Class 11 Statistics Vocabulary

Vocabulary terms and definitions from the Class 11 Statistics textbook, covering basic definitions, data representation, averages, dispersion, probability, and distributions.

Statistics (Achenwall's Definition)

The science of Statecraft concerning the collection and use of data by the state, first used by German scholar Gottfried Achenwall in the middle of the 18th century.

Population

The total group under discussion or the group to which the results of a study will be generalized.

Sample

A subset of the population chosen to draw inferences about the population, which must be representative of the population to be meaningful.

Parameter

A fixed or constant quantity computed from a population when the entire population is available.

Statistic

A quantity computed from a sample that varies from sample to sample.

Constant

Quantities which do not vary from individual to individual, such as $\boldsymbol{\pi} = 3.14159$ or $\boldsymbol{e} = 2.71828$.

Random Error ($\boldsymbol{\epsilon}$)

The chance variation in an observational process, often assumed to be from a population having zero mean.

Factorial ($\boldsymbol{n!}$)

The product of the first $\boldsymbol{n}$ positive integers, defined as $\boldsymbol{n! = n \times (n-1) \times (n-2) \dots 3 \times 2 \times 1}$, where $\boldsymbol{0! = 1}$.

Quantitative Variable

A variable capable of assuming a numerical value, such as height, weight, or number of students.

Continuous Variable

A type of quantitative variable that can take all possible values in an interval on the number line, such as temperature or atmospheric pressure.

Discrete Variable

Also known as a discontinuous variable, it takes only isolated points on the number line, usually arising from counting.

Qualitative (Categorical) Variable

A variable not capable of taking numerical measurements, where individuals are allocated to mutually exclusive categories like sex or color.

Descriptive Statistics

Procedures for organizing, summarizing, and presenting data collected from a sample in an understandable form.

Inferential Statistics

The procedure of inferring about the characteristics of a population based upon the characteristics of its sample.

Primary Data

Raw data which has just been collected from the source and has not undergone any statistical treatment like sorting or tabulation.

Secondary Data

Data which has already been collected by someone else and has undergone statistical treatment.

Frequency Distribution

A compact form of data in a table that displays categories of observations according to their magnitudes and frequencies.

Arithmetic Mean ($\boldsymbol{\bar{Y}}$)

Calculated by adding all observations and dividing the sum by the total number of observations: $\boldsymbol{\bar{Y} = \frac{\sum Y_i}{n}}$.

Geometric Mean (G.M.)

The $\boldsymbol{n^{th}}$ root of the product of $\boldsymbol{n}$ positive numbers: $\boldsymbol{G.M = \sqrt[n]{Y_1 \times Y_2 \times \dots \times Y_n}}$.

Harmonic Mean (H.M.)

The reciprocal of the arithmetic mean of the reciprocals of the values: $\boldsymbol{H.M = \frac{n}{\sum \frac{1}{Y_i}}}$.

Median

The value that divides an arranged data set into two equal parts; the middle value if the number of values is odd.

Mode

The most frequent value in a data set.

Range (R)

The difference between the largest and smallest observations in a data set: $\boldsymbol{R = Y_{(n)} - Y_{(1)}}$.

Quartile Deviation (Q.D.)

Also known as semi-interquartile range, it is calculated as half the difference between the third and first quartiles: $\boldsymbol{Q.D = \frac{Q_3 - Q_1}{2}}$.

Standard Deviation (S)

The positive square root of the variance, measuring the positive square root of the mean of the squares of deviations from the mean.

Coefficient of Variation (C.V.)

A relative measure of dispersion independent of units, expressed as a percentage: $\boldsymbol{C.V = \frac{S}{\bar{Y}} \times 100}$.

Leptokurtic

A symmetrical distribution that is more peaked than a normal distribution and has fatter tails.

Platykurtic

A symmetrical distribution that is flatter than a normal distribution.

Mesokurtic

A symmetrical distribution that follows the usual normal distribution curve shape.

Index Number

A ratio or an average of ratios, usually expressed as a percentage, that measures the relative change in a variable over time.

Laspeyre's Index Number

A weighted aggregate price index that uses base year quantities as weights: $\boldsymbol{P_{0n} = \frac{\sum P_{ni} q_{0i}}{\sum P_{0i} q_{0i}} \times 100}$.

Paasche's Index Number

A weighted aggregate price index that uses current year quantities as weights: $\boldsymbol{P_{0n} = \frac{\sum P_{ni} q_{ni}}{\sum P_{0i} q_{ni}} \times 100}$.

Fisher's Ideal Index Number

The geometric mean of Laspeyre's and Paasche's index numbers.

Link Relative

The price of an item for the current year divided by the price of the previous year, expressed as a percentage.

Sample Space (S)

A set representing all possible outcomes of a random experiment.

Mutually Exclusive Events

Two events that cannot occur together, meaning their intersection is a null set ($\boldsymbol{A \cap B = \phi}$).

Bernoulli Trials

Trials in a binomial experiment where there are only two possible outcomes: success and failure.

Random Variable

A variable whose values depend upon the outcomes of a random experiment.

Binomial Probability Distribution

A discrete distribution for the number of successes in $\boldsymbol{n}$ independent trials with a constant probability of success $\boldsymbol{p}$: $\boldsymbol{P(X=x) = \binom{n}{x} q^{n-x} p^x}$.

Hypergeometric Distribution

A discrete probability distribution used when successive trials are dependent, typically when sampling without replacement from a finite population.