and irregular components.

An average of a fixed number of consecutive observations that is recalculated as the window moves along the series. It smooths short-term fluctuations and helps reveal the underlying trend.

A statistical measure expressing the change in level of a variable, or of a group of related variables, from one period to another, with a chosen base period usually set equal to 100.

A weighted aggregative price index that uses quantities purchased in the base period as weights. It tends to overstate price rises because it holds the old consumption basket fixed.