AP Statistics Chapter 1

STUDY
PLAY
Variables
Characteristic of an individual
Categorical Variable
Places individual into a category
Quantitative Variable
Takes numerical values for which it makes sense to find an average
Frequency Table
Table of counts
Relative Frequency Table
Displays percents
Bar Graph
- Label axes
- Title graph
- Scale axes appropriately
- Each bar should correspond to the appropriate count
- Leave room between bars
Pie Chart
- Include all the categories that make up the whole
- Counts will be percentages
Shape
Symmetric, skewed
Measures of Center
Mean, Median
Mean
- Most common measure of center
- Arithmetic average
Median
- Midpoint of a distribution
Spread
Range, IQR
IQR
The middle 50%
IQR Equation
Q3 - Q1
Outlier Equation
Less than Q1 - 1.5IQR
Higher than Q3 + 1.5IQR
Dotplot
- Only need to properly label horizontal axis
- Title
- Each dot represents a count of 1
- Works well with a small data set
Stemplot
- Separate each piece of data into a "stem" and a "lead"
- Write the stems vertically in increasing order from top to bottom
- Write the leaves in increasing order out from the stem
- Be very neat and leave the same amount of space between leaves
- Title the graph
- Include a key identifying what the stem and leaves represent
- Works well with a small data set
Histogram
- Most common graph of a quantitative variable
- The x-axis is continuous, no gaps between bars
- Title the graph
- Divide the range of data into classes of equal width
- Label and scale the axes
Five-Number Summary
Minimum, Q1, Median, Q3, Maximum
Boxplot
- Drawn from Q1 to Q3
- Line in the middle marks the median
- Lines extend from the box to the smallest and largest observations that aren't outliers
Standard Deviation
- Find the distance of each observation from the mean
- Square each of these distances
- Average the distances by dividing their sum by n-1
- Take the square roon
Round-off Error
The error from rounding decimals
When describing the overall pattern of a distribution, you must address...
- Center
- Shape
- Spread
- Outliers
Dotplot
Histogram
Bar Graph
Frequency Table
Relative Frequency Table
Symmetric
Skewed Right
Skewed Left
Pie Chart
Segmented Bar Graph
Two-Way Table
Back-to-Back Stemplot
Boxplot
Is the mean sensitive to outliers?
The mean is sensitive to outliers.
If a distribution is skewed, use this measure of center
Median
Is the median sensitive to outliers?
The median is not sensitive to outliers.
If a distribution is exactly symmetric, the median and mean will be
Exactly the same
If the distribution is skewed left, the mean will
Fall to the left
If the distribution is skewed right, the mean will
Fall to the right
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