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AP Statistics

AP Statistics . Section 1.1: Displaying Distributions. Objective: To be able to represent categorical and quantitative data using a variety of graphs. Statistics : The science and art of learning from data. Part I: Exploratory Data Analysis Data: objects described in the data set

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AP Statistics

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  1. AP Statistics Section 1.1: Displaying Distributions

  2. Objective: To be able to represent categorical and quantitative data using a variety of graphs. • Statistics: The science and art of learning from data. • Part I: Exploratory Data Analysis • Data: objects described in the data set • a. Experimental Unit • b. Subject (individual) • Variable: any characteristic of the data

  3. Types of Variables • Qualitative (categorical): any variable that records what group an individual belongs. • Quantitative: a numerical value in which it makes sense to perform a mathematical operation. (average?) Examples: Distribution: refers to how the data looks. AP Graphing Points: • Label the title, axes and scales. • Provide comments.

  4. Types of Distributions: • Bar graph: used for comparing different groups. • Categorical graph • Categories on the horizontal axis. • Frequency on the vertical axis. • Bars do not touch. • Example: Gender of Pulse Rates

  5. Pie Chart: Used to compare categories. • Categorical graph • Make a table to find central angles. • Example: Gender of Pulse Rates

  6. Dotplot: Used for small quantitative data sets. • Values for the variable are placed on the horizontal axis. • Observations are represented by placing dots above the horizontal axis. Each point represents one observation. • Data may need to be rounded or truncated. (ex. 10.6, 12.3, 14.5, 8.1) • Example: Dotplot of pulse rates

  7. Stemplots: used for small quantitative data sets. • Stems increase going down. • No skipping stems. • Leaves increase going away from the stems. • Always include the leaf unit. • No punctuation. • Negative signs go with stems if necessary. (Caution with negatives) • Example: Stemplot of pulse rates

  8. Split stemplot: Used when the data does not have a large spread. • Can only split the stems in such a way that each stem as the same possible number of leaves. • Possible splits: • Example: Split stemplot for pulse data.

  9. Back-to-back stemplot: Used to compare a categorical variable with two possible outcomes. Example: Stemplot of pulse rates and gender.

  10. Describing Distributions: (3 things) • Center: the middle observation in an ordered data set. (median) May need to find the average of two observations. • Shape: describes the overall shape of the distribution. Bell shaped V-shaped Skewed left Exponential Skewed right Bimodal Uniform Outliers: observations that deviate from the overall pattern of the distribution. Outliers do not dictate the shape of the distribution. • Spread: max – min. (range)

  11. Histogram: used with large quantitative data sets. • Classes go on the horizontal axis • Label the horizontal axis with the lower class limits • Frequency (relative frequency) on the vertical axis. • Approximately 4 – 8 bars. • If an observation falls 2 or more bars away from the overall body of the data, it may be an outlier. • Must create a frequency table prior to construction. • Class width = (range)/(number of classes) • *** Always round up even if it is an integer!!! • Example: Histogram of pulse rates:

  12. Example: Histogram of pulse rates:

  13. Ogive: used to relate percentiles to the data and vice versa. • Horizontal axis is labeled with lower class limits. • Place each point for the cumulative relative frequency above the lower class limit of the next class. • Connect points with segments. • Vertical axis labeled from 0 to 100% or 0 to n. • Example: Ogive for pulse rates

  14. Timeplot: used to observe trends. • Time on the horizontal axis. • Variable on the vertical axis. • Connect the points with segments. • Example: Stock price over years.

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