St a t i st i c s a n d P r o b a b i l i t y
Dat a Co llect ion an d A n al y si s- Sampling techniques are used to gather data from real-world situations. If the data are
representative o f the large r p o p u la tio n , inferences can be m a d e a b o u t that p op ula tio n. - Biased sampling techniques yield data unlikely to be representative of the larger population.
- Sets of numerical data are described using measures of central tendency and dispersion.
Data Representation - The most appropriate data representations depend on the type of data—quantitative or
qualitative, and univariate or bivariate. - Line p lo ts, b o x p lo ts, a n d h is to g ra m s a re d iffe re n t w a y s to s h o w d is trib u tio n o f d a ta o v e r a
possible range of values.
Pr o b ab i l i t y - Probability expresses the likelihood that a particular event will occur.
- Data can be used to calculate an experimental probability, and mathematical properties can be
used to determ ine a theoretical probability. - Either experimental or theoretical probability can be used to make predictions or decisions about
future events. - Various counting methods can be used to develop theoretical probabilities.
Geo m et r y
Visualization- Visualization can help you see the relationships between two figures and help you connect
properties of real objects with two-dimensional drawings of these objects.
Transf orm at ions - Transformations are mathematical functions that model relationships with figures.
- Transformations may be described geometrically or by coordinates.
- Symmetries of figures may be defined and classified by transformations.
Measurement - Some attributes of geometric figures, such as length, area, volume, and angle measure, are
measurable. Units are used to describe these attributes.
Reaso n i n g & Pr o o f - Definitions establish meanings and remove possible misunderstanding.
- O th e r truths a re m o re c o m p le x a n d d iffic u lt to see. It is o fte n p o s s ib le to v e r ify c o m p le x truths
by reasoning from simpler ones using deductive reasoning.
Si m i l ar i t y - Two geometric figures are similar when corresponding lengths are proportional and
corresponding angles are congruent. - Areas of similar figures are proportional to the squares of their corresponding lengths.
- Volumes of similar figures are proportional to the cubes of their corresponding lengths.
Co o r d i n at e Ge o m e t r y - A c o o rd in a te system o n a lin e is a n u m b e r lin e o n w h ic h p o in ts a re la b e le d , c o r re s p o n d in g to the
real numbers. - A c o o rd in a te system in a p la n e is fo rm e d b y t w o p e rp e n d ic u la r n u m b e r lines, c a lle d the x- a n d
y-axes, and the quadrants they form. The coordinate plane can be used to graph m any functions. - It is p o s s ib le to v e r ify s o m e c o m p le x truths using d e d u c tiv e re a s o n in g in c o m b in a tio n w ith th e
distance, midpoint, and slope formulas.
Using Your Book f or Success XXV