Overview
The lecture introduces stem plots as an effective way to organize and visualize numerical data, making it easier to analyze distributions and identify key statistical features.
Introduction to Data Organization
- Raw data lists can be difficult to interpret and analyze directly.
- Rearranging data helps answer questions about distribution, such as which groups are larger or more common.
Stem Plots (Stem-and-Leaf Plots)
- A stem plot organizes data by separating each value into a "stem" (all but the final digit) and a "leaf" (the final digit).
- For consistency, all numbers should have the same number of digits (e.g., 9 written as 09).
- Stems represent the leading digit(s); leaves are the trailing digits.
- The entire range from the smallest to largest stem must be included, even if a stem has no entries.
Constructing the Stem Plot
- Write all data points as two-digit numbers for uniformity.
- Arrange stems vertically and list corresponding leaves horizontally in rows.
- Initially, the order of leaves does not matter; just distribute them by stem.
- For a true stem plot, reorder leaves within each stem from smallest to largest.
- Evenly space leaves to visually compare group sizes.
Interpreting Stem Plots
- Stem plots condense large data sets into a compact, organized format.
- You can quickly locate the smallest and largest values and reconstruct the original data.
- The number of leaves per stem visually shows the frequency of values in each group.
- The median (middle value) is easy to identify by counting entries from the ends; if there is an even number, the median is the average of the two middle values.
- Stem plots facilitate answers to questions about distribution that are difficult to answer with raw lists.
Key Terms & Definitions
- Stem Plot (Stem-and-Leaf Plot) — A graphical method for organizing data by place value, separating numbers into stems and leaves.
- Stem — The leading digit(s) in each data value, forming the row labels.
- Leaf — The final digit of each data value, listed beside its stem.
- Median — The value in the middle of an ordered data set, with half the data above and half below.
Action Items / Next Steps
- Practice constructing stem plots for provided data sets.
- Review chapter three for more on the median and measures of central tendency.