Chapter Objectives

  • Display data graphically and interpret the following graphs: stem-and-leaf plots, line graphs, bar graphs, frequency polygons, time series graphs, histograms, box plots, and dot plots
  • Recognize, describe, and calculate the measures of location of data with quartiles and percentiles
  • Recognize, describe, and calculate the measures of the center of data with mean, median, and mode
  • Recognize, describe, and calculate the measures of the spread of data with variance, standard deviation, and range

Assignment

One Number to Represent a Set

  • An average1 is a single number or value that best represents a set of data
  • Often also referred to as the center
  • Mean: add up all the numbers and divide by the number of numbers
  • Median: find the middle number (or 50th percentile)
  • Mode: Most frequent value

$\mu$ vs $\bar{x}$

  • $\mu$ (the Greek letter mu) represents the population mean
  • $\bar{x}$ represents the sample mean

Mean of Grouped Frequency Tables

  • Use the midpoint of each group as the value
  • Frequency is the number of times to count each midpoint.

Mean of a Frequency Table

Sum your midpoints multiplied by their frequency, then divide by the total frequency.

\[\begin{align} \mu &= \frac{\sum fm}{\sum f} \end{align}\]

  1. Colloquially, average and mean are used interchangeably. ↩