BGCSE Statistics 4040 key terms

The complete set of all individuals, items, or measurements that a study is concerned with. Every member that fits the research question belongs to it, and its size is usually denoted by N.

A subset of individuals or observations selected from a population, usually to estimate features of that population at lower cost. Its size is typically denoted by n.

Information collected first-hand by the researcher for the specific purpose of the current investigation, for example through surveys, experiments, or direct measurement, rather than taken from existing records.

Information that was gathered by someone else for a different purpose and is reused in a new study, such as government statistics, company reports, or published research articles.

A written set of questions used to gather information from respondents. Good design avoids leading, ambiguous, or double-barrelled questions and pre-tests the wording on a small group.

A list or register of the members of a population from which a sample is actually drawn, such as an electoral roll or school register. It should ideally match the target population.

A selection method in which every member of the population has an equal chance of being chosen and every possible sample of a given size is equally likely, often done with random numbers or a lottery.

A method that first divides the population into non-overlapping groups called strata, then draws a random sample from each stratum, often in proportion to its size, to improve precision.

A method that selects every kth item from an ordered list after a random start, where k equals the population size divided by the required sample size.

A non-random method in which the researcher decides in advance how many respondents of each type to include, then chooses them by convenience until each quota is filled.

A systematic distortion that occurs when the chosen sample is not representative of the population, so results tend to over-represent or under-represent particular groups.

Inaccuracy in survey results that arises from causes other than which units were selected, such as measurement mistakes, recording errors, non-response, or faulty question wording.

A distortion caused by the way respondents answer, for example giving socially desirable replies, guessing, or being influenced by the interviewer or by the wording of a question.

A table that lists the possible values or classes of a variable together with the number of observations falling in each, often extended with relative or cumulative frequencies.

One of the consecutive ranges into which continuous data are grouped for a grouped frequency table, defined by a lower and upper boundary and having a stated width.

A chart for continuous data in which adjacent bars, drawn with no gaps, show the frequency of each class. When class widths differ, bar area rather than height represents frequency.

A graph of cumulative frequency plotted against the upper class boundaries, forming an increasing smooth S-shaped curve. It is used to estimate medians, quartiles, and percentiles.

A display that splits each observation into a leading stem and a trailing leaf, preserving the original data values while still showing the shape of the distribution.

The arithmetic average, found by adding all values and dividing by the number of values. For grouped data an estimated mean uses class midpoints weighted by frequency.

The middle value of an ordered data set, or the average of the two middle values when the number of observations is even. It is unaffected by extreme values.

The value or class that occurs most frequently in a data set. A distribution may have one mode, several modes, or no mode at all.

One of three values that divide an ordered data set into four equal parts: the lower quartile, the median, and the upper quartile, with the interquartile range between the outer two.

The difference between the upper quartile and the lower quartile. It measures the spread of the middle half of the data and is resistant to outliers.

A measure of spread giving the typical distance of observations from the mean, calculated as the square root of the variance. Larger values indicate more dispersed data.

The average of the squared deviations of observations from their mean. It is the square of the standard deviation and is expressed in squared units of the original data.

An observation that lies unusually far from the rest of the data, often identified as falling more than 1.5 interquartile ranges below the lower quartile or above the upper quartile.

A diagram showing the lower quartile, median, and upper quartile as a box, with whiskers extending to the extremes or to the adjacent values, and outliers plotted separately.

A description of the asymmetry of a distribution. In a positively skewed distribution the tail extends to the right; in a negatively skewed one it extends to the left.

Two or more events that cannot happen at the same time, so their joint probability is zero and the probability that either occurs is the sum of their separate probabilities.

Events whose occurrences do not affect each other, so the probability that both happen equals the product of their individual probabilities.

The probability that an event occurs given that another event is known to have occurred, written P(A|B) and calculated as P(A and B) divided by P(B).

A branching diagram that displays the possible outcomes of a sequence of events together with their probabilities, useful for applying the multiplication and addition rules.

A graph plotting one variable against another for each individual, used to reveal the form, direction, and strength of any relationship between the two variables.

A number between minus one and plus one measuring the strength and direction of a linear relationship between two variables, commonly denoted by r.

A straight line drawn through a scatter diagram that best summarises the linear trend, chosen so that the sum of squared vertical distances from the points is minimised.

A method of fitting a line y = a + bx by choosing the intercept and slope that minimise the sum of squared vertical deviations between observed and predicted values.

A sequence of values of a variable recorded at successive, usually equally spaced, points in time, analysed to identify trend, seasonal, cyclical, and irregular components.

A series of averages computed over a fixed number of consecutive time periods and shifted forward one period at a time, used to smooth out short-term fluctuations and reveal trend.

A regular pattern of change that repeats within a period of one year or less, such as higher sales each December, identified by comparing values with a centred moving average.

A statistic expressing the value of a quantity in one period as a percentage of its value in a chosen base period, which is assigned the value 100.

An index number in which the items being combined are given weights reflecting their relative importance, for example by expenditure shares, before the weighted average is calculated.

The result that, for sufficiently large sample sizes, the distribution of sample means is approximately normal whatever the shape of the population, with mean equal to the population mean.

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

A range of values, calculated from sample data, that is likely to contain the unknown population parameter, together with a stated level of confidence such as 95 percent.

A formal procedure that compares sample evidence with a stated null hypothesis, using a test statistic and a significance level, to decide whether to reject that hypothesis.

The probability, chosen in advance and usually 0.05 or 0.01, of rejecting a true null hypothesis. It sets the threshold against which the calculated p-value is compared.

The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. Small values suggest the null hypothesis is unlikely.