CHSE Odisha Elective Statistics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Arithmetic mean

Sum of all observations divided by the number of observations; for grouped data, sum of frequency times midpoint divided by total frequency.

Median

The middle value when data are arranged in order; for grouped data, computed using cumulative frequency and the median class formula.

Mode

The value that occurs most frequently in a data set; for grouped data, found from the modal class using frequencies of adjacent classes.

Standard deviation

The positive square root of variance; measures average distance of observations from the mean in the original units.

Coefficient of variation

Standard deviation divided by mean, expressed as a percentage; used to compare variability between data sets with different units or means.

Quartile deviation

Half the difference between the third and first quartiles: (Q3 − Q1)/2; a measure of dispersion based on the middle 50% of data.

Karl Pearson correlation coefficient

A measure of linear association between two variables, ranging from −1 to 1, computed as covariance divided by the product of standard deviations.

Spearman rank correlation

A correlation measure based on ranks of observations, suitable for ordinal data or when linearity and normality assumptions are not met.

Regression coefficient

The slope in a regression line, representing the expected change in the dependent variable for a one-unit increase in the independent variable.

Coefficient of determination

The square of the correlation coefficient; represents the proportion of variance in the dependent variable explained by the independent variable in linear regression.

Conditional probability

The probability of event A given that event B has occurred, computed as P(A ∩ B) divided by P(B), provided P(B) > 0.

Bayes' theorem

A formula for updating probabilities: P(A|B) = P(B|A)P(A)/P(B); used to reverse conditional probabilities when prior information is available.

Expected value

The long-run average of a random variable; for discrete variables, the sum of each value times its probability.

Variance of random variable

The expected squared deviation from the mean: Var(X) = E(X²) − [E(X)]²; measures spread of the probability distribution.

Binomial distribution

Models the number of successes in n independent trials with constant success probability p; mean np, variance np(1−p).

Poisson distribution

Models counts of rare events in a fixed interval; parameter λ equals both mean and variance; limit of binomial when n is large and p small.

Standard normal distribution

Normal distribution with mean 0 and standard deviation 1; any normal variable is converted to it using Z = (X − μ)/σ.

Exponential distribution

A continuous distribution modeling waiting times between Poisson events; has memoryless property and mean equal to its scale parameter.

Central limit theorem

States that the sampling distribution of the sample mean approaches normality as sample size increases, regardless of the population shape.

Standard error of mean

The standard deviation of the sampling distribution of the sample mean; equals σ/√n for infinite population or sampling with replacement.

Finite population correction

A factor √((N−n)/(N−1)) applied to the standard error when sampling without replacement from a finite population of size N.

Stratified sampling

A sampling method where the population is divided into homogeneous strata and random samples are drawn from each stratum.

Type I error

The error of rejecting a true null hypothesis; its probability is denoted by α, the significance level of the test.

Type II error

The error of failing to reject a false null hypothesis; its probability is denoted by β, and power equals 1 − β.

t-test for one mean

A hypothesis test for a population mean when the population standard deviation is unknown and sample size is small; uses t distribution with n−1 degrees of freedom.

Chi-square goodness-of-fit test

Tests whether observed frequencies match expected frequencies from a hypothesized distribution; statistic is sum of (O−E)²/E.

Confidence interval

A range of values, computed from sample data, that is likely to contain the true population parameter with a specified confidence level.

Analysis of variance

A statistical method that partitions total variation into components attributable to different sources, used to test equality of several means.

Randomized block design

An experimental design where each treatment appears once in each block; blocks are homogeneous groups that control a nuisance factor.

F-test in ANOVA

The ratio of between-group mean square to within-group mean square; large values indicate significant differences among treatment means.

Laspeyres price index

A weighted price index using base-year quantities as weights; measures price change relative to a fixed consumption basket.

Fisher's ideal index

The geometric mean of Laspeyres and Paasche indices; satisfies both time reversal and factor reversal tests.