Elementary Glossary

The glossary below provides some of the key definitions for terms used across the learning materials provided on this website. Each term, as much as possible, has been cross-referenced with others in this glossary and a link (indicated in square brackets as such: [link]) to its initial definition in the learning materials.

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#

5-Number Summary: [DESC] A summary of a data set of scores which includes the minimum value ( $min$ ), the first quartile ( $Q_{1}$ ), the median ( $\tilde{x}$ ), the third quartile ( $Q_{3}$ ) and the maximum value ( $max$ ).

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A

Acceleration: the rate of change of a particle’s velocity with respect to time

Average acceleration:	The average acceleration of a particle for the time interval $\left[t_{1},t_{2}\right]$ , where $v_{2}$ is the velocity at time $t_{2}$ and $v_{1}$ is the velocity at time $t_{1}$ , is given by:	$\Large{\bar{a} = \dfrac{v_{2}-v_{1}}{t_{2}-t_{1}}}$
Instantaneous acceleration:	The instantaneous acceleration, $a$ , is given by the derivative:	$a = \dfrac{dv}{dt}$

Addition rule for probability: [BPT] The probability of $A$ or $B$ or both occurring is given by

$Pr\left(A \cup B\right) = Pr\left(A\right) + Pr\left(B\right) - Pr\left(A \cap B\right)$

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B

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C

Central Tendency, Measures of: [DESC] The three "M’s" of central tendency — Mean, Median and Mode

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D

Dispersion, Measures of: [DESC] Measures that are used to indicate the spread or variability of a distribution/data set, such as Range, IQR, Standard Deviation and Variance.

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E

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F

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G

"Grand-daddy" Equation: [GDE] An equation that summarises the effects of translations, dilations and reflections on functions $f\left(x\right)$ and how to find the inverse of a function in "Grand-daddy" form (if it exists).

$y = af\left(n\left(x-h\right)\right)+k$

and

$y^{-1} = \dfrac{1}{n}f^{-1}\left(\dfrac{\left(x-k\right)}{a}\right)+h$

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H

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I

Interquartile Range (IQR): [DESC] The difference between the third quartile, $Q_{3}$ , and the first quartile, $Q_{1}$ , is known as the interquartile range, symbolised by IQR.

$IQR=Q_{3}-Q_{1}$

Interval, variables: [LOM] Measures variables according to a number line where the difference between say a 1 and 2 is equal to the difference between 4 and 5. The interval scale has an arbitrary zero.

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J

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K

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L

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M

Mean, Arithmetic: [DESC] The mean is simply the arithmetic average of all the scores in a distribution. For a sample, the mean (denoted as $\bar{x}$ ) is given by:

$\bar{x} = \dfrac{1}{n}\sum_{i=1}^{n} x_{i} = \dfrac{1}{n}\left(x_{1} + x_{2} + \ldots + x_{n}\right)$

Mean, Geometric: [DESC] The average value or mean which signifies the central tendency of the set of numbers by finding the product of their values

$\bar{x}_{geo} = \left(\prod_{i=1}^{n} x_{i}\right)^{\frac{1}{n}} = \sqrt[n]{x_{1} \times x_{2} \times \ldots \times x_{n}}$

Mean, Harmonic: [DESC] The reciprocal of the average of the reciprocals

$\bar{x}_{harm} = \dfrac{1}{\dfrac{1}{n}\sum_{i=1}^{n} \dfrac{1}{x_{i}}}$

Measurement: [LOM] A process in which numbers do the job of summarising, describing, or quantifying some aspect of an object, person or philosophical concept

Median: [DESC] The median of a distribution of scores measured on the interval or ratio scale is given by the value which splits the distribution in half. In other words, 50% of the data lie above and 50% of the data lie below it. The sample median is denoted by the symbol $\tilde{x}$.

Mode: [DESC] The most frequently occurring score in a distribution.

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N

Nominal: [LOM] Measurements which use labels based on categories. Also known as categorical variables.

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O

Ordinal: [LOM] Measurements which rank a variable in terms of highest to lowest. Also known as rank order measurements.

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P

Percentiles: [DESC] Represents the value in a distribution of scores such that P% of all the scores are less than or equal to it, (and, therefore, (100-P)% of all the scores are greater than or equal to it).

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Q

Quartile Zero: [DESC] The smallest value (i.e. minimum) of a data set. No data is below this value. Denoted $Q_{0}$ .

Quartile One: [DESC] The value representing the point where 25% of a data set is below it and 75% of the data is above this value. Referred to in some texts as the lower quartile. Denoted $Q_{1}$ .

Quartile Two: [DESC] The value representing the halfway point of a data set (i.e. the median $\tilde{x}$ ). Half (50%) of the data is below this value and half the data is above this value. Denoted $Q_{2}$ .

Quartile Three: [DESC] The value representing the point where 75% of a data set is below it and 25% of the data is above this value. Referred to in some texts as the upper quartile. Denoted $Q_{3}$ .

Quartile Four: [DESC] The largest value (i.e. maximum) of a data set. No data is above this value. Denoted $Q_{4}$ .

Qualitative: [LOM] measurements convey descriptive, textual, or language based information about a variable

Quantitative: [LOM] variables convey meaningful numerical information

Quartiles: [DESC] They break up a distribution into four parts. Quartiles are denoted $Q_{0}$ , $Q_{1}$ , $Q_{2}$ , $Q_{3}$ and $Q_{4}$ .

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R

Range: [DESC] The difference between the two most extreme values in a distribution of scores.

$\textrm{range} = \textrm{max} - \textrm{min}$

Ratio, variables: [LOM] A measurement which has all the features of an interval measurement but has the added feature of a non-arbitrary zero.

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S

Standard Deviation: [DESC]

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T

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U

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V

Variance: [DESC]

Velocity:

average velocity	$\bar{v} = \dfrac{\textrm{change in position}}{\textrm{change in time}}$
instantaneous velocity:	$v = \dfrac{dx}{dt}$

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W

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X

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Y

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Z

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CITE THIS AS:
Ovens, Matthew. “Elementary Glossary” Retrieved from YourStatsGuru.

Last updated: 7 November 2024