Objectives for Measurement and Data
Total scored items on ATI TEAS: 16 questions out of 34
Table of Contents
Interpret Information from Charts, Tables, and Graphs
Types of Graphical displays
- Cartesian coordinate graphs: These graphs will have a pair of perpendicular lines, called axes, that intersect at a point called the origin. The axes are used to locate points on the graph.
- Scatter plots: A scatter plot is a graph that shows the relationship between two variables. The variables are plotted as points on the graph and the relationship between the variables is shown.
- Line graphs: A line graph is a graph that shows information that changes over time.
- Pie charts: A pie chart is a graph that is broken into sectors that each represent a proportion of a whole.
- Bar graphs: A bar graph is a diagram in which numerical values of variables are represented by the height or length of rectangles.
How to interpret graphs and tables
- The title of the graph or table: This will give you an idea of what the data is about.
- The axes: The x-axis (horizontal axis) and y-axis (vertical axis) will tell you what the variables are.
- The data: The data is what is being plotted on the graph or listed in the table.
- The scale: The scale is the range of values that are being used.
- The units: The units are the measurements that are being used.
- The trend: The trend is the overall pattern of the data.
- The quadrant: The quadrant is the area of the graph that is divided by the axes.
Evaluate the information of Data Sets, Charts, Tables, and Graphs using Statistics
Mean, Median, and Mode
- Standard deviation describes how spread out data is from the mean. A low standard deviation means that most of the data is close to the mean, while a high standard deviation means that the data is spread out from the mean.
- Symmetry occurs when data is equally distributed on either side of a line or point.
- The number of peaks occurs when data has multiple local maxima or minima. Data can be unimodal (one peak or bell-shaped) or bimodal (two peaks).
- Skewness occurs when data is not equally distributed on either side of a line or point. Data can be right-skewed (most of the data is on the right side of the graph), left-skewed (most of the data is on the left side of the graph), and uniform (the data is equally spread out across the graph).
Interpreting trends on graphs and tables
- The type of trend: The types of trends include linear, exponential, and quadratic.
- The direction of the trend: The direction of the trend can be positive (increasing), negative (decreasing), or no change (flat).
- The rate of change: The rate of change is the amount that the trend is increasing or decreasing by.
The Relationships between Two Variables
Dependent and Independent Variables
- A positive correlation means that as one variable increases, the other variable also increases.
- A negative correlation means that as one variable increases, the other variable decreases.
- No correlation means that there is no relationship between the two variables.
Comparing and Contrasting Direct and Inverse Relationships
Calculate Geometric Quantities
Perimeter and Circumference
- To find the area of a rectangle, use the formula A=lw (where l stands for length and w stands for width).
- To find the area of a triangle, use the formula A=½bh (where b stands for base and h stands for height).
- To find the area of a circle, use the formula A=πr² (where r stands for radius).
- To find the area of a parallelogram, use the formula A=hb (where h stands for height and b stands for base)
- To find the area of a trapezoid, use the formula A=½h(b1 + b2) where h stands for height, b1 stands for the smallest base, and b2 stands for the largest base.
- To find the volume of a rectangular prism, use the formula V=lwh (where l stands for length, w stands for width, and h stands for height).
- To find the volume of a triangular prism, use the formula V=bhl/2 (where b stands for the base, h stands for the height, and l stands for length)
- To find the volume of a cylinder, use the formula V=πr²h (where r stands for radius and h stands for height).
- To find the volume of a rectangular pyramid, use the formula V=⅓lwh (where l stands for length, w stands for width, and h stands for height).
- To find the volume of a cone, use the formula V=⅓πr²h (where r stands for radius and h stands for height).
Convert between Standard and Metric Systems
- Determine what you are converting. In this case, we are converting length from inches to feet.
- Determine the relationship between the units. In this case, there are 12 inches in one foot.
- Set up the equation. In this case, it would be 12 inches = x feet.
- Solve the unknown unit. In this case, x = 12/12 feet or x = one foot.
Converting between standard and metric systems
- 1 kilogram (kg) = 2.2 pounds (lbs)
- 1 inch (in) = 2.54 centimeters (cm)
- 1 meter (m) = 3.28 feet (ft)
- 1 ounce (oz) = 28.5 grams (g)
- 1 mile (mi) = 1.6 kilometers (km)