2. Tables, Graphs & Charts

Types of Graphical Displays on the TEAS

Cartesian Coordinate

When to use ?

• How one variable relates another

Scatter Plot

When to use ?

• Correlation btw variables

Line Graph

When to use ?

• Trends over time or continuous data

Pie or Circular Charts

When to use ?

• Parts of whole to compare promotions

Bar Graphs

When to use ?

• Compare btw different groups or categories

Overviews

Graphical Trend

• Linear: every equal step in xxx adds the same amount to yyy.

• Exponential: each step multiplies yyy by a constant factor.

• Quadratic: change in yyy accelerates (or decelerates) at a constant rate—producing a “U” or inverted “U.”

• Linear

y =mx +b

• Exponential

y = a(b)²

• Quadratic

y = ax²+bx+c

Direction of Trends in Graphs

What concave,

DENEPENDT & INDEPENDENT

Correlation/Covariance

Type of Correlation	Definition	Graphical Pattern	Direction of Change
Positive Correlation	As one variable increases, the other tends to increase.	Points clustered around an upward‐sloping line.	X ↑ → Y ↑
Negative Correlation	As one variable increases, the other tends to decrease.	Points clustered around a downward‐sloping line.	X ↑ → Y ↓
No Correlation	Changes in one variable do not consistently predict changes in the other.	Points scattered with no clear trend.	No consistent relationship

Direct & Inverse (Indirect) Relationship

Relationship	Equation	Description	Direction
Direct	y=kxy = kx	Two variables change proportionally in the same direction.	x↑  ⟹  y↑x\uparrow \implies y\uparrow
			x↓  ⟹  y↓x\downarrow \implies y\downarrow
Inverse (Indirect)	y=kxy = \tfrac{k}{x}	Two variables change proportionally but in opposite directions.	x↑  ⟹  y↓x\uparrow \implies y\downarrow
			x↓  ⟹  y↑x\downarrow \implies y\uparrow

• kkk is the constant of proportionality in both cases.

• Direct (also “directly proportional”) describes, for example, distance traveled as speed increases.

• Inverse (also “indirectly proportional”) describes, for example, the pressure of a fixed amount of gas as its volume changes.

Circle Circumference & Area Calculation

Concept	Definition	Formula	Memory Tip
Circumference	Perimeter of the circle, i.e. the distance around its edge	C=π×d C = \pi \times d	“Cherry pie’s delicious”
Area	Region covered or enclosed within the circle’s boundary	A=π×r2 A = \pi \times r^2	“Apple pies are too”

Triangle area calculation

Parallelogram & Trapezoid Area

Special Area

Triangle Prism Volume

3-D Space Volume - Cylinder

3-D Space Volume - Cone

3-D Space Volume - Rectangular Pyramid

3-D Space Volume - Sphere

Every time we deal with volume with circle, we Cube it

Every time we deal with are with circle, we Square it