Overview
This lecture connects the concept of "spread" from graphing (Chapter 2) with "standard deviation" (Chapter 3), showing how standard deviation quantifies data spread.
Spread in Graphs (Chapter 2)
- "Spread" refers to how data points are distributed across a graph.
- High spread means data points are widely distributed; low spread means data points are clustered together.
- Spread was previously described using visual cues and qualitative terms.
Standard Deviation (Chapter 3)
- Standard deviation measures how far data values typically fall from the mean (the center of the data).
- 68% of data lies within one standard deviation from the mean in a normal distribution.
- Standard deviation is the distance from the mean to the point covering 68% of the data.
- It provides a concrete, numerical value for data spread.
Connecting Spread and Standard Deviation
- The more spread out a graph is, the larger its standard deviation.
- The more clustered the data is around the mean, the smaller the standard deviation.
- Visually, wider graphs correspond to higher standard deviations; narrow, clustered graphs have lower standard deviations.
Identifying Standard Deviation from Graphs
- To determine standard deviation from a graph, see how far from the center you must go to include 68% of the data.
- Among three graphs (A, B, C):
- Graph with the data most clustered at the center (C) has the smallest standard deviation.
- Graph with data most spread out to the edges (A) has the largest standard deviation.
Key Terms & Definitions
- Spread — The extent to which data values are distributed out or clustered together in a graph.
- Standard Deviation — A numerical measure of data spread, indicating the average distance from the mean.
- Mean — The average value, representing the center of the data distribution.
Action Items / Next Steps
- Practice identifying graphs with high vs. low standard deviation.
- Review how to calculate standard deviation and interpret it in context.
- Complete assigned readings or exercises related to standard deviation and data spread.